1:HL["/_next/static/media/e4af272ccee01ff0-s.p.woff2","font",{"crossOrigin":"","type":"font/woff2"}] 2:HL["/_next/static/css/97132489b96da1d5.css","style",{"crossOrigin":""}] 0:["Y_TW_5cOL4VPb7FuqRz3I",[[["",{"children":[["slug","blog26","d"],{"children":["__PAGE__?{\"slug\":\"blog26\"}",{}]}]},"$undefined","$undefined",true],"$L3",[[["$","link","0",{"rel":"stylesheet","href":"/_next/static/css/97132489b96da1d5.css","precedence":"next","crossOrigin":""}]],"$L4"]]]] 5:HL["/_next/static/css/5b2728e81018a7be.css","style",{"crossOrigin":""}] 6:I[8326,["326","static/chunks/326-ead410bae2047633.js","986","static/chunks/986-f27c5a2c4d841870.js","42","static/chunks/app/%5Bslug%5D/page-419f452b4066bb25.js"],""] 7:I[6954,[],""] 8:I[7264,[],""] 3:[null,["$","html",null,{"lang":"ja","children":["$","body",null,{"className":"__className_f367f3 flex flex-col min-h-screen","children":[["$","header",null,{"className":"blog-header py-5","children":["$","div",null,{"className":"container mx-auto px-4","children":["$","div",null,{"className":"flex flex-col items-start","children":[["$","$L6",null,{"href":"/","className":"hover:no-underline","children":["$","h1",null,{"className":"text-6xl font-serif text-gray-800 mb-2 font-normal","children":"Shingoの数学ノート"}]}],["$","p",null,{"className":"text-xl text-gray-400 font-normal","children":"プログラミングと機械学習のメモ"}]]}]}]}],["$","main",null,{"className":"flex-grow","children":["$","$L7",null,{"parallelRouterKey":"children","segmentPath":["children"],"loading":"$undefined","loadingStyles":"$undefined","hasLoading":false,"error":"$undefined","errorStyles":"$undefined","template":["$","$L8",null,{}],"templateStyles":"$undefined","notFound":[["$","title",null,{"children":"404: This page could not be found."}],["$","div",null,{"style":{"fontFamily":"system-ui,\"Segoe UI\",Roboto,Helvetica,Arial,sans-serif,\"Apple Color Emoji\",\"Segoe UI Emoji\"","height":"100vh","textAlign":"center","display":"flex","flexDirection":"column","alignItems":"center","justifyContent":"center"},"children":["$","div",null,{"children":[["$","style",null,{"dangerouslySetInnerHTML":{"__html":"body{color:#000;background:#fff;margin:0}.next-error-h1{border-right:1px solid rgba(0,0,0,.3)}@media (prefers-color-scheme:dark){body{color:#fff;background:#000}.next-error-h1{border-right:1px solid rgba(255,255,255,.3)}}"}}],["$","h1",null,{"className":"next-error-h1","style":{"display":"inline-block","margin":"0 20px 0 0","padding":"0 23px 0 0","fontSize":24,"fontWeight":500,"verticalAlign":"top","lineHeight":"49px"},"children":"404"}],["$","div",null,{"style":{"display":"inline-block"},"children":["$","h2",null,{"style":{"fontSize":14,"fontWeight":400,"lineHeight":"49px","margin":0},"children":"This page could not be found."}]}]]}]}]],"notFoundStyles":[],"childProp":{"current":["$","$L7",null,{"parallelRouterKey":"children","segmentPath":["children",["slug","blog26","d"],"children"],"loading":"$undefined","loadingStyles":"$undefined","hasLoading":false,"error":"$undefined","errorStyles":"$undefined","template":["$","$L8",null,{}],"templateStyles":"$undefined","notFound":"$undefined","notFoundStyles":"$undefined","childProp":{"current":["$L9","$La",null],"segment":"__PAGE__?{\"slug\":\"blog26\"}"},"styles":[["$","link","0",{"rel":"stylesheet","href":"/_next/static/css/5b2728e81018a7be.css","precedence":"next","crossOrigin":""}]]}],"segment":["slug","blog26","d"]},"styles":[]}]}],["$","footer",null,{"className":"bg-[#DDDDDD] text-[#999999] py-8 mt-12 text-center border-t border-[#e5e5e5]","children":["$","div",null,{"className":"container mx-auto px-4","children":[["$","p",null,{"className":"mb-2","children":"© All rights reserved by Shingo Sekine."}],["$","p",null,{"children":["$","a",null,{"href":"#","className":"hover:text-blue-500 transition-colors","children":"Back to top"}]}]]}]}]]}]}],null] 4:[["$","meta","0",{"charSet":"utf-8"}],["$","title","1",{"children":"Shingoの数学ノート"}],["$","meta","2",{"name":"description","content":"プログラミング言語と機械学習のメモ"}],["$","meta","3",{"name":"viewport","content":"width=device-width, initial-scale=1"}],["$","link","4",{"rel":"icon","href":"/favicon.ico","type":"image/x-icon","sizes":"256x256"}],["$","meta","5",{"name":"next-size-adjust"}]] b:I[6180,["326","static/chunks/326-ead410bae2047633.js","986","static/chunks/986-f27c5a2c4d841870.js","42","static/chunks/app/%5Bslug%5D/page-419f452b4066bb25.js"],""] d:I[9703,["326","static/chunks/326-ead410bae2047633.js","986","static/chunks/986-f27c5a2c4d841870.js","42","static/chunks/app/%5Bslug%5D/page-419f452b4066bb25.js"],""] c:Tadee9,/*@jsxRuntime automatic @jsxImportSource react*/ const {Fragment: _Fragment, jsx: _jsx, jsxs: _jsxs} = arguments[0]; const {useMDXComponents: _provideComponents} = arguments[0]; function _createMdxContent(props) { const _components = Object.assign({ h3: "h3", p: "p", a: "a", span: "span", math: "math", semantics: "semantics", mrow: "mrow", mi: "mi", annotation: "annotation", mo: "mo", mfrac: "mfrac", msqrt: "msqrt", svg: "svg", path: "path", msub: "msub", mn: "mn", msup: "msup", mover: "mover", msubsup: "msubsup", ol: "ol", li: "li", mtext: "mtext" }, _provideComponents(), props.components); return _jsxs(_Fragment, { children: [_jsx(_components.h3, { children: "はじめに" }), "\n", _jsx(_components.p, { children: "今回は、あまり見かけることのない線形回帰分析におけるt値がt分布に従うことを証明していきます。" }), "\n", _jsxs(_components.p, { children: ["t値と仮説検定については、", _jsx(_components.a, { href: "./blog3.html", children: "仮説検定のブログ" }), "を参照してください"] }), "\n", _jsx(_components.p, { children: "なお、この証明を行うのに線形代数や統計学の知識は必須ですので、わからない方は適宜調べながら追っていってもらえればと思います。" }), "\n", _jsx(_components.h3, { children: "t分布について" }), "\n", _jsxs(_components.p, { children: ["まず、t分布のおさらいです。自由度を", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsx(_components.mrow, { children: _jsx(_components.mi, { children: "n" }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "n" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.4306em" } }), _jsx(_components.span, { className: "mord mathnormal", children: "n" })] }) })] }) }), "のt分布は", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsx(_components.mrow, { children: _jsx(_components.mi, { children: "z" }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "z" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.4306em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.04398em" }, children: "z" })] }) })] }) }), "を標準正規分布、", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsx(_components.mrow, { children: _jsx(_components.mi, { children: "v" }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "v" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.4306em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.03588em" }, children: "v" })] }) })] }) }), "を自由度", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsx(_components.mrow, { children: _jsx(_components.mi, { children: "n" }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "n" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.4306em" } }), _jsx(_components.span, { className: "mord mathnormal", children: "n" })] }) })] }) }), "のカイ２乗分布に従うとき、以下のように表されます。"] }), "\n", _jsx(_components.p, { children: _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsx(_components.mi, { children: "t" }), _jsx(_components.mo, { children: "=" }), _jsxs(_components.mfrac, { children: [_jsx(_components.mi, { children: "z" }), _jsx(_components.msqrt, { children: _jsxs(_components.mrow, { children: [_jsx(_components.mi, { children: "v" }), _jsx(_components.mi, { mathvariant: "normal", children: "/" }), _jsx(_components.mi, { children: "n" })] }) })] })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "t=\\frac{z}{\\sqrt{v/n}}" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6151em" } }), _jsx(_components.span, { className: "mord mathnormal", children: "t" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1.525em", verticalAlign: "-0.8296em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mopen nulldelimiter" }), _jsx(_components.span, { className: "mfrac", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsxs(_components.span, { className: "vlist", style: { height: "0.6954em" }, children: [_jsxs(_components.span, { style: { top: "-2.4642em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord sqrt mtight", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsxs(_components.span, { className: "vlist", style: { height: "1.0369em" }, children: [_jsxs(_components.span, { className: "svg-align", style: { top: "-3.4286em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3.4286em" } }), _jsxs(_components.span, { className: "mord mtight", style: { paddingLeft: "1.19em" }, children: [_jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.03588em" }, children: "v" }), _jsx(_components.span, { className: "mord mtight", children: "/" }), _jsx(_components.span, { className: "mord mathnormal mtight", children: "n" })] })] }), _jsxs(_components.span, { style: { top: "-3.0089em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3.4286em" } }), _jsx(_components.span, { className: "hide-tail mtight", style: { minWidth: "0.853em", height: "1.5429em" }, children: _jsx(_components.svg, { xmlns: "http://www.w3.org/2000/svg", width: "400em", height: "1.5429em", viewBox: "0 0 400000 1080", preserveAspectRatio: "xMinYMin slice", children: _jsx(_components.path, { d: "M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 80h400000v40h-400000z" }) }) })] })] }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.4197em" }, children: _jsx(_components.span, {}) }) })] }) }) }) })] }), _jsxs(_components.span, { style: { top: "-3.23em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "frac-line", style: { borderBottomWidth: "0.04em" } })] }), _jsxs(_components.span, { style: { top: "-3.394em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.04398em" }, children: "z" }) }) })] })] }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.8296em" }, children: _jsx(_components.span, {}) }) })] }) }), _jsx(_components.span, { className: "mclose nulldelimiter" })] })] })] })] }) }) }), "\n", _jsx(_components.h3, { children: "t値について" }), "\n", _jsx(_components.p, { children: "線形回帰分析の式は以下です。" }), "\n", _jsx(_components.p, { children: _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsxs(_components.msub, { children: [_jsx(_components.mi, { children: "y" }), _jsx(_components.mi, { children: "i" })] }), _jsx(_components.mo, { children: "=" }), _jsxs(_components.msub, { children: [_jsx(_components.mi, { children: "β" }), _jsx(_components.mn, { children: "0" })] }), _jsx(_components.mo, { children: "+" }), _jsxs(_components.msub, { children: [_jsx(_components.mi, { children: "β" }), _jsx(_components.mn, { children: "1" })] }), _jsxs(_components.msub, { children: [_jsx(_components.mi, { children: "x" }), _jsxs(_components.mrow, { children: [_jsx(_components.mi, { children: "i" }), _jsx(_components.mn, { children: "1" })] })] }), _jsx(_components.mo, { children: "+" }), _jsx(_components.mo, { children: "⋯" }), _jsx(_components.mo, { children: "+" }), _jsxs(_components.msub, { children: [_jsx(_components.mi, { children: "β" }), _jsx(_components.mi, { children: "k" })] }), _jsxs(_components.msub, { children: [_jsx(_components.mi, { children: "x" }), _jsxs(_components.mrow, { children: [_jsx(_components.mi, { children: "i" }), _jsx(_components.mi, { children: "k" })] })] }), _jsx(_components.mo, { children: "+" }), _jsxs(_components.msub, { children: [_jsx(_components.mi, { children: "u" }), _jsx(_components.mi, { children: "i" })] })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "y_i=\\beta_0+\\beta_1x_{i1}+\\cdots+\\beta_kx_{ik}+u_i" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.625em", verticalAlign: "-0.1944em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.03588em" }, children: "y" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.3117em" }, children: _jsxs(_components.span, { style: { top: "-2.55em", marginLeft: "-0.0359em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mathnormal mtight", children: "i" }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.15em" }, children: _jsx(_components.span, {}) }) })] }) })] }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.8889em", verticalAlign: "-0.1944em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.05278em" }, children: "β" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.3011em" }, children: _jsxs(_components.span, { style: { top: "-2.55em", marginLeft: "-0.0528em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: "0" }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.15em" }, children: _jsx(_components.span, {}) }) })] }) })] }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "+" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.8889em", verticalAlign: "-0.1944em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.05278em" }, children: "β" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.3011em" }, children: _jsxs(_components.span, { style: { top: "-2.55em", marginLeft: "-0.0528em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: "1" }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.15em" }, children: _jsx(_components.span, {}) }) })] }) })] }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", children: "x" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.3117em" }, children: _jsxs(_components.span, { style: { top: "-2.55em", marginLeft: "0em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsxs(_components.span, { className: "mord mtight", children: [_jsx(_components.span, { className: "mord mathnormal mtight", children: "i" }), _jsx(_components.span, { className: "mord mtight", children: "1" })] }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.15em" }, children: _jsx(_components.span, {}) }) })] }) })] }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "+" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6667em", verticalAlign: "-0.0833em" } }), _jsx(_components.span, { className: "minner", children: "⋯" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "+" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.8889em", verticalAlign: "-0.1944em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.05278em" }, children: "β" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.3361em" }, children: _jsxs(_components.span, { style: { top: "-2.55em", marginLeft: "-0.0528em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.03148em" }, children: "k" }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.15em" }, children: _jsx(_components.span, {}) }) })] }) })] }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", children: "x" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.3361em" }, children: _jsxs(_components.span, { style: { top: "-2.55em", marginLeft: "0em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.03148em" }, children: "ik" }) }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.15em" }, children: _jsx(_components.span, {}) }) })] }) })] }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "+" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.5806em", verticalAlign: "-0.15em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", children: "u" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.3117em" }, children: _jsxs(_components.span, { style: { top: "-2.55em", marginLeft: "0em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mathnormal mtight", children: "i" }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.15em" }, children: _jsx(_components.span, {}) }) })] }) })] })] })] })] }) }) }), "\n", _jsxs(_components.p, { children: ["ただし、", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsxs(_components.msub, { children: [_jsx(_components.mi, { children: "u" }), _jsx(_components.mi, { children: "i" })] }), _jsx(_components.mo, { children: "∼" }), _jsx(_components.mi, { children: "N" }), _jsx(_components.mo, { stretchy: "false", children: "(" }), _jsx(_components.mn, { children: "0" }), _jsx(_components.mo, { separator: "true", children: "," }), _jsxs(_components.msup, { children: [_jsx(_components.mi, { children: "σ" }), _jsx(_components.mn, { children: "2" })] }), _jsx(_components.mo, { stretchy: "false", children: ")" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "u_i \\sim N(0,\\sigma^2)" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.5806em", verticalAlign: "-0.15em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", children: "u" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.3117em" }, children: _jsxs(_components.span, { style: { top: "-2.55em", marginLeft: "0em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mathnormal mtight", children: "i" }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.15em" }, children: _jsx(_components.span, {}) }) })] }) })] }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "∼" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1.0641em", verticalAlign: "-0.25em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.10903em" }, children: "N" }), _jsx(_components.span, { className: "mopen", children: "(" }), _jsx(_components.span, { className: "mord", children: "0" }), _jsx(_components.span, { className: "mpunct", children: "," }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.1667em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.03588em" }, children: "σ" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.8141em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: "2" }) })] }) }) }) }) })] }), _jsx(_components.span, { className: "mclose", children: ")" })] })] })] }) }), "で独立同分布(i.i.d)です。"] }), "\n", _jsx(_components.p, { children: "行列表記にすると、以下になります。" }), "\n", _jsx(_components.p, { children: _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "y" }), _jsx(_components.mo, { children: "=" }), _jsx(_components.mi, { mathvariant: "bold", children: "X" }), _jsx(_components.mi, { mathvariant: "bold", children: "β" }), _jsx(_components.mo, { children: "+" }), _jsx(_components.mi, { mathvariant: "bold", children: "u" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\mathbf y=\\mathbf X\\mathbf \\beta+\\mathbf u" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6389em", verticalAlign: "-0.1944em" } }), _jsx(_components.span, { className: "mord mathbf", style: { marginRight: "0.01597em" }, children: "y" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.8889em", verticalAlign: "-0.1944em" } }), _jsx(_components.span, { className: "mord mathbf", children: "X" }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.05278em" }, children: "β" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "+" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.4444em" } }), _jsx(_components.span, { className: "mord mathbf", children: "u" })] })] })] }) }) }), "\n", _jsxs(_components.p, { children: ["また、", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsx(_components.mrow, { children: _jsx(_components.mi, { mathvariant: "bold", children: "y" }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\mathbf y" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6389em", verticalAlign: "-0.1944em" } }), _jsx(_components.span, { className: "mord mathbf", style: { marginRight: "0.01597em" }, children: "y" })] }) })] }) }), "の予測値", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsx(_components.mrow, { children: _jsxs(_components.mover, { accent: "true", children: [_jsx(_components.mi, { mathvariant: "bold", children: "y" }), _jsx(_components.mo, { children: "^" })] }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\mathbf{\\hat{y}}" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.9023em", verticalAlign: "-0.1944em" } }), _jsx(_components.span, { className: "mord accent", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsxs(_components.span, { className: "vlist", style: { height: "0.7079em" }, children: [_jsxs(_components.span, { style: { top: "-3em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "mord mathbf", style: { marginRight: "0.01597em" }, children: "y" })] }), _jsxs(_components.span, { style: { top: "-3.0134em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "accent-body", style: { left: "-0.2875em" }, children: _jsx(_components.span, { className: "mord mathbf", children: "^" }) })] })] }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.1944em" }, children: _jsx(_components.span, {}) }) })] }) })] }) })] }) }), "を以下で定義します。"] }), "\n", _jsx(_components.p, { children: _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsxs(_components.mover, { accent: "true", children: [_jsx(_components.mi, { mathvariant: "bold", children: "y" }), _jsx(_components.mo, { children: "^" })] }), _jsx(_components.mo, { children: "=" }), _jsx(_components.mi, { mathvariant: "bold", children: "X" }), _jsxs(_components.mover, { accent: "true", children: [_jsx(_components.mi, { mathvariant: "bold", children: "β" }), _jsx(_components.mo, { children: "^" })] })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\mathbf{\\hat{y}} = \\mathbf X \\mathbf{\\hat{\\beta}}" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.9023em", verticalAlign: "-0.1944em" } }), _jsx(_components.span, { className: "mord accent", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsxs(_components.span, { className: "vlist", style: { height: "0.7079em" }, children: [_jsxs(_components.span, { style: { top: "-3em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "mord mathbf", style: { marginRight: "0.01597em" }, children: "y" })] }), _jsxs(_components.span, { style: { top: "-3.0134em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "accent-body", style: { left: "-0.2875em" }, children: _jsx(_components.span, { className: "mord mathbf", children: "^" }) })] })] }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.1944em" }, children: _jsx(_components.span, {}) }) })] }) }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1.1523em", verticalAlign: "-0.1944em" } }), _jsx(_components.span, { className: "mord mathbf", children: "X" }), _jsx(_components.span, { className: "mord accent", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsxs(_components.span, { className: "vlist", style: { height: "0.9579em" }, children: [_jsxs(_components.span, { style: { top: "-3em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.05278em" }, children: "β" })] }), _jsxs(_components.span, { style: { top: "-3.2634em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "accent-body", style: { left: "-0.2042em" }, children: _jsx(_components.span, { className: "mord mathbf", children: "^" }) })] })] }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.1944em" }, children: _jsx(_components.span, {}) }) })] }) })] })] })] }) }) }), "\n", _jsxs(_components.p, { children: ["ただし、", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsx(_components.mrow, { children: _jsxs(_components.mover, { accent: "true", children: [_jsx(_components.mi, { mathvariant: "bold", children: "β" }), _jsx(_components.mo, { children: "^" })] }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\mathbf{\\hat{\\beta}}" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1.1523em", verticalAlign: "-0.1944em" } }), _jsx(_components.span, { className: "mord accent", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsxs(_components.span, { className: "vlist", style: { height: "0.9579em" }, children: [_jsxs(_components.span, { style: { top: "-3em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.05278em" }, children: "β" })] }), _jsxs(_components.span, { style: { top: "-3.2634em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "accent-body", style: { left: "-0.2042em" }, children: _jsx(_components.span, { className: "mord mathbf", children: "^" }) })] })] }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.1944em" }, children: _jsx(_components.span, {}) }) })] }) })] }) })] }) }), "は現在のデータから計算したパラメータです。"] }), "\n", _jsxs(_components.p, { children: ["残差", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsx(_components.mrow, { children: _jsx(_components.mi, { mathvariant: "bold", children: "e" }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\mathbf e" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.4444em" } }), _jsx(_components.span, { className: "mord mathbf", children: "e" })] }) })] }) }), "を次のように定義します。"] }), "\n", _jsx(_components.p, { children: _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "e" }), _jsx(_components.mo, { children: "=" }), _jsx(_components.mi, { mathvariant: "bold", children: "y" }), _jsx(_components.mo, { children: "−" }), _jsxs(_components.mover, { accent: "true", children: [_jsx(_components.mi, { mathvariant: "bold", children: "y" }), _jsx(_components.mo, { children: "^" })] })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\mathbf e = \\mathbf y-\\mathbf{\\hat{y}}" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.4444em" } }), _jsx(_components.span, { className: "mord mathbf", children: "e" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.7778em", verticalAlign: "-0.1944em" } }), _jsx(_components.span, { className: "mord mathbf", style: { marginRight: "0.01597em" }, children: "y" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "−" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.9023em", verticalAlign: "-0.1944em" } }), _jsx(_components.span, { className: "mord accent", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsxs(_components.span, { className: "vlist", style: { height: "0.7079em" }, children: [_jsxs(_components.span, { style: { top: "-3em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "mord mathbf", style: { marginRight: "0.01597em" }, children: "y" })] }), _jsxs(_components.span, { style: { top: "-3.0134em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "accent-body", style: { left: "-0.2875em" }, children: _jsx(_components.span, { className: "mord mathbf", children: "^" }) })] })] }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.1944em" }, children: _jsx(_components.span, {}) }) })] }) })] })] })] }) }) }), "\n", _jsx(_components.p, { children: "回帰分析のt値は以下で表されます。" }), "\n", _jsx(_components.p, { children: _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsx(_components.mi, { children: "t" }), _jsx(_components.mo, { children: "=" }), _jsxs(_components.mfrac, { children: [_jsxs(_components.msub, { children: [_jsxs(_components.mover, { accent: "true", children: [_jsx(_components.mi, { children: "β" }), _jsx(_components.mo, { children: "^" })] }), _jsx(_components.mi, { children: "j" })] }), _jsxs(_components.msub, { children: [_jsx(_components.mi, { children: "s" }), _jsx(_components.mi, { children: "j" })] })] })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "t=\\frac{\\hat{\\beta}_j}{s_{j}}" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6151em" } }), _jsx(_components.span, { className: "mord mathnormal", children: "t" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1.7202em", verticalAlign: "-0.5423em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mopen nulldelimiter" }), _jsx(_components.span, { className: "mfrac", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsxs(_components.span, { className: "vlist", style: { height: "1.1778em" }, children: [_jsxs(_components.span, { style: { top: "-2.655em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsxs(_components.span, { className: "mord mtight", children: [_jsx(_components.span, { className: "mord mathnormal mtight", children: "s" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.3281em" }, children: _jsxs(_components.span, { style: { top: "-2.357em", marginLeft: "0em", marginRight: "0.0714em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.5em" } }), _jsx(_components.span, { className: "sizing reset-size3 size1 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.05724em" }, children: "j" }) }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.2819em" }, children: _jsx(_components.span, {}) }) })] }) })] }) }) })] }), _jsxs(_components.span, { style: { top: "-3.23em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "frac-line", style: { borderBottomWidth: "0.04em" } })] }), _jsxs(_components.span, { style: { top: "-3.5073em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsxs(_components.span, { className: "mord mtight", children: [_jsx(_components.span, { className: "mord accent mtight", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsxs(_components.span, { className: "vlist", style: { height: "0.9579em" }, children: [_jsxs(_components.span, { style: { top: "-2.7em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.05278em" }, children: "β" })] }), _jsxs(_components.span, { style: { top: "-2.9634em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "accent-body", style: { left: "-0.1667em" }, children: _jsx(_components.span, { className: "mord mtight", children: "^" }) })] })] }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.1944em" }, children: _jsx(_components.span, {}) }) })] }) }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.3281em" }, children: _jsxs(_components.span, { style: { top: "-2.357em", marginLeft: "-0.0528em", marginRight: "0.0714em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.5em" } }), _jsx(_components.span, { className: "sizing reset-size3 size1 mtight", children: _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.05724em" }, children: "j" }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.2819em" }, children: _jsx(_components.span, {}) }) })] }) })] }) }) })] })] }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.5423em" }, children: _jsx(_components.span, {}) }) })] }) }), _jsx(_components.span, { className: "mclose nulldelimiter" })] })] })] })] }) }) }), "\n", _jsxs(_components.p, { children: ["ただし、", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsxs(_components.msub, { children: [_jsx(_components.mi, { children: "s" }), _jsx(_components.mi, { children: "j" })] }), _jsx(_components.mo, { children: "=" }), _jsxs(_components.msup, { children: [_jsx(_components.mi, { children: "s" }), _jsx(_components.mn, { children: "2" })] }), _jsxs(_components.msup, { children: [_jsx(_components.mi, { children: "q" }), _jsxs(_components.mrow, { children: [_jsx(_components.mi, { children: "j" }), _jsx(_components.mi, { children: "j" })] })] })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "s_j=s^2q^{jj}" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.7167em", verticalAlign: "-0.2861em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", children: "s" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.3117em" }, children: _jsxs(_components.span, { style: { top: "-2.55em", marginLeft: "0em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.05724em" }, children: "j" }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.2861em" }, children: _jsx(_components.span, {}) }) })] }) })] }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1.0191em", verticalAlign: "-0.1944em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", children: "s" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.8141em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: "2" }) })] }) }) }) }) })] }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.03588em" }, children: "q" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.8247em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.05724em" }, children: "jj" }) }) })] }) }) }) }) })] })] })] })] }) }), "、 ", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsxs(_components.msup, { children: [_jsx(_components.mi, { children: "s" }), _jsx(_components.mn, { children: "2" })] }), _jsx(_components.mo, { children: "=" }), _jsxs(_components.mfrac, { children: [_jsxs(_components.mrow, { children: [_jsxs(_components.msup, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "e" }), _jsx(_components.mo, { mathvariant: "normal", lspace: "0em", rspace: "0em", children: "′" })] }), _jsx(_components.mi, { mathvariant: "bold", children: "e" })] }), _jsxs(_components.mrow, { children: [_jsx(_components.mi, { children: "n" }), _jsx(_components.mo, { children: "−" }), _jsx(_components.mi, { children: "k" })] })] }), _jsx(_components.mo, { children: "=" }), _jsxs(_components.mfrac, { children: [_jsxs(_components.mrow, { children: [_jsxs(_components.msubsup, { children: [_jsx(_components.mo, { children: "∑" }), _jsxs(_components.mrow, { children: [_jsx(_components.mi, { children: "j" }), _jsx(_components.mo, { children: "=" }), _jsx(_components.mn, { children: "1" })] }), _jsx(_components.mi, { children: "k" })] }), _jsxs(_components.msubsup, { children: [_jsx(_components.mi, { children: "e" }), _jsx(_components.mi, { children: "j" }), _jsx(_components.mn, { children: "2" })] })] }), _jsxs(_components.mrow, { children: [_jsx(_components.mi, { children: "n" }), _jsx(_components.mo, { children: "−" }), _jsx(_components.mi, { children: "k" })] })] })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "s^2=\\frac{\\mathbf e'\\mathbf e}{n-k}=\\frac{\\sum_{j=1}^{k}e_j^2}{n-k}" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.8141em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", children: "s" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.8141em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: "2" }) })] }) }) }) }) })] }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1.3768em", verticalAlign: "-0.4033em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mopen nulldelimiter" }), _jsx(_components.span, { className: "mfrac", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsxs(_components.span, { className: "vlist", style: { height: "0.9735em" }, children: [_jsxs(_components.span, { style: { top: "-2.655em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsxs(_components.span, { className: "mord mtight", children: [_jsx(_components.span, { className: "mord mathnormal mtight", children: "n" }), _jsx(_components.span, { className: "mbin mtight", children: "−" }), _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.03148em" }, children: "k" })] }) })] }), _jsxs(_components.span, { style: { top: "-3.23em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "frac-line", style: { borderBottomWidth: "0.04em" } })] }), _jsxs(_components.span, { style: { top: "-3.394em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsxs(_components.span, { className: "mord mtight", children: [_jsxs(_components.span, { className: "mord mtight", children: [_jsx(_components.span, { className: "mord mathbf mtight", children: "e" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.8278em" }, children: _jsxs(_components.span, { style: { top: "-2.931em", marginRight: "0.0714em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.5em" } }), _jsx(_components.span, { className: "sizing reset-size3 size1 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord mtight", children: "′" }) }) })] }) }) }) }) })] }), _jsx(_components.span, { className: "mord mathbf mtight", children: "e" })] }) })] })] }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.4033em" }, children: _jsx(_components.span, {}) }) })] }) }), _jsx(_components.span, { className: "mclose nulldelimiter" })] }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1.6845em", verticalAlign: "-0.4033em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mopen nulldelimiter" }), _jsx(_components.span, { className: "mfrac", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsxs(_components.span, { className: "vlist", style: { height: "1.2811em" }, children: [_jsxs(_components.span, { style: { top: "-2.655em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsxs(_components.span, { className: "mord mtight", children: [_jsx(_components.span, { className: "mord mathnormal mtight", children: "n" }), _jsx(_components.span, { className: "mbin mtight", children: "−" }), _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.03148em" }, children: "k" })] }) })] }), _jsxs(_components.span, { style: { top: "-3.23em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "frac-line", style: { borderBottomWidth: "0.04em" } })] }), _jsxs(_components.span, { style: { top: "-3.6322em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsxs(_components.span, { className: "mord mtight", children: [_jsxs(_components.span, { className: "mop mtight", children: [_jsx(_components.span, { className: "mop op-symbol small-op mtight", style: { position: "relative", top: "0em" }, children: "∑" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsxs(_components.span, { className: "vlist", style: { height: "0.927em" }, children: [_jsxs(_components.span, { style: { top: "-2.1786em", marginLeft: "0em", marginRight: "0.0714em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.5em" } }), _jsx(_components.span, { className: "sizing reset-size3 size1 mtight", children: _jsxs(_components.span, { className: "mord mtight", children: [_jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.05724em" }, children: "j" }), _jsx(_components.span, { className: "mrel mtight", children: "=" }), _jsx(_components.span, { className: "mord mtight", children: "1" })] }) })] }), _jsxs(_components.span, { style: { top: "-2.931em", marginRight: "0.0714em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.5em" } }), _jsx(_components.span, { className: "sizing reset-size3 size1 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.03148em" }, children: "k" }) }) })] })] }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.4603em" }, children: _jsx(_components.span, {}) }) })] }) })] }), _jsx(_components.span, { className: "mspace mtight", style: { marginRight: "0.1952em" } }), _jsxs(_components.span, { className: "mord mtight", children: [_jsx(_components.span, { className: "mord mathnormal mtight", children: "e" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsxs(_components.span, { className: "vlist", style: { height: "0.8913em" }, children: [_jsxs(_components.span, { style: { top: "-2.214em", marginLeft: "0em", marginRight: "0.0714em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.5em" } }), _jsx(_components.span, { className: "sizing reset-size3 size1 mtight", children: _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.05724em" }, children: "j" }) })] }), _jsxs(_components.span, { style: { top: "-2.931em", marginRight: "0.0714em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.5em" } }), _jsx(_components.span, { className: "sizing reset-size3 size1 mtight", children: _jsx(_components.span, { className: "mord mtight", children: "2" }) })] })] }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.4249em" }, children: _jsx(_components.span, {}) }) })] }) })] })] }) })] })] }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.4033em" }, children: _jsx(_components.span, {}) }) })] }) }), _jsx(_components.span, { className: "mclose nulldelimiter" })] })] })] })] }) }), "、 ", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsx(_components.mrow, { children: _jsxs(_components.msup, { children: [_jsx(_components.mi, { children: "q" }), _jsxs(_components.mrow, { children: [_jsx(_components.mi, { children: "j" }), _jsx(_components.mi, { children: "j" })] })] }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "q^{jj}" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1.0191em", verticalAlign: "-0.1944em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.03588em" }, children: "q" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.8247em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.05724em" }, children: "jj" }) }) })] }) }) }) }) })] })] }) })] }) }), "は", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsx(_components.mo, { stretchy: "false", children: "(" }), _jsxs(_components.msup, { children: [_jsx(_components.mi, { children: "X" }), _jsx(_components.mo, { mathvariant: "normal", lspace: "0em", rspace: "0em", children: "′" })] }), _jsx(_components.mi, { children: "X" }), _jsxs(_components.msup, { children: [_jsx(_components.mo, { stretchy: "false", children: ")" }), _jsxs(_components.mrow, { children: [_jsx(_components.mo, { children: "−" }), _jsx(_components.mn, { children: "1" })] })] })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "(X'X)^{-1}" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1.0641em", verticalAlign: "-0.25em" } }), _jsx(_components.span, { className: "mopen", children: "(" }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.07847em" }, children: "X" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.7519em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord mtight", children: "′" }) }) })] }) }) }) }) })] }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.07847em" }, children: "X" }), _jsxs(_components.span, { className: "mclose", children: [_jsx(_components.span, { className: "mclose", children: ")" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.8141em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsxs(_components.span, { className: "mord mtight", children: [_jsx(_components.span, { className: "mord mtight", children: "−" }), _jsx(_components.span, { className: "mord mtight", children: "1" })] }) })] }) }) }) }) })] })] }) })] }) }), "の", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsx(_components.mo, { stretchy: "false", children: "(" }), _jsx(_components.mi, { children: "j" }), _jsx(_components.mo, { separator: "true", children: "," }), _jsx(_components.mi, { children: "j" }), _jsx(_components.mo, { stretchy: "false", children: ")" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "(j,j)" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1em", verticalAlign: "-0.25em" } }), _jsx(_components.span, { className: "mopen", children: "(" }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.05724em" }, children: "j" }), _jsx(_components.span, { className: "mpunct", children: "," }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.1667em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.05724em" }, children: "j" }), _jsx(_components.span, { className: "mclose", children: ")" })] }) })] }) }), "要素とします。"] }), "\n", _jsxs(_components.p, { children: ["ちなみに、", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsx(_components.mrow, { children: _jsxs(_components.msubsup, { children: [_jsx(_components.mi, { children: "s" }), _jsx(_components.mi, { children: "j" }), _jsx(_components.mn, { children: "2" })] }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "s_j^2" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1.2089em", verticalAlign: "-0.3948em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", children: "s" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsxs(_components.span, { className: "vlist", style: { height: "0.8141em" }, children: [_jsxs(_components.span, { style: { top: "-2.4413em", marginLeft: "0em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.05724em" }, children: "j" }) })] }), _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: "2" }) })] })] }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.3948em" }, children: _jsx(_components.span, {}) }) })] }) })] })] }) })] }) }), "は", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsx(_components.mi, { children: "V" }), _jsx(_components.mi, { children: "a" }), _jsx(_components.mi, { children: "r" }), _jsx(_components.mo, { stretchy: "false", children: "(" }), _jsxs(_components.msub, { children: [_jsxs(_components.mover, { accent: "true", children: [_jsx(_components.mi, { children: "β" }), _jsx(_components.mo, { children: "^" })] }), _jsx(_components.mi, { children: "j" })] }), _jsx(_components.mo, { stretchy: "false", children: ")" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "Var(\\hat\\beta_j)" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1.244em", verticalAlign: "-0.2861em" } }), _jsx(_components.span, { className: "mord mathnormal", children: "Va" }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.02778em" }, children: "r" }), _jsx(_components.span, { className: "mopen", children: "(" }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord accent", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsxs(_components.span, { className: "vlist", style: { height: "0.9579em" }, children: [_jsxs(_components.span, { style: { top: "-3em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.05278em" }, children: "β" })] }), _jsxs(_components.span, { style: { top: "-3.2634em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "accent-body", style: { left: "-0.1667em" }, children: _jsx(_components.span, { className: "mord", children: "^" }) })] })] }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.1944em" }, children: _jsx(_components.span, {}) }) })] }) }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.3117em" }, children: _jsxs(_components.span, { style: { top: "-2.55em", marginLeft: "-0.0528em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.05724em" }, children: "j" }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.2861em" }, children: _jsx(_components.span, {}) }) })] }) })] }), _jsx(_components.span, { className: "mclose", children: ")" })] }) })] }) }), "の不偏分散になります。", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsx(_components.mrow, { children: _jsxs(_components.msub, { children: [_jsx(_components.mi, { children: "s" }), _jsx(_components.mi, { children: "j" })] }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "s_j" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.7167em", verticalAlign: "-0.2861em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", children: "s" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.3117em" }, children: _jsxs(_components.span, { style: { top: "-2.55em", marginLeft: "0em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.05724em" }, children: "j" }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.2861em" }, children: _jsx(_components.span, {}) }) })] }) })] })] }) })] }) }), "は標本誤差とも呼ばれます。"] }), "\n", _jsxs(_components.p, { children: ["このt値が自由度", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsx(_components.mo, { stretchy: "false", children: "(" }), _jsx(_components.mi, { children: "n" }), _jsx(_components.mo, { children: "−" }), _jsx(_components.mi, { children: "k" }), _jsx(_components.mo, { stretchy: "false", children: ")" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "(n-k)" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1em", verticalAlign: "-0.25em" } }), _jsx(_components.span, { className: "mopen", children: "(" }), _jsx(_components.span, { className: "mord mathnormal", children: "n" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "−" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1em", verticalAlign: "-0.25em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.03148em" }, children: "k" }), _jsx(_components.span, { className: "mclose", children: ")" })] })] })] }) }), "のt分布に従うことを証明していきたいと思います。"] }), "\n", _jsx(_components.h3, { children: "証明の方針" }), "\n", _jsxs(_components.p, { children: [_jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsx(_components.mi, { children: "z" }), _jsx(_components.mo, { children: "=" }), _jsxs(_components.mfrac, { children: [_jsxs(_components.mover, { accent: "true", children: [_jsxs(_components.msub, { children: [_jsx(_components.mi, { children: "β" }), _jsx(_components.mi, { children: "j" })] }), _jsx(_components.mo, { children: "^" })] }), _jsxs(_components.mrow, { children: [_jsx(_components.mi, { children: "σ" }), _jsx(_components.msqrt, { children: _jsxs(_components.msup, { children: [_jsx(_components.mi, { children: "q" }), _jsxs(_components.mrow, { children: [_jsx(_components.mi, { children: "j" }), _jsx(_components.mi, { children: "j" })] })] }) })] })] })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "z=\\frac{\\hat{\\beta_j}}{\\sigma \\sqrt{q^{jj}}}" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.4306em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.04398em" }, children: "z" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "2.0074em", verticalAlign: "-0.8296em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mopen nulldelimiter" }), _jsx(_components.span, { className: "mfrac", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsxs(_components.span, { className: "vlist", style: { height: "1.1778em" }, children: [_jsxs(_components.span, { style: { top: "-2.4422em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsxs(_components.span, { className: "mord mtight", children: [_jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.03588em" }, children: "σ" }), _jsx(_components.span, { className: "mord sqrt mtight", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsxs(_components.span, { className: "vlist", style: { height: "1.0682em" }, children: [_jsxs(_components.span, { className: "svg-align", style: { top: "-3.4286em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3.4286em" } }), _jsx(_components.span, { className: "mord mtight", style: { paddingLeft: "1.19em" }, children: _jsxs(_components.span, { className: "mord mtight", children: [_jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.03588em" }, children: "q" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.7571em" }, children: _jsxs(_components.span, { style: { top: "-2.786em", marginRight: "0.0714em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.5em" } }), _jsx(_components.span, { className: "sizing reset-size3 size1 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.05724em" }, children: "jj" }) }) })] }) }) }) }) })] }) })] }), _jsxs(_components.span, { style: { top: "-3.0402em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3.4286em" } }), _jsx(_components.span, { className: "hide-tail mtight", style: { minWidth: "0.853em", height: "1.5429em" }, children: _jsx(_components.svg, { xmlns: "http://www.w3.org/2000/svg", width: "400em", height: "1.5429em", viewBox: "0 0 400000 1080", preserveAspectRatio: "xMinYMin slice", children: _jsx(_components.path, { d: "M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 80h400000v40h-400000z" }) }) })] })] }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.3883em" }, children: _jsx(_components.span, {}) }) })] }) })] }) })] }), _jsxs(_components.span, { style: { top: "-3.23em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "frac-line", style: { borderBottomWidth: "0.04em" } })] }), _jsxs(_components.span, { style: { top: "-3.5073em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord accent mtight", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsxs(_components.span, { className: "vlist", style: { height: "0.9579em" }, children: [_jsxs(_components.span, { style: { top: "-2.7em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsxs(_components.span, { className: "mord mtight", children: [_jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.05278em" }, children: "β" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.3281em" }, children: _jsxs(_components.span, { style: { top: "-2.357em", marginLeft: "-0.0528em", marginRight: "0.0714em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.5em" } }), _jsx(_components.span, { className: "sizing reset-size3 size1 mtight", children: _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.05724em" }, children: "j" }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.2819em" }, children: _jsx(_components.span, {}) }) })] }) })] })] }), _jsxs(_components.span, { style: { top: "-2.9634em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "accent-body", style: { left: "-0.25em" }, children: _jsx(_components.span, { className: "mord mtight", children: "^" }) })] })] }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.2819em" }, children: _jsx(_components.span, {}) }) })] }) }) }) })] })] }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.8296em" }, children: _jsx(_components.span, {}) }) })] }) }), _jsx(_components.span, { className: "mclose nulldelimiter" })] })] })] })] }) }), "、", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsx(_components.mi, { children: "v" }), _jsx(_components.mo, { children: "=" }), _jsxs(_components.mfrac, { children: [_jsxs(_components.mrow, { children: [_jsx(_components.mo, { stretchy: "false", children: "(" }), _jsx(_components.mi, { children: "n" }), _jsx(_components.mo, { children: "−" }), _jsx(_components.mi, { children: "k" }), _jsx(_components.mo, { stretchy: "false", children: ")" }), _jsxs(_components.msup, { children: [_jsx(_components.mi, { children: "s" }), _jsx(_components.mn, { children: "2" })] })] }), _jsxs(_components.msup, { children: [_jsx(_components.mi, { children: "σ" }), _jsx(_components.mn, { children: "2" })] })] })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "v=\\frac{(n-k)s^2}{\\sigma^2}" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.4306em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.03588em" }, children: "v" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1.4539em", verticalAlign: "-0.345em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mopen nulldelimiter" }), _jsx(_components.span, { className: "mfrac", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsxs(_components.span, { className: "vlist", style: { height: "1.1089em" }, children: [_jsxs(_components.span, { style: { top: "-2.655em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsxs(_components.span, { className: "mord mtight", children: [_jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.03588em" }, children: "σ" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.7463em" }, children: _jsxs(_components.span, { style: { top: "-2.786em", marginRight: "0.0714em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.5em" } }), _jsx(_components.span, { className: "sizing reset-size3 size1 mtight", children: _jsx(_components.span, { className: "mord mtight", children: "2" }) })] }) }) }) }) })] }) }) })] }), _jsxs(_components.span, { style: { top: "-3.23em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "frac-line", style: { borderBottomWidth: "0.04em" } })] }), _jsxs(_components.span, { style: { top: "-3.485em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsxs(_components.span, { className: "mord mtight", children: [_jsx(_components.span, { className: "mopen mtight", children: "(" }), _jsx(_components.span, { className: "mord mathnormal mtight", children: "n" }), _jsx(_components.span, { className: "mbin mtight", children: "−" }), _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.03148em" }, children: "k" }), _jsx(_components.span, { className: "mclose mtight", children: ")" }), _jsxs(_components.span, { className: "mord mtight", children: [_jsx(_components.span, { className: "mord mathnormal mtight", children: "s" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.8913em" }, children: _jsxs(_components.span, { style: { top: "-2.931em", marginRight: "0.0714em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.5em" } }), _jsx(_components.span, { className: "sizing reset-size3 size1 mtight", children: _jsx(_components.span, { className: "mord mtight", children: "2" }) })] }) }) }) }) })] })] }) })] })] }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.345em" }, children: _jsx(_components.span, {}) }) })] }) }), _jsx(_components.span, { className: "mclose nulldelimiter" })] })] })] })] }) }), "としたとき、t値は", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsx(_components.mi, { children: "t" }), _jsx(_components.mo, { children: "=" }), _jsxs(_components.mfrac, { children: [_jsx(_components.mi, { children: "z" }), _jsx(_components.msqrt, { children: _jsxs(_components.mrow, { children: [_jsx(_components.mi, { children: "v" }), _jsx(_components.mi, { mathvariant: "normal", children: "/" }), _jsx(_components.mo, { stretchy: "false", children: "(" }), _jsx(_components.mi, { children: "n" }), _jsx(_components.mo, { children: "−" }), _jsx(_components.mi, { children: "k" }), _jsx(_components.mo, { stretchy: "false", children: ")" })] }) })] })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "t=\\frac{z}{\\sqrt{v/(n-k)}}" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6151em" } }), _jsx(_components.span, { className: "mord mathnormal", children: "t" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1.525em", verticalAlign: "-0.8296em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mopen nulldelimiter" }), _jsx(_components.span, { className: "mfrac", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsxs(_components.span, { className: "vlist", style: { height: "0.6954em" }, children: [_jsxs(_components.span, { style: { top: "-2.4642em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord sqrt mtight", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsxs(_components.span, { className: "vlist", style: { height: "1.0369em" }, children: [_jsxs(_components.span, { className: "svg-align", style: { top: "-3.4286em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3.4286em" } }), _jsxs(_components.span, { className: "mord mtight", style: { paddingLeft: "1.19em" }, children: [_jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.03588em" }, children: "v" }), _jsx(_components.span, { className: "mord mtight", children: "/" }), _jsx(_components.span, { className: "mopen mtight", children: "(" }), _jsx(_components.span, { className: "mord mathnormal mtight", children: "n" }), _jsx(_components.span, { className: "mbin mtight", children: "−" }), _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.03148em" }, children: "k" }), _jsx(_components.span, { className: "mclose mtight", children: ")" })] })] }), _jsxs(_components.span, { style: { top: "-3.0089em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3.4286em" } }), _jsx(_components.span, { className: "hide-tail mtight", style: { minWidth: "0.853em", height: "1.5429em" }, children: _jsx(_components.svg, { xmlns: "http://www.w3.org/2000/svg", width: "400em", height: "1.5429em", viewBox: "0 0 400000 1080", preserveAspectRatio: "xMinYMin slice", children: _jsx(_components.path, { d: "M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 80h400000v40h-400000z" }) }) })] })] }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.4197em" }, children: _jsx(_components.span, {}) }) })] }) }) }) })] }), _jsxs(_components.span, { style: { top: "-3.23em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "frac-line", style: { borderBottomWidth: "0.04em" } })] }), _jsxs(_components.span, { style: { top: "-3.394em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.04398em" }, children: "z" }) }) })] })] }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.8296em" }, children: _jsx(_components.span, {}) }) })] }) }), _jsx(_components.span, { className: "mclose nulldelimiter" })] })] })] })] }) }), "と表すことができます。"] }), "\n", _jsxs(_components.p, { children: [_jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsx(_components.mrow, { children: _jsx(_components.mi, { children: "z" }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "z" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.4306em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.04398em" }, children: "z" })] }) })] }) }), "が標準正規分布であること、", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsx(_components.mrow, { children: _jsx(_components.mi, { children: "v" }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "v" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.4306em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.03588em" }, children: "v" })] }) })] }) }), "が自由度", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsx(_components.mo, { stretchy: "false", children: "(" }), _jsx(_components.mi, { children: "n" }), _jsx(_components.mo, { children: "−" }), _jsx(_components.mi, { children: "k" }), _jsx(_components.mo, { stretchy: "false", children: ")" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "(n-k)" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1em", verticalAlign: "-0.25em" } }), _jsx(_components.span, { className: "mopen", children: "(" }), _jsx(_components.span, { className: "mord mathnormal", children: "n" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "−" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1em", verticalAlign: "-0.25em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.03148em" }, children: "k" }), _jsx(_components.span, { className: "mclose", children: ")" })] })] })] }) }), "のカイ二乗分布に従うことが示されればt分布に従うことを証明できるので、これを目標とします。"] }), "\n", _jsx(_components.p, { children: "かなり長いので、証明のアウトラインを載せます。" }), "\n", _jsxs(_components.ol, { children: ["\n", _jsxs(_components.li, { children: [_jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsx(_components.mrow, { children: _jsx(_components.mi, { children: "z" }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "z" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.4306em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.04398em" }, children: "z" })] }) })] }) }), "が標準正規分布に従うこと"] }), "\n", _jsxs(_components.li, { children: ["あるべき等対称行列", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsx(_components.mrow, { children: _jsx(_components.mi, { mathvariant: "bold", children: "M" }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\mathbf M" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6861em" } }), _jsx(_components.span, { className: "mord mathbf", children: "M" })] }) })] }) }), "を用いて、", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "e" }), _jsx(_components.mo, { children: "=" }), _jsx(_components.mi, { mathvariant: "bold", children: "M" }), _jsx(_components.mi, { mathvariant: "bold", children: "u" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\mathbf e=\\mathbf M\\mathbf u" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.4444em" } }), _jsx(_components.span, { className: "mord mathbf", children: "e" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6861em" } }), _jsx(_components.span, { className: "mord mathbf", children: "Mu" })] })] })] }) }), "と表される。ただし、べき等対称行列とは", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "M" }), _jsx(_components.mo, { children: "=" }), _jsxs(_components.msup, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "M" }), _jsx(_components.mo, { mathvariant: "normal", lspace: "0em", rspace: "0em", children: "′" })] }), _jsx(_components.mo, { children: "=" }), _jsxs(_components.msup, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "M" }), _jsx(_components.mn, { children: "2" })] })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\mathbf M=\\mathbf M'=\\mathbf M^2" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6861em" } }), _jsx(_components.span, { className: "mord mathbf", children: "M" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.7519em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathbf", children: "M" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.7519em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord mtight", children: "′" }) }) })] }) }) }) }) })] }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.8141em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathbf", children: "M" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.8141em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: "2" }) })] }) }) }) }) })] })] })] })] }) }), "を満たす", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsx(_components.mrow, { children: _jsx(_components.mi, { mathvariant: "bold", children: "M" }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\mathbf M" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6861em" } }), _jsx(_components.span, { className: "mord mathbf", children: "M" })] }) })] }) }), "である。"] }), "\n", _jsx(_components.li, { children: _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsxs(_components.msup, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "e" }), _jsx(_components.mo, { mathvariant: "normal", lspace: "0em", rspace: "0em", children: "′" })] }), _jsx(_components.mi, { mathvariant: "bold", children: "e" }), _jsx(_components.mo, { children: "=" }), _jsxs(_components.msup, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "u" }), _jsx(_components.mo, { mathvariant: "normal", lspace: "0em", rspace: "0em", children: "′" })] }), _jsx(_components.mi, { mathvariant: "bold", children: "M" }), _jsx(_components.mi, { mathvariant: "bold", children: "u" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\mathbf e'\\mathbf e=\\mathbf u'\\mathbf M\\mathbf u" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.7519em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathbf", children: "e" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.7519em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord mtight", children: "′" }) }) })] }) }) }) }) })] }), _jsx(_components.span, { className: "mord mathbf", children: "e" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.7519em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathbf", children: "u" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.7519em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord mtight", children: "′" }) }) })] }) }) }) }) })] }), _jsx(_components.span, { className: "mord mathbf", children: "Mu" })] })] })] }) }) }), "\n", _jsxs(_components.li, { children: [_jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsxs(_components.msup, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "P" }), _jsx(_components.mo, { mathvariant: "normal", lspace: "0em", rspace: "0em", children: "′" })] }), _jsx(_components.mi, { mathvariant: "bold", children: "M" }), _jsx(_components.mi, { mathvariant: "bold", children: "P" }), _jsx(_components.mo, { children: "=" }), _jsxs(_components.msub, { children: [_jsx(_components.mi, { children: "I" }), _jsxs(_components.mrow, { children: [_jsx(_components.mi, { children: "n" }), _jsx(_components.mo, { separator: "true", children: "," }), _jsx(_components.mi, { children: "n" }), _jsx(_components.mo, { children: "−" }), _jsx(_components.mi, { children: "k" })] })] })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\mathbf P'\\mathbf M\\mathbf P=I_{n,n-k}" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.7519em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathbf", children: "P" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.7519em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord mtight", children: "′" }) }) })] }) }) }) }) })] }), _jsx(_components.span, { className: "mord mathbf", children: "MP" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.9694em", verticalAlign: "-0.2861em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.07847em" }, children: "I" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.3361em" }, children: _jsxs(_components.span, { style: { top: "-2.55em", marginLeft: "-0.0785em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsxs(_components.span, { className: "mord mtight", children: [_jsx(_components.span, { className: "mord mathnormal mtight", children: "n" }), _jsx(_components.span, { className: "mpunct mtight", children: "," }), _jsx(_components.span, { className: "mord mathnormal mtight", children: "n" }), _jsx(_components.span, { className: "mbin mtight", children: "−" }), _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.03148em" }, children: "k" })] }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.2861em" }, children: _jsx(_components.span, {}) }) })] }) })] })] })] })] }) }), "となる直交行列", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsx(_components.mrow, { children: _jsx(_components.mi, { mathvariant: "bold", children: "P" }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\mathbf P" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6861em" } }), _jsx(_components.span, { className: "mord mathbf", children: "P" })] }) })] }) }), "が存在すること（ただし", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsx(_components.mrow, { children: _jsxs(_components.msub, { children: [_jsx(_components.mi, { children: "I" }), _jsxs(_components.mrow, { children: [_jsx(_components.mi, { children: "n" }), _jsx(_components.mo, { separator: "true", children: "," }), _jsx(_components.mi, { children: "n" }), _jsx(_components.mo, { children: "−" }), _jsx(_components.mi, { children: "k" })] })] }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "I_{n,n-k}" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.9694em", verticalAlign: "-0.2861em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.07847em" }, children: "I" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.3361em" }, children: _jsxs(_components.span, { style: { top: "-2.55em", marginLeft: "-0.0785em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsxs(_components.span, { className: "mord mtight", children: [_jsx(_components.span, { className: "mord mathnormal mtight", children: "n" }), _jsx(_components.span, { className: "mpunct mtight", children: "," }), _jsx(_components.span, { className: "mord mathnormal mtight", children: "n" }), _jsx(_components.span, { className: "mbin mtight", children: "−" }), _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.03148em" }, children: "k" })] }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.2861em" }, children: _jsx(_components.span, {}) }) })] }) })] })] }) })] }) }), "とは、", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsx(_components.mo, { stretchy: "false", children: "(" }), _jsx(_components.mi, { children: "n" }), _jsx(_components.mo, { children: "−" }), _jsx(_components.mi, { children: "k" }), _jsx(_components.mo, { stretchy: "false", children: ")" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "(n-k)" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1em", verticalAlign: "-0.25em" } }), _jsx(_components.span, { className: "mopen", children: "(" }), _jsx(_components.span, { className: "mord mathnormal", children: "n" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "−" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1em", verticalAlign: "-0.25em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.03148em" }, children: "k" }), _jsx(_components.span, { className: "mclose", children: ")" })] })] })] }) }), "個の対角成分が1、それ以外が0の", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsx(_components.mi, { children: "n" }), _jsx(_components.mo, { children: "×" }), _jsx(_components.mi, { children: "n" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "n \\times n" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6667em", verticalAlign: "-0.0833em" } }), _jsx(_components.span, { className: "mord mathnormal", children: "n" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "×" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.4306em" } }), _jsx(_components.span, { className: "mord mathnormal", children: "n" })] })] })] }) }), "行列とする。）"] }), "\n", _jsx(_components.li, { children: _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsxs(_components.mfrac, { children: [_jsxs(_components.mrow, { children: [_jsxs(_components.msup, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "u" }), _jsx(_components.mo, { mathvariant: "normal", lspace: "0em", rspace: "0em", children: "′" })] }), _jsx(_components.mi, { mathvariant: "bold", children: "M" }), _jsx(_components.mi, { mathvariant: "bold", children: "u" })] }), _jsxs(_components.msup, { children: [_jsx(_components.mi, { children: "σ" }), _jsx(_components.mn, { children: "2" })] })] }), _jsx(_components.mo, { children: "∼" }), _jsxs(_components.msup, { children: [_jsx(_components.mi, { children: "χ" }), _jsx(_components.mn, { children: "2" })] }), _jsx(_components.mo, { stretchy: "false", children: "(" }), _jsx(_components.mi, { children: "n" }), _jsx(_components.mo, { children: "−" }), _jsx(_components.mi, { children: "k" }), _jsx(_components.mo, { stretchy: "false", children: ")" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\frac{\\mathbf u'\\mathbf M\\mathbf u}{\\sigma^2} \\sim \\chi^2(n-k)" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1.3185em", verticalAlign: "-0.345em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mopen nulldelimiter" }), _jsx(_components.span, { className: "mfrac", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsxs(_components.span, { className: "vlist", style: { height: "0.9735em" }, children: [_jsxs(_components.span, { style: { top: "-2.655em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsxs(_components.span, { className: "mord mtight", children: [_jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.03588em" }, children: "σ" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.7463em" }, children: _jsxs(_components.span, { style: { top: "-2.786em", marginRight: "0.0714em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.5em" } }), _jsx(_components.span, { className: "sizing reset-size3 size1 mtight", children: _jsx(_components.span, { className: "mord mtight", children: "2" }) })] }) }) }) }) })] }) }) })] }), _jsxs(_components.span, { style: { top: "-3.23em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "frac-line", style: { borderBottomWidth: "0.04em" } })] }), _jsxs(_components.span, { style: { top: "-3.394em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsxs(_components.span, { className: "mord mtight", children: [_jsxs(_components.span, { className: "mord mtight", children: [_jsx(_components.span, { className: "mord mathbf mtight", children: "u" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.8278em" }, children: _jsxs(_components.span, { style: { top: "-2.931em", marginRight: "0.0714em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.5em" } }), _jsx(_components.span, { className: "sizing reset-size3 size1 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord mtight", children: "′" }) }) })] }) }) }) }) })] }), _jsx(_components.span, { className: "mord mathbf mtight", children: "Mu" })] }) })] })] }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.345em" }, children: _jsx(_components.span, {}) }) })] }) }), _jsx(_components.span, { className: "mclose nulldelimiter" })] }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "∼" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1.0641em", verticalAlign: "-0.25em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", children: "χ" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.8141em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: "2" }) })] }) }) }) }) })] }), _jsx(_components.span, { className: "mopen", children: "(" }), _jsx(_components.span, { className: "mord mathnormal", children: "n" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "−" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1em", verticalAlign: "-0.25em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.03148em" }, children: "k" }), _jsx(_components.span, { className: "mclose", children: ")" })] })] })] }) }) }), "\n", _jsx(_components.li, { children: _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsxs(_components.mfrac, { children: [_jsxs(_components.mrow, { children: [_jsx(_components.mo, { stretchy: "false", children: "(" }), _jsx(_components.mi, { children: "n" }), _jsx(_components.mo, { children: "−" }), _jsx(_components.mi, { children: "k" }), _jsx(_components.mo, { stretchy: "false", children: ")" }), _jsxs(_components.msup, { children: [_jsx(_components.mi, { children: "s" }), _jsx(_components.mn, { children: "2" })] })] }), _jsxs(_components.msup, { children: [_jsx(_components.mi, { children: "σ" }), _jsx(_components.mn, { children: "2" })] })] }), _jsx(_components.mo, { children: "∼" }), _jsxs(_components.msup, { children: [_jsx(_components.mi, { children: "χ" }), _jsx(_components.mn, { children: "2" })] }), _jsx(_components.mo, { stretchy: "false", children: "(" }), _jsx(_components.mi, { children: "n" }), _jsx(_components.mo, { children: "−" }), _jsx(_components.mi, { children: "k" }), _jsx(_components.mo, { stretchy: "false", children: ")" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\frac{(n-k)s^2}{\\sigma^2}\\sim\\chi^2(n-k)" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1.4539em", verticalAlign: "-0.345em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mopen nulldelimiter" }), _jsx(_components.span, { className: "mfrac", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsxs(_components.span, { className: "vlist", style: { height: "1.1089em" }, children: [_jsxs(_components.span, { style: { top: "-2.655em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsxs(_components.span, { className: "mord mtight", children: [_jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.03588em" }, children: "σ" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.7463em" }, children: _jsxs(_components.span, { style: { top: "-2.786em", marginRight: "0.0714em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.5em" } }), _jsx(_components.span, { className: "sizing reset-size3 size1 mtight", children: _jsx(_components.span, { className: "mord mtight", children: "2" }) })] }) }) }) }) })] }) }) })] }), _jsxs(_components.span, { style: { top: "-3.23em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "frac-line", style: { borderBottomWidth: "0.04em" } })] }), _jsxs(_components.span, { style: { top: "-3.485em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsxs(_components.span, { className: "mord mtight", children: [_jsx(_components.span, { className: "mopen mtight", children: "(" }), _jsx(_components.span, { className: "mord mathnormal mtight", children: "n" }), _jsx(_components.span, { className: "mbin mtight", children: "−" }), _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.03148em" }, children: "k" }), _jsx(_components.span, { className: "mclose mtight", children: ")" }), _jsxs(_components.span, { className: "mord mtight", children: [_jsx(_components.span, { className: "mord mathnormal mtight", children: "s" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.8913em" }, children: _jsxs(_components.span, { style: { top: "-2.931em", marginRight: "0.0714em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.5em" } }), _jsx(_components.span, { className: "sizing reset-size3 size1 mtight", children: _jsx(_components.span, { className: "mord mtight", children: "2" }) })] }) }) }) }) })] })] }) })] })] }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.345em" }, children: _jsx(_components.span, {}) }) })] }) }), _jsx(_components.span, { className: "mclose nulldelimiter" })] }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "∼" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1.0641em", verticalAlign: "-0.25em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", children: "χ" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.8141em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: "2" }) })] }) }) }) }) })] }), _jsx(_components.span, { className: "mopen", children: "(" }), _jsx(_components.span, { className: "mord mathnormal", children: "n" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "−" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1em", verticalAlign: "-0.25em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.03148em" }, children: "k" }), _jsx(_components.span, { className: "mclose", children: ")" })] })] })] }) }) }), "\n"] }), "\n", _jsxs(_components.p, { children: ["1と6から、", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsx(_components.mrow, { children: _jsx(_components.mi, { children: "z" }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "z" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.4306em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.04398em" }, children: "z" })] }) })] }) }), "が標準正規分布であること、", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsx(_components.mrow, { children: _jsx(_components.mi, { children: "v" }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "v" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.4306em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.03588em" }, children: "v" })] }) })] }) }), "が自由度", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsx(_components.mo, { stretchy: "false", children: "(" }), _jsx(_components.mi, { children: "n" }), _jsx(_components.mo, { children: "−" }), _jsx(_components.mi, { children: "k" }), _jsx(_components.mo, { stretchy: "false", children: ")" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "(n-k)" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1em", verticalAlign: "-0.25em" } }), _jsx(_components.span, { className: "mopen", children: "(" }), _jsx(_components.span, { className: "mord mathnormal", children: "n" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "−" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1em", verticalAlign: "-0.25em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.03148em" }, children: "k" }), _jsx(_components.span, { className: "mclose", children: ")" })] })] })] }) }), "のカイ二乗分布に従うことが証明され、t値がt分布に従うことが証明されます。"] }), "\n", _jsxs(_components.h3, { children: ["1. ", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsx(_components.mrow, { children: _jsx(_components.mi, { children: "z" }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "z" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.4306em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.04398em" }, children: "z" })] }) })] }) }), "が標準正規分布に従うこと"] }), "\n", _jsxs(_components.p, { children: [_jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsxs(_components.msub, { children: [_jsxs(_components.mover, { accent: "true", children: [_jsx(_components.mi, { children: "β" }), _jsx(_components.mo, { children: "^" })] }), _jsx(_components.mi, { children: "j" })] }), _jsx(_components.mo, { children: "∼" }), _jsx(_components.mi, { children: "N" }), _jsx(_components.mo, { stretchy: "false", children: "(" }), _jsxs(_components.msub, { children: [_jsx(_components.mi, { children: "β" }), _jsx(_components.mi, { children: "j" })] }), _jsx(_components.mo, { separator: "true", children: "," }), _jsxs(_components.msup, { children: [_jsx(_components.mi, { children: "σ" }), _jsx(_components.mn, { children: "2" })] }), _jsxs(_components.msup, { children: [_jsx(_components.mi, { children: "q" }), _jsxs(_components.mrow, { children: [_jsx(_components.mi, { children: "j" }), _jsx(_components.mi, { children: "j" })] })] }), _jsx(_components.mo, { stretchy: "false", children: ")" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\hat\\beta_j\\sim N(\\beta_j,\\sigma^2 q^{jj})" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1.244em", verticalAlign: "-0.2861em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord accent", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsxs(_components.span, { className: "vlist", style: { height: "0.9579em" }, children: [_jsxs(_components.span, { style: { top: "-3em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.05278em" }, children: "β" })] }), _jsxs(_components.span, { style: { top: "-3.2634em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "accent-body", style: { left: "-0.1667em" }, children: _jsx(_components.span, { className: "mord", children: "^" }) })] })] }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.1944em" }, children: _jsx(_components.span, {}) }) })] }) }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.3117em" }, children: _jsxs(_components.span, { style: { top: "-2.55em", marginLeft: "-0.0528em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.05724em" }, children: "j" }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.2861em" }, children: _jsx(_components.span, {}) }) })] }) })] }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "∼" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1.1108em", verticalAlign: "-0.2861em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.10903em" }, children: "N" }), _jsx(_components.span, { className: "mopen", children: "(" }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.05278em" }, children: "β" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.3117em" }, children: _jsxs(_components.span, { style: { top: "-2.55em", marginLeft: "-0.0528em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.05724em" }, children: "j" }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.2861em" }, children: _jsx(_components.span, {}) }) })] }) })] }), _jsx(_components.span, { className: "mpunct", children: "," }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.1667em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.03588em" }, children: "σ" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.8141em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: "2" }) })] }) }) }) }) })] }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.03588em" }, children: "q" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.8247em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.05724em" }, children: "jj" }) }) })] }) }) }) }) })] }), _jsx(_components.span, { className: "mclose", children: ")" })] })] })] }) }), "を示せば", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsx(_components.mrow, { children: _jsx(_components.mi, { children: "z" }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "z" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.4306em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.04398em" }, children: "z" })] }) })] }) }), "が標準正規分布に従うことが示せるので、これを示します。"] }), "\n", _jsxs(_components.p, { children: [_jsx(_components.a, { href: "./blog25.html", children: "以前のブログ" }), "から、", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsxs(_components.mover, { accent: "true", children: [_jsx(_components.mi, { children: "β" }), _jsx(_components.mo, { children: "^" })] }), _jsx(_components.mo, { children: "=" }), _jsx(_components.mo, { stretchy: "false", children: "(" }), _jsxs(_components.msup, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "X" }), _jsx(_components.mo, { mathvariant: "normal", lspace: "0em", rspace: "0em", children: "′" })] }), _jsx(_components.mi, { mathvariant: "bold", children: "X" }), _jsxs(_components.msup, { children: [_jsx(_components.mo, { stretchy: "false", children: ")" }), _jsxs(_components.mrow, { children: [_jsx(_components.mo, { children: "−" }), _jsx(_components.mn, { children: "1" })] })] }), _jsxs(_components.msup, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "X" }), _jsx(_components.mo, { mathvariant: "normal", lspace: "0em", rspace: "0em", children: "′" })] }), _jsx(_components.mi, { mathvariant: "bold", children: "y" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\hat\\beta=(\\mathbf X'\\mathbf X)^{-1}\\mathbf X'\\mathbf y" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1.1523em", verticalAlign: "-0.1944em" } }), _jsx(_components.span, { className: "mord accent", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsxs(_components.span, { className: "vlist", style: { height: "0.9579em" }, children: [_jsxs(_components.span, { style: { top: "-3em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.05278em" }, children: "β" })] }), _jsxs(_components.span, { style: { top: "-3.2634em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "accent-body", style: { left: "-0.1667em" }, children: _jsx(_components.span, { className: "mord", children: "^" }) })] })] }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.1944em" }, children: _jsx(_components.span, {}) }) })] }) }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1.0641em", verticalAlign: "-0.25em" } }), _jsx(_components.span, { className: "mopen", children: "(" }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathbf", children: "X" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.7519em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord mtight", children: "′" }) }) })] }) }) }) }) })] }), _jsx(_components.span, { className: "mord mathbf", children: "X" }), _jsxs(_components.span, { className: "mclose", children: [_jsx(_components.span, { className: "mclose", children: ")" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.8141em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsxs(_components.span, { className: "mord mtight", children: [_jsx(_components.span, { className: "mord mtight", children: "−" }), _jsx(_components.span, { className: "mord mtight", children: "1" })] }) })] }) }) }) }) })] }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathbf", children: "X" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.7519em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord mtight", children: "′" }) }) })] }) }) }) }) })] }), _jsx(_components.span, { className: "mord mathbf", style: { marginRight: "0.01597em" }, children: "y" })] })] })] }) }), "であることを示したので、これを使います。"] }), "\n", _jsx(_components.p, { children: _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsxs(_components.mover, { accent: "true", children: [_jsx(_components.mi, { mathvariant: "bold", children: "β" }), _jsx(_components.mo, { children: "^" })] }), _jsx(_components.mo, { children: "=" }), _jsx(_components.mo, { stretchy: "false", children: "(" }), _jsxs(_components.msup, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "X" }), _jsx(_components.mo, { mathvariant: "normal", lspace: "0em", rspace: "0em", children: "′" })] }), _jsx(_components.mi, { mathvariant: "bold", children: "X" }), _jsxs(_components.msup, { children: [_jsx(_components.mo, { stretchy: "false", children: ")" }), _jsxs(_components.mrow, { children: [_jsx(_components.mo, { children: "−" }), _jsx(_components.mn, { children: "1" })] })] }), _jsxs(_components.msup, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "X" }), _jsx(_components.mo, { mathvariant: "normal", lspace: "0em", rspace: "0em", children: "′" })] }), _jsx(_components.mi, { mathvariant: "bold", children: "y" }), _jsx(_components.mo, { children: "=" }), _jsx(_components.mo, { stretchy: "false", children: "(" }), _jsxs(_components.msup, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "X" }), _jsx(_components.mo, { mathvariant: "normal", lspace: "0em", rspace: "0em", children: "′" })] }), _jsx(_components.mi, { mathvariant: "bold", children: "X" }), _jsxs(_components.msup, { children: [_jsx(_components.mo, { stretchy: "false", children: ")" }), _jsxs(_components.mrow, { children: [_jsx(_components.mo, { children: "−" }), _jsx(_components.mn, { children: "1" })] })] }), _jsxs(_components.msup, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "X" }), _jsx(_components.mo, { mathvariant: "normal", lspace: "0em", rspace: "0em", children: "′" })] }), _jsx(_components.mo, { stretchy: "false", children: "(" }), _jsx(_components.mi, { mathvariant: "bold", children: "X" }), _jsx(_components.mi, { mathvariant: "bold", children: "β" }), _jsx(_components.mo, { children: "+" }), _jsx(_components.mi, { mathvariant: "bold", children: "u" }), _jsx(_components.mo, { stretchy: "false", children: ")" }), _jsx(_components.mo, { children: "=" }), _jsx(_components.mi, { mathvariant: "bold", children: "β" }), _jsx(_components.mo, { children: "+" }), _jsx(_components.mo, { stretchy: "false", children: "(" }), _jsx(_components.mi, { mathvariant: "bold", children: "X" }), _jsx(_components.mtext, { children: "’" }), _jsx(_components.mi, { mathvariant: "bold", children: "X" }), _jsxs(_components.msup, { children: [_jsx(_components.mo, { stretchy: "false", children: ")" }), _jsxs(_components.mrow, { children: [_jsx(_components.mo, { children: "−" }), _jsx(_components.mn, { children: "1" })] })] }), _jsxs(_components.msup, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "X" }), _jsx(_components.mo, { mathvariant: "normal", lspace: "0em", rspace: "0em", children: "′" })] }), _jsx(_components.mi, { mathvariant: "bold", children: "u" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\mathbf{\\hat\\beta}=(\\mathbf X'\\mathbf X)^{-1}\\mathbf X'\\mathbf y=(\\mathbf X'\\mathbf X)^{-1}\\mathbf X'(\\mathbf X\\mathbf{\\beta}+\\mathbf u)=\\mathbf{\\beta}+(\\mathbf X’\\mathbf X)^{-1}\\mathbf X'\\mathbf u" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1.1523em", verticalAlign: "-0.1944em" } }), _jsx(_components.span, { className: "mord accent", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsxs(_components.span, { className: "vlist", style: { height: "0.9579em" }, children: [_jsxs(_components.span, { style: { top: "-3em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.05278em" }, children: "β" })] }), _jsxs(_components.span, { style: { top: "-3.2634em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "accent-body", style: { left: "-0.2042em" }, children: _jsx(_components.span, { className: "mord mathbf", children: "^" }) })] })] }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.1944em" }, children: _jsx(_components.span, {}) }) })] }) }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1.0641em", verticalAlign: "-0.25em" } }), _jsx(_components.span, { className: "mopen", children: "(" }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathbf", children: "X" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.7519em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord mtight", children: "′" }) }) })] }) }) }) }) })] }), _jsx(_components.span, { className: "mord mathbf", children: "X" }), _jsxs(_components.span, { className: "mclose", children: [_jsx(_components.span, { className: "mclose", children: ")" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.8141em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsxs(_components.span, { className: "mord mtight", children: [_jsx(_components.span, { className: "mord mtight", children: "−" }), _jsx(_components.span, { className: "mord mtight", children: "1" })] }) })] }) }) }) }) })] }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathbf", children: "X" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.7519em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord mtight", children: "′" }) }) })] }) }) }) }) })] }), _jsx(_components.span, { className: "mord mathbf", style: { marginRight: "0.01597em" }, children: "y" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1.0641em", verticalAlign: "-0.25em" } }), _jsx(_components.span, { className: "mopen", children: "(" }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathbf", children: "X" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.7519em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord mtight", children: "′" }) }) })] }) }) }) }) })] }), _jsx(_components.span, { className: "mord mathbf", children: "X" }), _jsxs(_components.span, { className: "mclose", children: [_jsx(_components.span, { className: "mclose", children: ")" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.8141em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsxs(_components.span, { className: "mord mtight", children: [_jsx(_components.span, { className: "mord mtight", children: "−" }), _jsx(_components.span, { className: "mord mtight", children: "1" })] }) })] }) }) }) }) })] }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathbf", children: "X" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.7519em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord mtight", children: "′" }) }) })] }) }) }) }) })] }), _jsx(_components.span, { className: "mopen", children: "(" }), _jsx(_components.span, { className: "mord mathbf", children: "X" }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.05278em" }, children: "β" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "+" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1em", verticalAlign: "-0.25em" } }), _jsx(_components.span, { className: "mord mathbf", children: "u" }), _jsx(_components.span, { className: "mclose", children: ")" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.8889em", verticalAlign: "-0.1944em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.05278em" }, children: "β" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "+" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1.0641em", verticalAlign: "-0.25em" } }), _jsx(_components.span, { className: "mopen", children: "(" }), _jsx(_components.span, { className: "mord mathbf", children: "X" }), _jsx(_components.span, { className: "mord", children: "’" }), _jsx(_components.span, { className: "mord mathbf", children: "X" }), _jsxs(_components.span, { className: "mclose", children: [_jsx(_components.span, { className: "mclose", children: ")" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.8141em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsxs(_components.span, { className: "mord mtight", children: [_jsx(_components.span, { className: "mord mtight", children: "−" }), _jsx(_components.span, { className: "mord mtight", children: "1" })] }) })] }) }) }) }) })] }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathbf", children: "X" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.7519em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord mtight", children: "′" }) }) })] }) }) }) }) })] }), _jsx(_components.span, { className: "mord mathbf", children: "u" })] })] })] }) }) }), "\n", _jsxs(_components.p, { children: [_jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsxs(_components.msub, { children: [_jsx(_components.mi, { children: "u" }), _jsx(_components.mi, { children: "i" })] }), _jsx(_components.mo, { children: "∼" }), _jsx(_components.mi, { children: "N" }), _jsx(_components.mo, { stretchy: "false", children: "(" }), _jsx(_components.mn, { children: "0" }), _jsx(_components.mo, { separator: "true", children: "," }), _jsxs(_components.msup, { children: [_jsx(_components.mi, { children: "σ" }), _jsx(_components.mn, { children: "2" })] }), _jsx(_components.mo, { stretchy: "false", children: ")" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "u_i \\sim N(0,\\sigma^2)" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.5806em", verticalAlign: "-0.15em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", children: "u" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.3117em" }, children: _jsxs(_components.span, { style: { top: "-2.55em", marginLeft: "0em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mathnormal mtight", children: "i" }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.15em" }, children: _jsx(_components.span, {}) }) })] }) })] }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "∼" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1.0641em", verticalAlign: "-0.25em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.10903em" }, children: "N" }), _jsx(_components.span, { className: "mopen", children: "(" }), _jsx(_components.span, { className: "mord", children: "0" }), _jsx(_components.span, { className: "mpunct", children: "," }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.1667em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.03588em" }, children: "σ" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.8141em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: "2" }) })] }) }) }) }) })] }), _jsx(_components.span, { className: "mclose", children: ")" })] })] })] }) }), "ですので、正規分布の再生性から", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsx(_components.mrow, { children: _jsxs(_components.mover, { accent: "true", children: [_jsx(_components.mi, { mathvariant: "bold", children: "β" }), _jsx(_components.mo, { children: "^" })] }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\mathbf{\\hat\\beta}" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1.1523em", verticalAlign: "-0.1944em" } }), _jsx(_components.span, { className: "mord accent", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsxs(_components.span, { className: "vlist", style: { height: "0.9579em" }, children: [_jsxs(_components.span, { style: { top: "-3em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.05278em" }, children: "β" })] }), _jsxs(_components.span, { style: { top: "-3.2634em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "accent-body", style: { left: "-0.2042em" }, children: _jsx(_components.span, { className: "mord mathbf", children: "^" }) })] })] }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.1944em" }, children: _jsx(_components.span, {}) }) })] }) })] }) })] }) }), "は多変量正規分布に従い、", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsx(_components.mi, { children: "E" }), _jsx(_components.mo, { stretchy: "false", children: "[" }), _jsxs(_components.mover, { accent: "true", children: [_jsx(_components.mi, { mathvariant: "bold", children: "β" }), _jsx(_components.mo, { children: "^" })] }), _jsx(_components.mo, { stretchy: "false", children: "]" }), _jsx(_components.mo, { children: "=" }), _jsx(_components.mi, { mathvariant: "bold", children: "β" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "E[\\mathbf{\\hat\\beta}]=\\mathbf{\\beta}" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1.2079em", verticalAlign: "-0.25em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.05764em" }, children: "E" }), _jsx(_components.span, { className: "mopen", children: "[" }), _jsx(_components.span, { className: "mord accent", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsxs(_components.span, { className: "vlist", style: { height: "0.9579em" }, children: [_jsxs(_components.span, { style: { top: "-3em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.05278em" }, children: "β" })] }), _jsxs(_components.span, { style: { top: "-3.2634em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "accent-body", style: { left: "-0.2042em" }, children: _jsx(_components.span, { className: "mord mathbf", children: "^" }) })] })] }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.1944em" }, children: _jsx(_components.span, {}) }) })] }) }), _jsx(_components.span, { className: "mclose", children: "]" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.8889em", verticalAlign: "-0.1944em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.05278em" }, children: "β" })] })] })] }) }), "となります。"] }), "\n", _jsx(_components.p, { children: "また、分散については、以下のように計算できます。" }), "\n", _jsx(_components.p, { children: "(数式省略)" }), "\n", _jsxs(_components.p, { children: [_jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsx(_components.mrow, { children: _jsxs(_components.msup, { children: [_jsx(_components.mi, { children: "q" }), _jsxs(_components.mrow, { children: [_jsx(_components.mi, { children: "j" }), _jsx(_components.mi, { children: "j" })] })] }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "q^{jj}" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1.0191em", verticalAlign: "-0.1944em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.03588em" }, children: "q" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.8247em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.05724em" }, children: "jj" }) }) })] }) }) }) }) })] })] }) })] }) }), "は", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsx(_components.mo, { stretchy: "false", children: "(" }), _jsxs(_components.msup, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "X" }), _jsx(_components.mo, { mathvariant: "normal", lspace: "0em", rspace: "0em", children: "′" })] }), _jsx(_components.mi, { mathvariant: "bold", children: "X" }), _jsxs(_components.msup, { children: [_jsx(_components.mo, { stretchy: "false", children: ")" }), _jsxs(_components.mrow, { children: [_jsx(_components.mo, { children: "−" }), _jsx(_components.mn, { children: "1" })] })] })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "(\\mathbf X'\\mathbf X)^{-1}" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1.0641em", verticalAlign: "-0.25em" } }), _jsx(_components.span, { className: "mopen", children: "(" }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathbf", children: "X" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.7519em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord mtight", children: "′" }) }) })] }) }) }) }) })] }), _jsx(_components.span, { className: "mord mathbf", children: "X" }), _jsxs(_components.span, { className: "mclose", children: [_jsx(_components.span, { className: "mclose", children: ")" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.8141em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsxs(_components.span, { className: "mord mtight", children: [_jsx(_components.span, { className: "mord mtight", children: "−" }), _jsx(_components.span, { className: "mord mtight", children: "1" })] }) })] }) }) }) }) })] })] }) })] }) }), "の", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsx(_components.mo, { stretchy: "false", children: "(" }), _jsx(_components.mi, { children: "j" }), _jsx(_components.mo, { separator: "true", children: "," }), _jsx(_components.mi, { children: "j" }), _jsx(_components.mo, { stretchy: "false", children: ")" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "(j,j)" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1em", verticalAlign: "-0.25em" } }), _jsx(_components.span, { className: "mopen", children: "(" }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.05724em" }, children: "j" }), _jsx(_components.span, { className: "mpunct", children: "," }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.1667em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.05724em" }, children: "j" }), _jsx(_components.span, { className: "mclose", children: ")" })] }) })] }) }), "要素であるので、", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsx(_components.mi, { children: "V" }), _jsx(_components.mi, { children: "a" }), _jsx(_components.mi, { children: "r" }), _jsx(_components.mo, { stretchy: "false", children: "(" }), _jsxs(_components.mover, { accent: "true", children: [_jsx(_components.mi, { mathvariant: "bold", children: "β" }), _jsx(_components.mo, { children: "^" })] }), _jsx(_components.mo, { stretchy: "false", children: ")" }), _jsx(_components.mo, { children: "=" }), _jsxs(_components.msup, { children: [_jsx(_components.mi, { children: "σ" }), _jsx(_components.mn, { children: "2" })] }), _jsxs(_components.msup, { children: [_jsx(_components.mi, { children: "q" }), _jsxs(_components.mrow, { children: [_jsx(_components.mi, { children: "j" }), _jsx(_components.mi, { children: "j" })] })] })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "Var(\\mathbf{\\hat\\beta})=\\sigma^2q^{jj}" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1.2079em", verticalAlign: "-0.25em" } }), _jsx(_components.span, { className: "mord mathnormal", children: "Va" }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.02778em" }, children: "r" }), _jsx(_components.span, { className: "mopen", children: "(" }), _jsx(_components.span, { className: "mord accent", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsxs(_components.span, { className: "vlist", style: { height: "0.9579em" }, children: [_jsxs(_components.span, { style: { top: "-3em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.05278em" }, children: "β" })] }), _jsxs(_components.span, { style: { top: "-3.2634em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "accent-body", style: { left: "-0.2042em" }, children: _jsx(_components.span, { className: "mord mathbf", children: "^" }) })] })] }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.1944em" }, children: _jsx(_components.span, {}) }) })] }) }), _jsx(_components.span, { className: "mclose", children: ")" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1.0191em", verticalAlign: "-0.1944em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.03588em" }, children: "σ" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.8141em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: "2" }) })] }) }) }) }) })] }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.03588em" }, children: "q" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.8247em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.05724em" }, children: "jj" }) }) })] }) }) }) }) })] })] })] })] }) }), "となり、", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsxs(_components.msub, { children: [_jsxs(_components.mover, { accent: "true", children: [_jsx(_components.mi, { children: "β" }), _jsx(_components.mo, { children: "^" })] }), _jsx(_components.mi, { children: "j" })] }), _jsx(_components.mo, { children: "∼" }), _jsx(_components.mi, { children: "N" }), _jsx(_components.mo, { stretchy: "false", children: "(" }), _jsxs(_components.msub, { children: [_jsx(_components.mi, { children: "β" }), _jsx(_components.mi, { children: "j" })] }), _jsx(_components.mo, { separator: "true", children: "," }), _jsxs(_components.msup, { children: [_jsx(_components.mi, { children: "σ" }), _jsx(_components.mn, { children: "2" })] }), _jsxs(_components.msup, { children: [_jsx(_components.mi, { children: "q" }), _jsxs(_components.mrow, { children: [_jsx(_components.mi, { children: "j" }), _jsx(_components.mi, { children: "j" })] })] }), _jsx(_components.mo, { stretchy: "false", children: ")" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\hat\\beta_j\\sim N(\\beta_j,\\sigma^2 q^{jj})" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1.244em", verticalAlign: "-0.2861em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord accent", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsxs(_components.span, { className: "vlist", style: { height: "0.9579em" }, children: [_jsxs(_components.span, { style: { top: "-3em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.05278em" }, children: "β" })] }), _jsxs(_components.span, { style: { top: "-3.2634em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "accent-body", style: { left: "-0.1667em" }, children: _jsx(_components.span, { className: "mord", children: "^" }) })] })] }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.1944em" }, children: _jsx(_components.span, {}) }) })] }) }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.3117em" }, children: _jsxs(_components.span, { style: { top: "-2.55em", marginLeft: "-0.0528em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.05724em" }, children: "j" }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.2861em" }, children: _jsx(_components.span, {}) }) })] }) })] }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "∼" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1.1108em", verticalAlign: "-0.2861em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.10903em" }, children: "N" }), _jsx(_components.span, { className: "mopen", children: "(" }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.05278em" }, children: "β" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.3117em" }, children: _jsxs(_components.span, { style: { top: "-2.55em", marginLeft: "-0.0528em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.05724em" }, children: "j" }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.2861em" }, children: _jsx(_components.span, {}) }) })] }) })] }), _jsx(_components.span, { className: "mpunct", children: "," }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.1667em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.03588em" }, children: "σ" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.8141em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: "2" }) })] }) }) }) }) })] }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.03588em" }, children: "q" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.8247em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.05724em" }, children: "jj" }) }) })] }) }) }) }) })] }), _jsx(_components.span, { className: "mclose", children: ")" })] })] })] }) }), "が示されます。"] }), "\n", _jsxs(_components.h3, { children: ["2. あるべき等対称行列", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsx(_components.mrow, { children: _jsx(_components.mi, { mathvariant: "bold", children: "M" }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\mathbf M" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6861em" } }), _jsx(_components.span, { className: "mord mathbf", children: "M" })] }) })] }) }), "を用いて、", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "e" }), _jsx(_components.mo, { children: "=" }), _jsx(_components.mi, { mathvariant: "bold", children: "M" }), _jsx(_components.mi, { mathvariant: "bold", children: "u" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\mathbf e=\\mathbf M\\mathbf u" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.4444em" } }), _jsx(_components.span, { className: "mord mathbf", children: "e" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6861em" } }), _jsx(_components.span, { className: "mord mathbf", children: "Mu" })] })] })] }) }), "と表される。"] }), "\n", _jsx(_components.p, { children: "(数式省略)" }), "\n", _jsxs(_components.p, { children: ["ただし、", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "M" }), _jsx(_components.mo, { children: "=" }), _jsxs(_components.msub, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "I" }), _jsx(_components.mi, { children: "n" })] }), _jsx(_components.mo, { children: "−" }), _jsx(_components.mi, { mathvariant: "bold", children: "X" }), _jsx(_components.mo, { stretchy: "false", children: "(" }), _jsxs(_components.msup, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "X" }), _jsx(_components.mo, { mathvariant: "normal", lspace: "0em", rspace: "0em", children: "′" })] }), _jsx(_components.mi, { mathvariant: "bold", children: "X" }), _jsxs(_components.msup, { children: [_jsx(_components.mo, { stretchy: "false", children: ")" }), _jsxs(_components.mrow, { children: [_jsx(_components.mo, { children: "−" }), _jsx(_components.mn, { children: "1" })] })] }), _jsxs(_components.msup, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "X" }), _jsx(_components.mo, { mathvariant: "normal", lspace: "0em", rspace: "0em", children: "′" })] })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\mathbf M=\\mathbf I_n-\\mathbf X(\\mathbf X'\\mathbf X)^{-1}\\mathbf X'" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6861em" } }), _jsx(_components.span, { className: "mord mathbf", children: "M" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.8361em", verticalAlign: "-0.15em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathbf", children: "I" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.1514em" }, children: _jsxs(_components.span, { style: { top: "-2.55em", marginLeft: "0em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mathnormal mtight", children: "n" }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.15em" }, children: _jsx(_components.span, {}) }) })] }) })] }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "−" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1.0641em", verticalAlign: "-0.25em" } }), _jsx(_components.span, { className: "mord mathbf", children: "X" }), _jsx(_components.span, { className: "mopen", children: "(" }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathbf", children: "X" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.7519em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord mtight", children: "′" }) }) })] }) }) }) }) })] }), _jsx(_components.span, { className: "mord mathbf", children: "X" }), _jsxs(_components.span, { className: "mclose", children: [_jsx(_components.span, { className: "mclose", children: ")" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.8141em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsxs(_components.span, { className: "mord mtight", children: [_jsx(_components.span, { className: "mord mtight", children: "−" }), _jsx(_components.span, { className: "mord mtight", children: "1" })] }) })] }) }) }) }) })] }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathbf", children: "X" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.7519em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord mtight", children: "′" }) }) })] }) }) }) }) })] })] })] })] }) }), "とします。"] }), "\n", _jsxs(_components.p, { children: ["これは、計算すると", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "M" }), _jsx(_components.mo, { children: "=" }), _jsxs(_components.msup, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "M" }), _jsx(_components.mo, { mathvariant: "normal", lspace: "0em", rspace: "0em", children: "′" })] })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\mathbf M=\\mathbf M'" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6861em" } }), _jsx(_components.span, { className: "mord mathbf", children: "M" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.7519em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathbf", children: "M" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.7519em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord mtight", children: "′" }) }) })] }) }) }) }) })] })] })] })] }) }), "、", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsxs(_components.msup, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "M" }), _jsx(_components.mn, { children: "2" })] }), _jsx(_components.mo, { children: "=" }), _jsx(_components.mi, { mathvariant: "bold", children: "M" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\mathbf M^2=\\mathbf M" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.8141em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathbf", children: "M" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.8141em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: "2" }) })] }) }) }) }) })] }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6861em" } }), _jsx(_components.span, { className: "mord mathbf", children: "M" })] })] })] }) }), "を示すことができ、べき等行列です。"] }), "\n", _jsxs(_components.p, { children: ["さらに、", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "M" }), _jsx(_components.mi, { mathvariant: "bold", children: "X" }), _jsx(_components.mo, { children: "=" }), _jsx(_components.mn, { children: "0" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\mathbf M\\mathbf X=0" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6861em" } }), _jsx(_components.span, { className: "mord mathbf", children: "MX" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6444em" } }), _jsx(_components.span, { className: "mord", children: "0" })] })] })] }) }), "を満たすので、以下の式が成り立ちます。"] }), "\n", _jsx(_components.p, { children: _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "e" }), _jsx(_components.mo, { children: "=" }), _jsx(_components.mi, { mathvariant: "bold", children: "M" }), _jsx(_components.mi, { mathvariant: "bold", children: "y" }), _jsx(_components.mo, { children: "=" }), _jsx(_components.mi, { mathvariant: "bold", children: "M" }), _jsx(_components.mo, { stretchy: "false", children: "(" }), _jsx(_components.mi, { mathvariant: "bold", children: "X" }), _jsx(_components.mi, { mathvariant: "bold", children: "β" }), _jsx(_components.mo, { children: "+" }), _jsx(_components.mi, { mathvariant: "bold", children: "u" }), _jsx(_components.mo, { stretchy: "false", children: ")" }), _jsx(_components.mo, { children: "=" }), _jsx(_components.mi, { mathvariant: "bold", children: "M" }), _jsx(_components.mi, { mathvariant: "bold", children: "u" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\mathbf e=\\mathbf M\\mathbf y=\\mathbf M(\\mathbf X\\mathbf{\\beta}+\\mathbf u)=\\mathbf M\\mathbf u" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.4444em" } }), _jsx(_components.span, { className: "mord mathbf", children: "e" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.8805em", verticalAlign: "-0.1944em" } }), _jsx(_components.span, { className: "mord mathbf", style: { marginRight: "0.01597em" }, children: "My" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1em", verticalAlign: "-0.25em" } }), _jsx(_components.span, { className: "mord mathbf", children: "M" }), _jsx(_components.span, { className: "mopen", children: "(" }), _jsx(_components.span, { className: "mord mathbf", children: "X" }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.05278em" }, children: "β" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "+" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1em", verticalAlign: "-0.25em" } }), _jsx(_components.span, { className: "mord mathbf", children: "u" }), _jsx(_components.span, { className: "mclose", children: ")" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6861em" } }), _jsx(_components.span, { className: "mord mathbf", children: "Mu" })] })] })] }) }) }), "\n", _jsxs(_components.h3, { children: ["3. ", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsxs(_components.msup, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "e" }), _jsx(_components.mo, { mathvariant: "normal", lspace: "0em", rspace: "0em", children: "′" })] }), _jsx(_components.mi, { mathvariant: "bold", children: "e" }), _jsx(_components.mo, { children: "=" }), _jsxs(_components.msup, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "u" }), _jsx(_components.mo, { mathvariant: "normal", lspace: "0em", rspace: "0em", children: "′" })] }), _jsx(_components.mi, { mathvariant: "bold", children: "M" }), _jsx(_components.mi, { mathvariant: "bold", children: "u" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\mathbf e'\\mathbf e=\\mathbf u'\\mathbf M\\mathbf u" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.7519em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathbf", children: "e" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.7519em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord mtight", children: "′" }) }) })] }) }) }) }) })] }), _jsx(_components.span, { className: "mord mathbf", children: "e" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.7519em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathbf", children: "u" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.7519em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord mtight", children: "′" }) }) })] }) }) }) }) })] }), _jsx(_components.span, { className: "mord mathbf", children: "Mu" })] })] })] }) })] }), "\n", _jsx(_components.p, { children: "上記から、以下の式が成り立ちます。" }), "\n", _jsx(_components.p, { children: _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsxs(_components.msup, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "e" }), _jsx(_components.mo, { mathvariant: "normal", lspace: "0em", rspace: "0em", children: "′" })] }), _jsx(_components.mi, { mathvariant: "bold", children: "e" }), _jsx(_components.mo, { children: "=" }), _jsx(_components.mo, { stretchy: "false", children: "(" }), _jsx(_components.mi, { mathvariant: "bold", children: "M" }), _jsx(_components.mi, { mathvariant: "bold", children: "u" }), _jsxs(_components.msup, { children: [_jsx(_components.mo, { stretchy: "false", children: ")" }), _jsx(_components.mo, { mathvariant: "normal", lspace: "0em", rspace: "0em", children: "′" })] }), _jsx(_components.mo, { stretchy: "false", children: "(" }), _jsx(_components.mi, { mathvariant: "bold", children: "M" }), _jsx(_components.mi, { mathvariant: "bold", children: "u" }), _jsx(_components.mo, { stretchy: "false", children: ")" }), _jsx(_components.mo, { children: "=" }), _jsxs(_components.msup, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "u" }), _jsx(_components.mo, { mathvariant: "normal", lspace: "0em", rspace: "0em", children: "′" })] }), _jsxs(_components.msup, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "M" }), _jsx(_components.mn, { children: "2" })] }), _jsx(_components.mi, { mathvariant: "bold", children: "u" }), _jsx(_components.mo, { children: "=" }), _jsxs(_components.msup, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "u" }), _jsx(_components.mo, { mathvariant: "normal", lspace: "0em", rspace: "0em", children: "′" })] }), _jsx(_components.mi, { mathvariant: "bold", children: "M" }), _jsx(_components.mi, { mathvariant: "bold", children: "u" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\mathbf e'\\mathbf e=(\\mathbf M\\mathbf u)'(\\mathbf M\\mathbf u)=\\mathbf u'\\mathbf M^2\\mathbf u=\\mathbf u'\\mathbf M\\mathbf u" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.7519em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathbf", children: "e" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.7519em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord mtight", children: "′" }) }) })] }) }) }) }) })] }), _jsx(_components.span, { className: "mord mathbf", children: "e" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1.0019em", verticalAlign: "-0.25em" } }), _jsx(_components.span, { className: "mopen", children: "(" }), _jsx(_components.span, { className: "mord mathbf", children: "Mu" }), _jsxs(_components.span, { className: "mclose", children: [_jsx(_components.span, { className: "mclose", children: ")" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.7519em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord mtight", children: "′" }) }) })] }) }) }) }) })] }), _jsx(_components.span, { className: "mopen", children: "(" }), _jsx(_components.span, { className: "mord mathbf", children: "Mu" }), _jsx(_components.span, { className: "mclose", children: ")" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.8141em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathbf", children: "u" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.7519em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord mtight", children: "′" }) }) })] }) }) }) }) })] }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathbf", children: "M" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.8141em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: "2" }) })] }) }) }) }) })] }), _jsx(_components.span, { className: "mord mathbf", children: "u" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.7519em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathbf", children: "u" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.7519em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord mtight", children: "′" }) }) })] }) }) }) }) })] }), _jsx(_components.span, { className: "mord mathbf", children: "Mu" })] })] })] }) }) }), "\n", _jsxs(_components.h3, { children: ["4. ", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsxs(_components.msup, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "P" }), _jsx(_components.mo, { mathvariant: "normal", lspace: "0em", rspace: "0em", children: "′" })] }), _jsx(_components.mi, { mathvariant: "bold", children: "M" }), _jsx(_components.mi, { mathvariant: "bold", children: "P" }), _jsx(_components.mo, { children: "=" }), _jsxs(_components.msub, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "I" }), _jsxs(_components.mrow, { children: [_jsx(_components.mi, { children: "n" }), _jsx(_components.mo, { separator: "true", children: "," }), _jsx(_components.mi, { children: "n" }), _jsx(_components.mo, { children: "−" }), _jsx(_components.mi, { children: "k" })] })] })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\mathbf P'\\mathbf M\\mathbf P=\\mathbf I_{n,n-k}" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.7519em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathbf", children: "P" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.7519em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord mtight", children: "′" }) }) })] }) }) }) }) })] }), _jsx(_components.span, { className: "mord mathbf", children: "MP" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.9722em", verticalAlign: "-0.2861em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathbf", children: "I" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.3361em" }, children: _jsxs(_components.span, { style: { top: "-2.55em", marginLeft: "0em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsxs(_components.span, { className: "mord mtight", children: [_jsx(_components.span, { className: "mord mathnormal mtight", children: "n" }), _jsx(_components.span, { className: "mpunct mtight", children: "," }), _jsx(_components.span, { className: "mord mathnormal mtight", children: "n" }), _jsx(_components.span, { className: "mbin mtight", children: "−" }), _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.03148em" }, children: "k" })] }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.2861em" }, children: _jsx(_components.span, {}) }) })] }) })] })] })] })] }) }), "となる直交行列", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsx(_components.mrow, { children: _jsx(_components.mi, { mathvariant: "bold", children: "P" }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\mathbf P" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6861em" } }), _jsx(_components.span, { className: "mord mathbf", children: "P" })] }) })] }) }), "が存在すること"] }), "\n", _jsxs(_components.p, { children: [_jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsx(_components.mrow, { children: _jsx(_components.mi, { mathvariant: "bold", children: "M" }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\mathbf M" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6861em" } }), _jsx(_components.span, { className: "mord mathbf", children: "M" })] }) })] }) }), "は対称行列より対角化可能です。すなわち、", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsxs(_components.msup, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "P" }), _jsx(_components.mo, { mathvariant: "normal", lspace: "0em", rspace: "0em", children: "′" })] }), _jsx(_components.mi, { mathvariant: "bold", children: "M" }), _jsx(_components.mi, { mathvariant: "bold", children: "P" }), _jsx(_components.mo, { children: "=" }), _jsx(_components.mi, { children: "d" }), _jsx(_components.mi, { children: "i" }), _jsx(_components.mi, { children: "a" }), _jsx(_components.mi, { children: "g" }), _jsx(_components.mo, { stretchy: "false", children: "(" }), _jsxs(_components.msub, { children: [_jsx(_components.mi, { children: "λ" }), _jsx(_components.mn, { children: "1" })] }), _jsx(_components.mo, { separator: "true", children: "," }), _jsxs(_components.msub, { children: [_jsx(_components.mi, { children: "λ" }), _jsx(_components.mn, { children: "2" })] }), _jsx(_components.mo, { separator: "true", children: "," }), _jsx(_components.mo, { children: "⋯" }), _jsx(_components.mtext, { children: " " }), _jsx(_components.mo, { separator: "true", children: "," }), _jsxs(_components.msub, { children: [_jsx(_components.mi, { children: "λ" }), _jsx(_components.mi, { children: "n" })] }), _jsx(_components.mo, { stretchy: "false", children: ")" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\mathbf P'\\mathbf M\\mathbf P=diag(\\lambda_1,\\lambda_2,\\cdots,\\lambda_n)" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.7519em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathbf", children: "P" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.7519em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord mtight", children: "′" }) }) })] }) }) }) }) })] }), _jsx(_components.span, { className: "mord mathbf", children: "MP" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1em", verticalAlign: "-0.25em" } }), _jsx(_components.span, { className: "mord mathnormal", children: "d" }), _jsx(_components.span, { className: "mord mathnormal", children: "ia" }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.03588em" }, children: "g" }), _jsx(_components.span, { className: "mopen", children: "(" }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", children: "λ" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.3011em" }, children: _jsxs(_components.span, { style: { top: "-2.55em", marginLeft: "0em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: "1" }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.15em" }, children: _jsx(_components.span, {}) }) })] }) })] }), _jsx(_components.span, { className: "mpunct", children: "," }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.1667em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", children: "λ" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.3011em" }, children: _jsxs(_components.span, { style: { top: "-2.55em", marginLeft: "0em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: "2" }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.15em" }, children: _jsx(_components.span, {}) }) })] }) })] }), _jsx(_components.span, { className: "mpunct", children: "," }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.1667em" } }), _jsx(_components.span, { className: "minner", children: "⋯" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.1667em" } }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.1667em" } }), _jsx(_components.span, { className: "mpunct", children: "," }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.1667em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", children: "λ" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.1514em" }, children: _jsxs(_components.span, { style: { top: "-2.55em", marginLeft: "0em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mathnormal mtight", children: "n" }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.15em" }, children: _jsx(_components.span, {}) }) })] }) })] }), _jsx(_components.span, { className: "mclose", children: ")" })] })] })] }) }), "となる直交行列", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsx(_components.mrow, { children: _jsx(_components.mi, { mathvariant: "bold", children: "P" }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\mathbf P" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6861em" } }), _jsx(_components.span, { className: "mord mathbf", children: "P" })] }) })] }) }), "が存在します。"] }), "\n", _jsxs(_components.p, { children: ["また、", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "M" }), _jsxs(_components.msub, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "p" }), _jsx(_components.mi, { children: "i" })] }), _jsx(_components.mo, { children: "=" }), _jsxs(_components.msub, { children: [_jsx(_components.mi, { children: "λ" }), _jsx(_components.mi, { children: "i" })] }), _jsxs(_components.msub, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "p" }), _jsx(_components.mi, { children: "i" })] })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\mathbf M\\mathbf p_i=\\lambda_i\\mathbf p_i" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.8805em", verticalAlign: "-0.1944em" } }), _jsx(_components.span, { className: "mord mathbf", children: "M" }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathbf", children: "p" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.3117em" }, children: _jsxs(_components.span, { style: { top: "-2.55em", marginLeft: "0em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mathnormal mtight", children: "i" }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.15em" }, children: _jsx(_components.span, {}) }) })] }) })] }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.8889em", verticalAlign: "-0.1944em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", children: "λ" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.3117em" }, children: _jsxs(_components.span, { style: { top: "-2.55em", marginLeft: "0em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mathnormal mtight", children: "i" }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.15em" }, children: _jsx(_components.span, {}) }) })] }) })] }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathbf", children: "p" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.3117em" }, children: _jsxs(_components.span, { style: { top: "-2.55em", marginLeft: "0em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mathnormal mtight", children: "i" }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.15em" }, children: _jsx(_components.span, {}) }) })] }) })] })] })] })] }) }), "となる", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsx(_components.mrow, { children: _jsxs(_components.msub, { children: [_jsx(_components.mi, { children: "λ" }), _jsx(_components.mi, { children: "i" })] }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\lambda_i" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.8444em", verticalAlign: "-0.15em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", children: "λ" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.3117em" }, children: _jsxs(_components.span, { style: { top: "-2.55em", marginLeft: "0em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mathnormal mtight", children: "i" }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.15em" }, children: _jsx(_components.span, {}) }) })] }) })] })] }) })] }) }), "は、", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsxs(_components.msup, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "M" }), _jsx(_components.mn, { children: "2" })] }), _jsx(_components.mo, { children: "=" }), _jsx(_components.mi, { mathvariant: "bold", children: "M" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\mathbf M^2=\\mathbf M" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.8141em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathbf", children: "M" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.8141em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: "2" }) })] }) }) }) }) })] }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6861em" } }), _jsx(_components.span, { className: "mord mathbf", children: "M" })] })] })] }) }), "から", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsxs(_components.msubsup, { children: [_jsx(_components.mi, { children: "λ" }), _jsx(_components.mi, { children: "i" }), _jsx(_components.mn, { children: "2" })] }), _jsx(_components.mo, { children: "=" }), _jsxs(_components.msub, { children: [_jsx(_components.mi, { children: "λ" }), _jsx(_components.mi, { children: "i" })] })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\lambda_i^2=\\lambda_i" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1.0728em", verticalAlign: "-0.2587em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", children: "λ" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsxs(_components.span, { className: "vlist", style: { height: "0.8141em" }, children: [_jsxs(_components.span, { style: { top: "-2.4413em", marginLeft: "0em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mathnormal mtight", children: "i" }) })] }), _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: "2" }) })] })] }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.2587em" }, children: _jsx(_components.span, {}) }) })] }) })] }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.8444em", verticalAlign: "-0.15em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", children: "λ" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.3117em" }, children: _jsxs(_components.span, { style: { top: "-2.55em", marginLeft: "0em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mathnormal mtight", children: "i" }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.15em" }, children: _jsx(_components.span, {}) }) })] }) })] })] })] })] }) }), "を満たします。すなわち、", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsx(_components.mrow, { children: _jsxs(_components.msub, { children: [_jsx(_components.mi, { children: "λ" }), _jsx(_components.mi, { children: "i" })] }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\lambda_i" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.8444em", verticalAlign: "-0.15em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", children: "λ" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.3117em" }, children: _jsxs(_components.span, { style: { top: "-2.55em", marginLeft: "0em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mathnormal mtight", children: "i" }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.15em" }, children: _jsx(_components.span, {}) }) })] }) })] })] }) })] }) }), "は0または1です。"] }), "\n", _jsxs(_components.p, { children: ["また、1の個数を", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsx(_components.mrow, { children: _jsx(_components.mi, { children: "r" }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "r" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.4306em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.02778em" }, children: "r" })] }) })] }) }), "とおくと、", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsxs(_components.msup, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "P" }), _jsx(_components.mo, { mathvariant: "normal", lspace: "0em", rspace: "0em", children: "′" })] }), _jsx(_components.mi, { mathvariant: "bold", children: "M" }), _jsx(_components.mi, { mathvariant: "bold", children: "P" }), _jsx(_components.mo, { children: "=" }), _jsxs(_components.msub, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "I" }), _jsxs(_components.mrow, { children: [_jsx(_components.mi, { children: "n" }), _jsx(_components.mo, { separator: "true", children: "," }), _jsx(_components.mi, { children: "r" })] })] })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\mathbf P'\\mathbf M\\mathbf P=\\mathbf I_{n,r}" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.7519em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathbf", children: "P" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.7519em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord mtight", children: "′" }) }) })] }) }) }) }) })] }), _jsx(_components.span, { className: "mord mathbf", children: "MP" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.9722em", verticalAlign: "-0.2861em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathbf", children: "I" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.1514em" }, children: _jsxs(_components.span, { style: { top: "-2.55em", marginLeft: "0em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsxs(_components.span, { className: "mord mtight", children: [_jsx(_components.span, { className: "mord mathnormal mtight", children: "n" }), _jsx(_components.span, { className: "mpunct mtight", children: "," }), _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.02778em" }, children: "r" })] }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.2861em" }, children: _jsx(_components.span, {}) }) })] }) })] })] })] })] }) }), "であり、"] }), "\n", _jsx(_components.p, { children: "(数式省略)" }), "\n", _jsxs(_components.p, { children: ["となります。したがって、", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsxs(_components.msup, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "P" }), _jsx(_components.mo, { mathvariant: "normal", lspace: "0em", rspace: "0em", children: "′" })] }), _jsx(_components.mi, { mathvariant: "bold", children: "M" }), _jsx(_components.mi, { mathvariant: "bold", children: "P" }), _jsx(_components.mo, { children: "=" }), _jsxs(_components.msub, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "I" }), _jsxs(_components.mrow, { children: [_jsx(_components.mi, { children: "n" }), _jsx(_components.mo, { separator: "true", children: "," }), _jsx(_components.mi, { children: "n" }), _jsx(_components.mo, { children: "−" }), _jsx(_components.mi, { children: "k" })] })] })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\mathbf P'\\mathbf M\\mathbf P=\\mathbf I_{n,n-k}" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.7519em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathbf", children: "P" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.7519em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord mtight", children: "′" }) }) })] }) }) }) }) })] }), _jsx(_components.span, { className: "mord mathbf", children: "MP" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.9722em", verticalAlign: "-0.2861em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathbf", children: "I" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.3361em" }, children: _jsxs(_components.span, { style: { top: "-2.55em", marginLeft: "0em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsxs(_components.span, { className: "mord mtight", children: [_jsx(_components.span, { className: "mord mathnormal mtight", children: "n" }), _jsx(_components.span, { className: "mpunct mtight", children: "," }), _jsx(_components.span, { className: "mord mathnormal mtight", children: "n" }), _jsx(_components.span, { className: "mbin mtight", children: "−" }), _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.03148em" }, children: "k" })] }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.2861em" }, children: _jsx(_components.span, {}) }) })] }) })] })] })] })] }) }), "となる直交行列", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsx(_components.mrow, { children: _jsx(_components.mi, { mathvariant: "bold", children: "P" }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\mathbf P" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6861em" } }), _jsx(_components.span, { className: "mord mathbf", children: "P" })] }) })] }) }), "が存在します。"] }), "\n", _jsxs(_components.h3, { children: ["5. ", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsxs(_components.mfrac, { children: [_jsxs(_components.mrow, { children: [_jsxs(_components.msup, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "u" }), _jsx(_components.mo, { mathvariant: "normal", lspace: "0em", rspace: "0em", children: "′" })] }), _jsx(_components.mi, { mathvariant: "bold", children: "M" }), _jsx(_components.mi, { mathvariant: "bold", children: "u" })] }), _jsxs(_components.msup, { children: [_jsx(_components.mi, { children: "σ" }), _jsx(_components.mn, { children: "2" })] })] }), _jsx(_components.mo, { children: "∼" }), _jsxs(_components.msup, { children: [_jsx(_components.mi, { children: "χ" }), _jsx(_components.mn, { children: "2" })] }), _jsx(_components.mo, { stretchy: "false", children: "(" }), _jsx(_components.mi, { children: "n" }), _jsx(_components.mo, { children: "−" }), _jsx(_components.mi, { children: "k" }), _jsx(_components.mo, { stretchy: "false", children: ")" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\frac{\\mathbf u'\\mathbf M\\mathbf u}{\\sigma^2} \\sim \\chi^2(n-k)" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1.3185em", verticalAlign: "-0.345em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mopen nulldelimiter" }), _jsx(_components.span, { className: "mfrac", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsxs(_components.span, { className: "vlist", style: { height: "0.9735em" }, children: [_jsxs(_components.span, { style: { top: "-2.655em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsxs(_components.span, { className: "mord mtight", children: [_jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.03588em" }, children: "σ" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.7463em" }, children: _jsxs(_components.span, { style: { top: "-2.786em", marginRight: "0.0714em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.5em" } }), _jsx(_components.span, { className: "sizing reset-size3 size1 mtight", children: _jsx(_components.span, { className: "mord mtight", children: "2" }) })] }) }) }) }) })] }) }) })] }), _jsxs(_components.span, { style: { top: "-3.23em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "frac-line", style: { borderBottomWidth: "0.04em" } })] }), _jsxs(_components.span, { style: { top: "-3.394em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsxs(_components.span, { className: "mord mtight", children: [_jsxs(_components.span, { className: "mord mtight", children: [_jsx(_components.span, { className: "mord mathbf mtight", children: "u" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.8278em" }, children: _jsxs(_components.span, { style: { top: "-2.931em", marginRight: "0.0714em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.5em" } }), _jsx(_components.span, { className: "sizing reset-size3 size1 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord mtight", children: "′" }) }) })] }) }) }) }) })] }), _jsx(_components.span, { className: "mord mathbf mtight", children: "Mu" })] }) })] })] }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.345em" }, children: _jsx(_components.span, {}) }) })] }) }), _jsx(_components.span, { className: "mclose nulldelimiter" })] }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "∼" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1.0641em", verticalAlign: "-0.25em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", children: "χ" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.8141em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: "2" }) })] }) }) }) }) })] }), _jsx(_components.span, { className: "mopen", children: "(" }), _jsx(_components.span, { className: "mord mathnormal", children: "n" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "−" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1em", verticalAlign: "-0.25em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.03148em" }, children: "k" }), _jsx(_components.span, { className: "mclose", children: ")" })] })] })] }) })] }), "\n", _jsxs(_components.p, { children: ["上記の", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsx(_components.mrow, { children: _jsx(_components.mi, { mathvariant: "bold", children: "P" }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\mathbf P" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6861em" } }), _jsx(_components.span, { className: "mord mathbf", children: "P" })] }) })] }) }), "を用いて、", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "z" }), _jsx(_components.mo, { children: "=" }), _jsxs(_components.mfrac, { children: [_jsx(_components.mn, { children: "1" }), _jsx(_components.mi, { children: "σ" })] }), _jsxs(_components.msup, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "P" }), _jsx(_components.mo, { mathvariant: "normal", lspace: "0em", rspace: "0em", children: "′" })] }), _jsx(_components.mi, { mathvariant: "bold", children: "u" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\mathbf z=\\frac{1}{\\sigma}\\mathbf P'\\mathbf u" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.4444em" } }), _jsx(_components.span, { className: "mord mathbf", children: "z" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1.1901em", verticalAlign: "-0.345em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mopen nulldelimiter" }), _jsx(_components.span, { className: "mfrac", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsxs(_components.span, { className: "vlist", style: { height: "0.8451em" }, children: [_jsxs(_components.span, { style: { top: "-2.655em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.03588em" }, children: "σ" }) }) })] }), _jsxs(_components.span, { style: { top: "-3.23em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "frac-line", style: { borderBottomWidth: "0.04em" } })] }), _jsxs(_components.span, { style: { top: "-3.394em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord mtight", children: "1" }) }) })] })] }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.345em" }, children: _jsx(_components.span, {}) }) })] }) }), _jsx(_components.span, { className: "mclose nulldelimiter" })] }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathbf", children: "P" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.7519em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord mtight", children: "′" }) }) })] }) }) }) }) })] }), _jsx(_components.span, { className: "mord mathbf", children: "u" })] })] })] }) }), "となる", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsx(_components.mrow, { children: _jsx(_components.mi, { mathvariant: "bold", children: "z" }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\mathbf z" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.4444em" } }), _jsx(_components.span, { className: "mord mathbf", children: "z" })] }) })] }) }), "を定義します。"] }), "\n", _jsxs(_components.p, { children: [_jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsxs(_components.msub, { children: [_jsx(_components.mi, { children: "u" }), _jsx(_components.mi, { children: "i" })] }), _jsx(_components.mo, { children: "∼" }), _jsx(_components.mi, { children: "N" }), _jsx(_components.mo, { stretchy: "false", children: "(" }), _jsx(_components.mn, { children: "0" }), _jsx(_components.mo, { separator: "true", children: "," }), _jsx(_components.mi, { children: "σ" }), _jsx(_components.mo, { stretchy: "false", children: ")" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "u_i\\sim N(0,\\sigma)" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.5806em", verticalAlign: "-0.15em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", children: "u" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.3117em" }, children: _jsxs(_components.span, { style: { top: "-2.55em", marginLeft: "0em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mathnormal mtight", children: "i" }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.15em" }, children: _jsx(_components.span, {}) }) })] }) })] }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "∼" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1em", verticalAlign: "-0.25em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.10903em" }, children: "N" }), _jsx(_components.span, { className: "mopen", children: "(" }), _jsx(_components.span, { className: "mord", children: "0" }), _jsx(_components.span, { className: "mpunct", children: "," }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.1667em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.03588em" }, children: "σ" }), _jsx(_components.span, { className: "mclose", children: ")" })] })] })] }) }), "かつi.i.dから", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsx(_components.mrow, { children: _jsxs(_components.msub, { children: [_jsx(_components.mi, { children: "z" }), _jsx(_components.mi, { children: "i" })] }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "z_i" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.5806em", verticalAlign: "-0.15em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.04398em" }, children: "z" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.3117em" }, children: _jsxs(_components.span, { style: { top: "-2.55em", marginLeft: "-0.044em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mathnormal mtight", children: "i" }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.15em" }, children: _jsx(_components.span, {}) }) })] }) })] })] }) })] }) }), "は正規分布に従い、平均は0です。"] }), "\n", _jsxs(_components.p, { children: ["さらに、", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsx(_components.mi, { children: "V" }), _jsx(_components.mi, { children: "a" }), _jsx(_components.mi, { children: "r" }), _jsx(_components.mo, { stretchy: "false", children: "(" }), _jsx(_components.mi, { mathvariant: "bold", children: "z" }), _jsx(_components.mo, { stretchy: "false", children: ")" }), _jsx(_components.mo, { children: "=" }), _jsxs(_components.mfrac, { children: [_jsx(_components.mn, { children: "1" }), _jsxs(_components.msup, { children: [_jsx(_components.mi, { children: "σ" }), _jsx(_components.mn, { children: "2" })] })] }), _jsx(_components.mi, { children: "V" }), _jsx(_components.mi, { children: "a" }), _jsx(_components.mi, { children: "r" }), _jsx(_components.mo, { stretchy: "false", children: "(" }), _jsxs(_components.msup, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "P" }), _jsx(_components.mo, { mathvariant: "normal", lspace: "0em", rspace: "0em", children: "′" })] }), _jsx(_components.mi, { mathvariant: "bold", children: "u" }), _jsx(_components.mo, { stretchy: "false", children: ")" }), _jsx(_components.mo, { children: "=" }), _jsxs(_components.mfrac, { children: [_jsx(_components.mn, { children: "1" }), _jsxs(_components.msup, { children: [_jsx(_components.mi, { children: "σ" }), _jsx(_components.mn, { children: "2" })] })] }), _jsxs(_components.msup, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "P" }), _jsx(_components.mo, { mathvariant: "normal", lspace: "0em", rspace: "0em", children: "′" })] }), _jsx(_components.mo, { stretchy: "false", children: "(" }), _jsxs(_components.msup, { children: [_jsx(_components.mi, { children: "σ" }), _jsx(_components.mn, { children: "2" })] }), _jsxs(_components.msub, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "I" }), _jsx(_components.mi, { children: "n" })] }), _jsx(_components.mo, { stretchy: "false", children: ")" }), _jsx(_components.mi, { children: "P" }), _jsx(_components.mo, { children: "=" }), _jsxs(_components.msub, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "I" }), _jsx(_components.mi, { children: "n" })] })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "Var(\\mathbf z)=\\frac{1}{\\sigma^2}Var(\\mathbf P'\\mathbf u)=\\frac{1}{\\sigma^2}\\mathbf P'(\\sigma^2\\mathbf I_n)P=\\mathbf I_n" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1em", verticalAlign: "-0.25em" } }), _jsx(_components.span, { className: "mord mathnormal", children: "Va" }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.02778em" }, children: "r" }), _jsx(_components.span, { className: "mopen", children: "(" }), _jsx(_components.span, { className: "mord mathbf", children: "z" }), _jsx(_components.span, { className: "mclose", children: ")" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1.1901em", verticalAlign: "-0.345em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mopen nulldelimiter" }), _jsx(_components.span, { className: "mfrac", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsxs(_components.span, { className: "vlist", style: { height: "0.8451em" }, children: [_jsxs(_components.span, { style: { top: "-2.655em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsxs(_components.span, { className: "mord mtight", children: [_jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.03588em" }, children: "σ" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.7463em" }, children: _jsxs(_components.span, { style: { top: "-2.786em", marginRight: "0.0714em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.5em" } }), _jsx(_components.span, { className: "sizing reset-size3 size1 mtight", children: _jsx(_components.span, { className: "mord mtight", children: "2" }) })] }) }) }) }) })] }) }) })] }), _jsxs(_components.span, { style: { top: "-3.23em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "frac-line", style: { borderBottomWidth: "0.04em" } })] }), _jsxs(_components.span, { style: { top: "-3.394em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord mtight", children: "1" }) }) })] })] }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.345em" }, children: _jsx(_components.span, {}) }) })] }) }), _jsx(_components.span, { className: "mclose nulldelimiter" })] }), _jsx(_components.span, { className: "mord mathnormal", children: "Va" }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.02778em" }, children: "r" }), _jsx(_components.span, { className: "mopen", children: "(" }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathbf", children: "P" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.7519em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord mtight", children: "′" }) }) })] }) }) }) }) })] }), _jsx(_components.span, { className: "mord mathbf", children: "u" }), _jsx(_components.span, { className: "mclose", children: ")" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1.1901em", verticalAlign: "-0.345em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mopen nulldelimiter" }), _jsx(_components.span, { className: "mfrac", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsxs(_components.span, { className: "vlist", style: { height: "0.8451em" }, children: [_jsxs(_components.span, { style: { top: "-2.655em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsxs(_components.span, { className: "mord mtight", children: [_jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.03588em" }, children: "σ" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.7463em" }, children: _jsxs(_components.span, { style: { top: "-2.786em", marginRight: "0.0714em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.5em" } }), _jsx(_components.span, { className: "sizing reset-size3 size1 mtight", children: _jsx(_components.span, { className: "mord mtight", children: "2" }) })] }) }) }) }) })] }) }) })] }), _jsxs(_components.span, { style: { top: "-3.23em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "frac-line", style: { borderBottomWidth: "0.04em" } })] }), _jsxs(_components.span, { style: { top: "-3.394em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord mtight", children: "1" }) }) })] })] }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.345em" }, children: _jsx(_components.span, {}) }) })] }) }), _jsx(_components.span, { className: "mclose nulldelimiter" })] }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathbf", children: "P" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.7519em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord mtight", children: "′" }) }) })] }) }) }) }) })] }), _jsx(_components.span, { className: "mopen", children: "(" }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.03588em" }, children: "σ" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.8141em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: "2" }) })] }) }) }) }) })] }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathbf", children: "I" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.1514em" }, children: _jsxs(_components.span, { style: { top: "-2.55em", marginLeft: "0em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mathnormal mtight", children: "n" }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.15em" }, children: _jsx(_components.span, {}) }) })] }) })] }), _jsx(_components.span, { className: "mclose", children: ")" }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.13889em" }, children: "P" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.8361em", verticalAlign: "-0.15em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathbf", children: "I" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.1514em" }, children: _jsxs(_components.span, { style: { top: "-2.55em", marginLeft: "0em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mathnormal mtight", children: "n" }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.15em" }, children: _jsx(_components.span, {}) }) })] }) })] })] })] })] }) }), "(", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsx(_components.mrow, { children: _jsx(_components.mi, { mathvariant: "bold", children: "P" }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\mathbf P" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6861em" } }), _jsx(_components.span, { className: "mord mathbf", children: "P" })] }) })] }) }), "は直交行列より)となるので、", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsxs(_components.msub, { children: [_jsx(_components.mi, { children: "z" }), _jsx(_components.mi, { children: "i" })] }), _jsx(_components.mo, { children: "∼" }), _jsx(_components.mi, { children: "N" }), _jsx(_components.mo, { stretchy: "false", children: "(" }), _jsx(_components.mn, { children: "0" }), _jsx(_components.mo, { separator: "true", children: "," }), _jsx(_components.mn, { children: "1" }), _jsx(_components.mo, { stretchy: "false", children: ")" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "z_i\\sim N(0,1)" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.5806em", verticalAlign: "-0.15em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.04398em" }, children: "z" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.3117em" }, children: _jsxs(_components.span, { style: { top: "-2.55em", marginLeft: "-0.044em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mathnormal mtight", children: "i" }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.15em" }, children: _jsx(_components.span, {}) }) })] }) })] }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "∼" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1em", verticalAlign: "-0.25em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.10903em" }, children: "N" }), _jsx(_components.span, { className: "mopen", children: "(" }), _jsx(_components.span, { className: "mord", children: "0" }), _jsx(_components.span, { className: "mpunct", children: "," }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.1667em" } }), _jsx(_components.span, { className: "mord", children: "1" }), _jsx(_components.span, { className: "mclose", children: ")" })] })] })] }) }), "かつi.i.dです。"] }), "\n", _jsxs(_components.p, { children: ["したがって、", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "u" }), _jsx(_components.mo, { children: "=" }), _jsx(_components.mi, { children: "σ" }), _jsx(_components.mi, { mathvariant: "bold", children: "P" }), _jsx(_components.mi, { mathvariant: "bold", children: "z" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\mathbf u=\\sigma \\mathbf P\\mathbf z" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.4444em" } }), _jsx(_components.span, { className: "mord mathbf", children: "u" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6861em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.03588em" }, children: "σ" }), _jsx(_components.span, { className: "mord mathbf", children: "Pz" })] })] })] }) }), " より以下が成り立ちます。"] }), "\n", _jsx(_components.p, { children: _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsxs(_components.mfrac, { children: [_jsx(_components.mn, { children: "1" }), _jsxs(_components.msup, { children: [_jsx(_components.mi, { children: "σ" }), _jsx(_components.mn, { children: "2" })] })] }), _jsxs(_components.msup, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "u" }), _jsx(_components.mo, { mathvariant: "normal", lspace: "0em", rspace: "0em", children: "′" })] }), _jsx(_components.mi, { mathvariant: "bold", children: "M" }), _jsx(_components.mi, { mathvariant: "bold", children: "u" }), _jsx(_components.mo, { children: "=" }), _jsx(_components.mo, { stretchy: "false", children: "(" }), _jsx(_components.mi, { mathvariant: "bold", children: "P" }), _jsx(_components.mi, { mathvariant: "bold", children: "z" }), _jsxs(_components.msup, { children: [_jsx(_components.mo, { stretchy: "false", children: ")" }), _jsx(_components.mo, { mathvariant: "normal", lspace: "0em", rspace: "0em", children: "′" })] }), _jsx(_components.mi, { mathvariant: "bold", children: "M" }), _jsx(_components.mo, { stretchy: "false", children: "(" }), _jsx(_components.mi, { mathvariant: "bold", children: "P" }), _jsx(_components.mi, { mathvariant: "bold", children: "z" }), _jsx(_components.mo, { stretchy: "false", children: ")" }), _jsx(_components.mo, { children: "=" }), _jsxs(_components.msup, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "z" }), _jsx(_components.mo, { mathvariant: "normal", lspace: "0em", rspace: "0em", children: "′" })] }), _jsxs(_components.msup, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "P" }), _jsx(_components.mo, { mathvariant: "normal", lspace: "0em", rspace: "0em", children: "′" })] }), _jsx(_components.mi, { mathvariant: "bold", children: "M" }), _jsx(_components.mi, { mathvariant: "bold", children: "P" }), _jsx(_components.mi, { mathvariant: "bold", children: "z" }), _jsx(_components.mo, { children: "=" }), _jsxs(_components.msup, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "z" }), _jsx(_components.mo, { mathvariant: "normal", lspace: "0em", rspace: "0em", children: "′" })] }), _jsxs(_components.msub, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "I" }), _jsxs(_components.mrow, { children: [_jsx(_components.mi, { children: "n" }), _jsx(_components.mo, { separator: "true", children: "," }), _jsx(_components.mi, { children: "n" }), _jsx(_components.mo, { children: "−" }), _jsx(_components.mi, { children: "k" })] })] }), _jsx(_components.mi, { mathvariant: "bold", children: "z" }), _jsx(_components.mo, { children: "=" }), _jsxs(_components.msubsup, { children: [_jsx(_components.mo, { children: "∑" }), _jsxs(_components.mrow, { children: [_jsx(_components.mi, { children: "i" }), _jsx(_components.mo, { children: "=" }), _jsx(_components.mn, { children: "1" })] }), _jsxs(_components.mrow, { children: [_jsx(_components.mi, { children: "n" }), _jsx(_components.mo, { children: "−" }), _jsx(_components.mi, { children: "k" })] })] }), _jsxs(_components.msubsup, { children: [_jsx(_components.mi, { children: "z" }), _jsx(_components.mi, { children: "i" }), _jsx(_components.mn, { children: "2" })] })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\frac{1}{\\sigma^2}\\mathbf u'\\mathbf M\\mathbf u=(\\mathbf P\\mathbf z)'\\mathbf M(\\mathbf P\\mathbf z)=\\mathbf z'\\mathbf P'\\mathbf M\\mathbf P\\mathbf z=\\mathbf z'\\mathbf I_{n,n-k}\\mathbf z=\\sum_{i=1}^{n-k}z_i^2" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1.1901em", verticalAlign: "-0.345em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mopen nulldelimiter" }), _jsx(_components.span, { className: "mfrac", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsxs(_components.span, { className: "vlist", style: { height: "0.8451em" }, children: [_jsxs(_components.span, { style: { top: "-2.655em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsxs(_components.span, { className: "mord mtight", children: [_jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.03588em" }, children: "σ" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.7463em" }, children: _jsxs(_components.span, { style: { top: "-2.786em", marginRight: "0.0714em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.5em" } }), _jsx(_components.span, { className: "sizing reset-size3 size1 mtight", children: _jsx(_components.span, { className: "mord mtight", children: "2" }) })] }) }) }) }) })] }) }) })] }), _jsxs(_components.span, { style: { top: "-3.23em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "frac-line", style: { borderBottomWidth: "0.04em" } })] }), _jsxs(_components.span, { style: { top: "-3.394em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord mtight", children: "1" }) }) })] })] }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.345em" }, children: _jsx(_components.span, {}) }) })] }) }), _jsx(_components.span, { className: "mclose nulldelimiter" })] }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathbf", children: "u" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.7519em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord mtight", children: "′" }) }) })] }) }) }) }) })] }), _jsx(_components.span, { className: "mord mathbf", children: "Mu" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1.0019em", verticalAlign: "-0.25em" } }), _jsx(_components.span, { className: "mopen", children: "(" }), _jsx(_components.span, { className: "mord mathbf", children: "Pz" }), _jsxs(_components.span, { className: "mclose", children: [_jsx(_components.span, { className: "mclose", children: ")" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.7519em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord mtight", children: "′" }) }) })] }) }) }) }) })] }), _jsx(_components.span, { className: "mord mathbf", children: "M" }), _jsx(_components.span, { className: "mopen", children: "(" }), _jsx(_components.span, { className: "mord mathbf", children: "Pz" }), _jsx(_components.span, { className: "mclose", children: ")" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.7519em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathbf", children: "z" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.7519em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord mtight", children: "′" }) }) })] }) }) }) }) })] }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathbf", children: "P" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.7519em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord mtight", children: "′" }) }) })] }) }) }) }) })] }), _jsx(_components.span, { className: "mord mathbf", children: "MPz" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1.038em", verticalAlign: "-0.2861em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathbf", children: "z" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.7519em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord mtight", children: "′" }) }) })] }) }) }) }) })] }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathbf", children: "I" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsx(_components.span, { className: "vlist", style: { height: "0.3361em" }, children: _jsxs(_components.span, { style: { top: "-2.55em", marginLeft: "0em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsxs(_components.span, { className: "mord mtight", children: [_jsx(_components.span, { className: "mord mathnormal mtight", children: "n" }), _jsx(_components.span, { className: "mpunct mtight", children: "," }), _jsx(_components.span, { className: "mord mathnormal mtight", children: "n" }), _jsx(_components.span, { className: "mbin mtight", children: "−" }), _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.03148em" }, children: "k" })] }) })] }) }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.2861em" }, children: _jsx(_components.span, {}) }) })] }) })] }), _jsx(_components.span, { className: "mord mathbf", children: "z" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1.2887em", verticalAlign: "-0.2997em" } }), _jsxs(_components.span, { className: "mop", children: [_jsx(_components.span, { className: "mop op-symbol small-op", style: { position: "relative", top: "0em" }, children: "∑" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsxs(_components.span, { className: "vlist", style: { height: "0.989em" }, children: [_jsxs(_components.span, { style: { top: "-2.4003em", marginLeft: "0em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsxs(_components.span, { className: "mord mtight", children: [_jsx(_components.span, { className: "mord mathnormal mtight", children: "i" }), _jsx(_components.span, { className: "mrel mtight", children: "=" }), _jsx(_components.span, { className: "mord mtight", children: "1" })] }) })] }), _jsxs(_components.span, { style: { top: "-3.2029em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsxs(_components.span, { className: "mord mtight", children: [_jsx(_components.span, { className: "mord mathnormal mtight", children: "n" }), _jsx(_components.span, { className: "mbin mtight", children: "−" }), _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.03148em" }, children: "k" })] }) })] })] }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.2997em" }, children: _jsx(_components.span, {}) }) })] }) })] }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.1667em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.04398em" }, children: "z" }), _jsx(_components.span, { className: "msupsub", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsxs(_components.span, { className: "vlist", style: { height: "0.8141em" }, children: [_jsxs(_components.span, { style: { top: "-2.4413em", marginLeft: "-0.044em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mathnormal mtight", children: "i" }) })] }), _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: "2" }) })] })] }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.2587em" }, children: _jsx(_components.span, {}) }) })] }) })] })] })] })] }) }) }), "\n", _jsxs(_components.p, { children: ["i.i.dの標準正規分布の二乗和はカイ二乗分布に従い、和の個数が自由度となるため、", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsxs(_components.mfrac, { children: [_jsx(_components.mn, { children: "1" }), _jsxs(_components.msup, { children: [_jsx(_components.mi, { children: "σ" }), _jsx(_components.mn, { children: "2" })] })] }), _jsxs(_components.msup, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "u" }), _jsx(_components.mo, { mathvariant: "normal", lspace: "0em", rspace: "0em", children: "′" })] }), _jsx(_components.mi, { mathvariant: "bold", children: "M" }), _jsx(_components.mi, { mathvariant: "bold", children: "u" }), _jsx(_components.mo, { children: "∼" }), _jsxs(_components.msup, { children: [_jsx(_components.mi, { children: "χ" }), _jsx(_components.mn, { children: "2" })] }), _jsx(_components.mo, { stretchy: "false", children: "(" }), _jsx(_components.mi, { children: "n" }), _jsx(_components.mo, { children: "−" }), _jsx(_components.mi, { children: "k" }), _jsx(_components.mo, { stretchy: "false", children: ")" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\frac{1}{\\sigma^2}\\mathbf u'\\mathbf M\\mathbf u\\sim \\chi^2(n-k)" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1.1901em", verticalAlign: "-0.345em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mopen nulldelimiter" }), _jsx(_components.span, { className: "mfrac", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsxs(_components.span, { className: "vlist", style: { height: "0.8451em" }, children: [_jsxs(_components.span, { style: { top: "-2.655em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsxs(_components.span, { className: "mord mtight", children: [_jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.03588em" }, children: "σ" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.7463em" }, children: _jsxs(_components.span, { style: { top: "-2.786em", marginRight: "0.0714em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.5em" } }), _jsx(_components.span, { className: "sizing reset-size3 size1 mtight", children: _jsx(_components.span, { className: "mord mtight", children: "2" }) })] }) }) }) }) })] }) }) })] }), _jsxs(_components.span, { style: { top: "-3.23em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "frac-line", style: { borderBottomWidth: "0.04em" } })] }), _jsxs(_components.span, { style: { top: "-3.394em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord mtight", children: "1" }) }) })] })] }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.345em" }, children: _jsx(_components.span, {}) }) })] }) }), _jsx(_components.span, { className: "mclose nulldelimiter" })] }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathbf", children: "u" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.7519em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord mtight", children: "′" }) }) })] }) }) }) }) })] }), _jsx(_components.span, { className: "mord mathbf", children: "Mu" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "∼" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1.0641em", verticalAlign: "-0.25em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", children: "χ" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.8141em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: "2" }) })] }) }) }) }) })] }), _jsx(_components.span, { className: "mopen", children: "(" }), _jsx(_components.span, { className: "mord mathnormal", children: "n" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "−" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1em", verticalAlign: "-0.25em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.03148em" }, children: "k" }), _jsx(_components.span, { className: "mclose", children: ")" })] })] })] }) }), "が証明されました。"] }), "\n", _jsxs(_components.h3, { children: ["6. ", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsxs(_components.mfrac, { children: [_jsxs(_components.mrow, { children: [_jsx(_components.mo, { stretchy: "false", children: "(" }), _jsx(_components.mi, { children: "n" }), _jsx(_components.mo, { children: "−" }), _jsx(_components.mi, { children: "k" }), _jsx(_components.mo, { stretchy: "false", children: ")" }), _jsxs(_components.msup, { children: [_jsx(_components.mi, { children: "s" }), _jsx(_components.mn, { children: "2" })] })] }), _jsxs(_components.msup, { children: [_jsx(_components.mi, { children: "σ" }), _jsx(_components.mn, { children: "2" })] })] }), _jsx(_components.mo, { children: "∼" }), _jsxs(_components.msup, { children: [_jsx(_components.mi, { children: "χ" }), _jsx(_components.mn, { children: "2" })] }), _jsx(_components.mo, { stretchy: "false", children: "(" }), _jsx(_components.mi, { children: "n" }), _jsx(_components.mo, { children: "−" }), _jsx(_components.mi, { children: "k" }), _jsx(_components.mo, { stretchy: "false", children: ")" })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\frac{(n-k)s^2}{\\sigma^2}\\sim\\chi^2(n-k)" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1.4539em", verticalAlign: "-0.345em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mopen nulldelimiter" }), _jsx(_components.span, { className: "mfrac", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsxs(_components.span, { className: "vlist", style: { height: "1.1089em" }, children: [_jsxs(_components.span, { style: { top: "-2.655em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsxs(_components.span, { className: "mord mtight", children: [_jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.03588em" }, children: "σ" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.7463em" }, children: _jsxs(_components.span, { style: { top: "-2.786em", marginRight: "0.0714em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.5em" } }), _jsx(_components.span, { className: "sizing reset-size3 size1 mtight", children: _jsx(_components.span, { className: "mord mtight", children: "2" }) })] }) }) }) }) })] }) }) })] }), _jsxs(_components.span, { style: { top: "-3.23em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "frac-line", style: { borderBottomWidth: "0.04em" } })] }), _jsxs(_components.span, { style: { top: "-3.485em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsxs(_components.span, { className: "mord mtight", children: [_jsx(_components.span, { className: "mopen mtight", children: "(" }), _jsx(_components.span, { className: "mord mathnormal mtight", children: "n" }), _jsx(_components.span, { className: "mbin mtight", children: "−" }), _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.03148em" }, children: "k" }), _jsx(_components.span, { className: "mclose mtight", children: ")" }), _jsxs(_components.span, { className: "mord mtight", children: [_jsx(_components.span, { className: "mord mathnormal mtight", children: "s" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.8913em" }, children: _jsxs(_components.span, { style: { top: "-2.931em", marginRight: "0.0714em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.5em" } }), _jsx(_components.span, { className: "sizing reset-size3 size1 mtight", children: _jsx(_components.span, { className: "mord mtight", children: "2" }) })] }) }) }) }) })] })] }) })] })] }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.345em" }, children: _jsx(_components.span, {}) }) })] }) }), _jsx(_components.span, { className: "mclose nulldelimiter" })] }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "∼" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1.0641em", verticalAlign: "-0.25em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", children: "χ" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.8141em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: "2" }) })] }) }) }) }) })] }), _jsx(_components.span, { className: "mopen", children: "(" }), _jsx(_components.span, { className: "mord mathnormal", children: "n" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } }), _jsx(_components.span, { className: "mbin", children: "−" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2222em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1em", verticalAlign: "-0.25em" } }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.03148em" }, children: "k" }), _jsx(_components.span, { className: "mclose", children: ")" })] })] })] }) })] }), "\n", _jsxs(_components.p, { children: ["「", _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsxs(_components.msup, { children: [_jsx(_components.mi, { children: "s" }), _jsx(_components.mn, { children: "2" })] }), _jsx(_components.mo, { children: "=" }), _jsxs(_components.mfrac, { children: [_jsxs(_components.mrow, { children: [_jsxs(_components.msup, { children: [_jsx(_components.mi, { mathvariant: "bold", children: "e" }), _jsx(_components.mo, { mathvariant: "normal", lspace: "0em", rspace: "0em", children: "′" })] }), _jsx(_components.mi, { mathvariant: "bold", children: "e" })] }), _jsxs(_components.mrow, { children: [_jsx(_components.mi, { children: "n" }), _jsx(_components.mo, { children: "−" }), _jsx(_components.mi, { children: "k" })] })] })] }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "s^2=\\frac{\\mathbf e'\\mathbf e}{n-k}" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.8141em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mord mathnormal", children: "s" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.8141em" }, children: _jsxs(_components.span, { style: { top: "-3.063em", marginRight: "0.05em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.7em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsx(_components.span, { className: "mord mtight", children: "2" }) })] }) }) }) }) })] }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } }), _jsx(_components.span, { className: "mrel", children: "=" }), _jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "1.3768em", verticalAlign: "-0.4033em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mopen nulldelimiter" }), _jsx(_components.span, { className: "mfrac", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsxs(_components.span, { className: "vlist", style: { height: "0.9735em" }, children: [_jsxs(_components.span, { style: { top: "-2.655em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsxs(_components.span, { className: "mord mtight", children: [_jsx(_components.span, { className: "mord mathnormal mtight", children: "n" }), _jsx(_components.span, { className: "mbin mtight", children: "−" }), _jsx(_components.span, { className: "mord mathnormal mtight", style: { marginRight: "0.03148em" }, children: "k" })] }) })] }), _jsxs(_components.span, { style: { top: "-3.23em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "frac-line", style: { borderBottomWidth: "0.04em" } })] }), _jsxs(_components.span, { style: { top: "-3.394em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "sizing reset-size6 size3 mtight", children: _jsxs(_components.span, { className: "mord mtight", children: [_jsxs(_components.span, { className: "mord mtight", children: [_jsx(_components.span, { className: "mord mathbf mtight", children: "e" }), _jsx(_components.span, { className: "msupsub", children: _jsx(_components.span, { className: "vlist-t", children: _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.8278em" }, children: _jsxs(_components.span, { style: { top: "-2.931em", marginRight: "0.0714em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "2.5em" } }), _jsx(_components.span, { className: "sizing reset-size3 size1 mtight", children: _jsx(_components.span, { className: "mord mtight", children: _jsx(_components.span, { className: "mord mtight", children: "′" }) }) })] }) }) }) }) })] }), _jsx(_components.span, { className: "mord mathbf mtight", children: "e" })] }) })] })] }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.4033em" }, children: _jsx(_components.span, {}) }) })] }) }), _jsx(_components.span, { className: "mclose nulldelimiter" })] })] })] })] }) }), "」と、証明3、5から示すことができます。"] }), "\n", _jsx(_components.p, { children: "以上で証明が終了となります。" }), "\n", _jsx(_components.p, { children: "文献は以下を参考にしていますので、より詳しく知りたい方は是非読んでみてください。" }), "\n", _jsx(_components.h3, { children: "参考文献" }), "\n", _jsxs(_components.ol, { children: ["\n", _jsx(_components.li, { children: "蓑谷 千凰彦 著. 線形回帰分析(2015). 朝倉書店" }), "\n"] })] }); } function MDXContent(props = {}) { const {wrapper: MDXLayout} = Object.assign({}, _provideComponents(), props.components); return MDXLayout ? _jsx(MDXLayout, Object.assign({}, props, { children: _jsx(_createMdxContent, props) })) : _createMdxContent(props); } return { default: MDXContent }; a:["$","div",null,{"className":"container mx-auto px-4 py-8 max-w-7xl","children":["$","div",null,{"className":"flex flex-col md:flex-row gap-8","children":[["$","article",null,{"className":"w-full md:w-[70%] bg-white shadow-lg rounded-lg p-8","children":[["$","header",null,{"className":"mb-8 border-b pb-4","children":[["$","div",null,{"className":"flex items-center gap-2 mb-2","children":[["$","$L6",null,{"href":"/","className":"text-gray-500 hover:text-orange-500","children":"Home"}],["$","span",null,{"className":"text-gray-300","children":">"}],["$","span",null,{"className":"text-gray-500","children":"$undefined"}]]}],["$","h1",null,{"className":"text-3xl font-bold mb-4","children":"線形回帰分析のt値がt分布に従う理由(証明)"}],["$","div",null,{"className":"text-gray-500 flex flex-wrap gap-4 items-center mb-6","children":[["$","time",null,{"className":"flex items-center gap-1 text-sm","children":[["$","svg",null,{"xmlns":"http://www.w3.org/2000/svg","height":"18px","viewBox":"0 0 24 24","width":"18px","fill":"#666666","className":"mr-1","children":[["$","path",null,{"d":"M0 0h24v24H0V0z","fill":"none"}],["$","path",null,{"d":"M19 3h-1V1h-2v2H8V1H6v2H5c-1.11 0-2 .9-2 2v14c0 1.1.89 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2zm0 16H5V8h14v11zM7 10h5v5H7z"}]]}],"日付: ","2020-09-02"]}],["$","div",null,{"className":"flex flex-wrap gap-2","children":[["$","$L6","データ分析",{"href":"/tags/データ分析","className":"bg-gray-100 hover:bg-blue-100 px-2 py-1 rounded text-sm text-gray-600 hover:text-blue-600 transition-colors","children":["#","データ分析"]}]]}]]}]]}],["$","div",null,{"className":"prose max-w-none prose-headings:border-b prose-headings:pb-2 prose-a:text-orange-600","children":["$","$Lb",null,{"compiledSource":"$c","frontmatter":{},"scope":{}}]}],["$","div",null,{"className":"flex justify-between items-center mt-12","children":[["$","div",null,{"className":"flex-1","children":["$","$L6",null,{"href":"/blog25","className":"group flex flex-col items-start p-4 rounded-lg border border-gray-100 hover:border-orange-200 hover:bg-orange-50 transition-all","children":[["$","span",null,{"className":"text-sm text-gray-500 mb-1 group-hover:text-orange-600 flex items-center","children":[["$","svg",null,{"xmlns":"http://www.w3.org/2000/svg","className":"h-4 w-4 mr-1","fill":"none","viewBox":"0 0 24 24","stroke":"currentColor","children":["$","path",null,{"strokeLinecap":"round","strokeLinejoin":"round","strokeWidth":2,"d":"M15 19l-7-7 7-7"}]}],"Previous"]}],["$","span",null,{"className":"font-medium text-gray-800 dark:text-gray-200 line-clamp-2","children":"線形回帰分析と最尤推定法"}]]}]}],["$","div",null,{"className":"w-8"}],["$","div",null,{"className":"flex-1 text-right","children":["$","$L6",null,{"href":"/blog27","className":"group flex flex-col items-end p-4 rounded-lg border border-gray-100 hover:border-orange-200 hover:bg-orange-50 transition-all","children":[["$","span",null,{"className":"text-sm text-gray-500 mb-1 group-hover:text-orange-600 flex items-center","children":["Next",["$","svg",null,{"xmlns":"http://www.w3.org/2000/svg","className":"h-4 w-4 ml-1","fill":"none","viewBox":"0 0 24 24","stroke":"currentColor","children":["$","path",null,{"strokeLinecap":"round","strokeLinejoin":"round","strokeWidth":2,"d":"M9 5l7 7-7 7"}]}]]}],["$","span",null,{"className":"font-medium text-gray-800 dark:text-gray-200 line-clamp-2","children":"PythonでLDA(トピックモデル)の実装"}]]}]}]]}],["$","$Ld",null,{}]]}],["$","div",null,{"className":"w-full md:w-[30%]","children":"$Le"}]]}]}] 9:null f:I[9009,["326","static/chunks/326-ead410bae2047633.js","986","static/chunks/986-f27c5a2c4d841870.js","42","static/chunks/app/%5Bslug%5D/page-419f452b4066bb25.js"],""] e:["$","aside",null,{"className":"w-full flex flex-col gap-6","children":[["$","div",null,{"className":"bg-white p-6 rounded shadow-sm border","children":[["$","h3",null,{"className":"font-bold text-lg mb-4 text-[#494949] border-b pb-2","children":"プロフィール"}],["$","div",null,{"className":"flex items-center mb-4","children":[["$","$Lf",null,{}],["$","span",null,{"className":"font-bold","children":"Shingo.S"}]]}],["$","p",null,{"className":"mb-4 text-base leading-relaxed text-gray-600","children":["データサイエンティストとして働いています。仕事では主にPythonやSAS、Rを用いて分析しています。",["$","br",null,{}],["$","br",null,{}],"統計検定1級、Kaggle Expert。",["$","br",null,{}],"自然言語処理に興味があります。"]}],["$","div",null,{"className":"mt-4 flex items-center","children":["$","a",null,{"href":"https://x.com/shingo97358922","target":"_blank","rel":"noopener noreferrer","className":"flex items-center gap-2 text-gray-600 hover:text-black transition-colors","children":[["$","svg",null,{"className":"w-5 h-5","fill":"currentColor","viewBox":"0 0 24 24","aria-hidden":"true","children":["$","path",null,{"d":"M18.244 2.25h3.308l-7.227 8.26 8.502 11.24H16.17l-5.214-6.817L4.99 21.75H1.68l7.73-8.835L1.254 2.25H8.08l4.713 6.231zm-1.161 17.52h1.833L7.084 4.126H5.117z"}]}],["$","span",null,{"className":"text-sm font-medium","children":"@shingo97358922"}]]}]}]]}],["$","div",null,{"className":"bg-white p-6 rounded shadow-sm border","children":[["$","h3",null,{"className":"font-bold text-lg mb-4 text-[#494949] border-b pb-2","children":"アクセスカウンター"}],["$","div",null,{"className":"flex flex-col gap-2 text-gray-600 pl-2","children":[["$","div",null,{"className":"flex items-center gap-4","children":[["$","span",null,{"className":"w-12 text-right","children":"累計"}],["$","span",null,{"children":":"}],["$","span",null,{"className":"font-mono text-lg font-bold","children":"72320"}]]}],["$","div",null,{"className":"flex items-center gap-4","children":[["$","span",null,{"className":"w-12 text-right","children":"本日"}],["$","span",null,{"children":":"}],["$","span",null,{"className":"font-mono text-lg font-bold","children":"17"}]]}],["$","div",null,{"className":"flex items-center gap-4","children":[["$","span",null,{"className":"w-12 text-right","children":"昨日"}],["$","span",null,{"children":":"}],["$","span",null,{"className":"font-mono text-lg font-bold","children":"33"}]]}]]}]]}],["$","div",null,{"className":"bg-white p-6 rounded shadow-sm border","children":[["$","h3",null,{"className":"font-bold text-lg mb-4 text-[#494949] border-b pb-2","children":"月別アーカイブ"}],["$","ul",null,{"className":"text-base text-gray-600","children":[["$","li","2026年2月",{"className":"mb-2 border-b border-dashed border-gray-200 pb-1 last:border-none","children":["$","$L6",null,{"href":"/archives/2026-02","className":"hover:text-blue-500 transition-colors block","children":["2026年2月"," (",1,")"]}]}],["$","li","2025年2月",{"className":"mb-2 border-b border-dashed border-gray-200 pb-1 last:border-none","children":["$","$L6",null,{"href":"/archives/2025-02","className":"hover:text-blue-500 transition-colors block","children":["2025年2月"," (",1,")"]}]}],["$","li","2024年10月",{"className":"mb-2 border-b border-dashed border-gray-200 pb-1 last:border-none","children":["$","$L6",null,{"href":"/archives/2024-10","className":"hover:text-blue-500 transition-colors block","children":["2024年10月"," (",1,")"]}]}],["$","li","2024年7月",{"className":"mb-2 border-b border-dashed border-gray-200 pb-1 last:border-none","children":["$","$L6",null,{"href":"/archives/2024-07","className":"hover:text-blue-500 transition-colors block","children":["2024年7月"," (",1,")"]}]}],["$","li","2024年2月",{"className":"mb-2 border-b border-dashed border-gray-200 pb-1 last:border-none","children":["$","$L6",null,{"href":"/archives/2024-02","className":"hover:text-blue-500 transition-colors block","children":["2024年2月"," (",1,")"]}]}],["$","li","2023年6月",{"className":"mb-2 border-b border-dashed border-gray-200 pb-1 last:border-none","children":["$","$L6",null,{"href":"/archives/2023-06","className":"hover:text-blue-500 transition-colors block","children":["2023年6月"," (",1,")"]}]}],["$","li","2023年5月",{"className":"mb-2 border-b border-dashed border-gray-200 pb-1 last:border-none","children":["$","$L6",null,{"href":"/archives/2023-05","className":"hover:text-blue-500 transition-colors block","children":["2023年5月"," (",1,")"]}]}],["$","li","2023年3月",{"className":"mb-2 border-b border-dashed border-gray-200 pb-1 last:border-none","children":["$","$L6",null,{"href":"/archives/2023-03","className":"hover:text-blue-500 transition-colors block","children":["2023年3月"," (",2,")"]}]}],["$","li","2022年10月",{"className":"mb-2 border-b border-dashed border-gray-200 pb-1 last:border-none","children":["$","$L6",null,{"href":"/archives/2022-10","className":"hover:text-blue-500 transition-colors block","children":["2022年10月"," (",2,")"]}]}],["$","li","2022年9月",{"className":"mb-2 border-b border-dashed border-gray-200 pb-1 last:border-none","children":["$","$L6",null,{"href":"/archives/2022-09","className":"hover:text-blue-500 transition-colors block","children":["2022年9月"," (",2,")"]}]}],["$","li","2022年7月",{"className":"mb-2 border-b border-dashed border-gray-200 pb-1 last:border-none","children":["$","$L6",null,{"href":"/archives/2022-07","className":"hover:text-blue-500 transition-colors block","children":["2022年7月"," (",1,")"]}]}],["$","li","2022年3月",{"className":"mb-2 border-b border-dashed border-gray-200 pb-1 last:border-none","children":["$","$L6",null,{"href":"/archives/2022-03","className":"hover:text-blue-500 transition-colors block","children":["2022年3月"," (",1,")"]}]}],["$","li","2021年11月",{"className":"mb-2 border-b border-dashed border-gray-200 pb-1 last:border-none","children":["$","$L6",null,{"href":"/archives/2021-11","className":"hover:text-blue-500 transition-colors block","children":["2021年11月"," (",1,")"]}]}],["$","li","2021年10月",{"className":"mb-2 border-b border-dashed border-gray-200 pb-1 last:border-none","children":["$","$L6",null,{"href":"/archives/2021-10","className":"hover:text-blue-500 transition-colors block","children":["2021年10月"," (",2,")"]}]}],["$","li","2021年7月",{"className":"mb-2 border-b border-dashed border-gray-200 pb-1 last:border-none","children":["$","$L6",null,{"href":"/archives/2021-07","className":"hover:text-blue-500 transition-colors block","children":["2021年7月"," (",2,")"]}]}],["$","li","2021年5月",{"className":"mb-2 border-b border-dashed border-gray-200 pb-1 last:border-none","children":["$","$L6",null,{"href":"/archives/2021-05","className":"hover:text-blue-500 transition-colors block","children":["2021年5月"," (",2,")"]}]}],["$","li","2021年4月",{"className":"mb-2 border-b border-dashed border-gray-200 pb-1 last:border-none","children":["$","$L6",null,{"href":"/archives/2021-04","className":"hover:text-blue-500 transition-colors block","children":["2021年4月"," (",2,")"]}]}],["$","li","2021年2月",{"className":"mb-2 border-b border-dashed border-gray-200 pb-1 last:border-none","children":["$","$L6",null,{"href":"/archives/2021-02","className":"hover:text-blue-500 transition-colors block","children":["2021年2月"," (",1,")"]}]}],["$","li","2020年10月",{"className":"mb-2 border-b border-dashed border-gray-200 pb-1 last:border-none","children":["$","$L6",null,{"href":"/archives/2020-10","className":"hover:text-blue-500 transition-colors block","children":["2020年10月"," (",1,")"]}]}],["$","li","2020年9月",{"className":"mb-2 border-b border-dashed border-gray-200 pb-1 last:border-none","children":["$","$L6",null,{"href":"/archives/2020-09","className":"hover:text-blue-500 transition-colors block","children":["2020年9月"," (",1,")"]}]}],["$","li","2020年7月",{"className":"mb-2 border-b border-dashed border-gray-200 pb-1 last:border-none","children":["$","$L6",null,{"href":"/archives/2020-07","className":"hover:text-blue-500 transition-colors block","children":["2020年7月"," (",1,")"]}]}],["$","li","2020年6月",{"className":"mb-2 border-b border-dashed border-gray-200 pb-1 last:border-none","children":["$","$L6",null,{"href":"/archives/2020-06","className":"hover:text-blue-500 transition-colors block","children":["2020年6月"," (",1,")"]}]}],["$","li","2020年5月",{"className":"mb-2 border-b border-dashed border-gray-200 pb-1 last:border-none","children":["$","$L6",null,{"href":"/archives/2020-05","className":"hover:text-blue-500 transition-colors block","children":["2020年5月"," (",1,")"]}]}],["$","li","2020年4月",{"className":"mb-2 border-b border-dashed border-gray-200 pb-1 last:border-none","children":["$","$L6",null,{"href":"/archives/2020-04","className":"hover:text-blue-500 transition-colors block","children":["2020年4月"," (",1,")"]}]}],["$","li","2020年3月",{"className":"mb-2 border-b border-dashed border-gray-200 pb-1 last:border-none","children":["$","$L6",null,{"href":"/archives/2020-03","className":"hover:text-blue-500 transition-colors block","children":["2020年3月"," (",1,")"]}]}],["$","li","2020年2月",{"className":"mb-2 border-b border-dashed border-gray-200 pb-1 last:border-none","children":["$","$L6",null,{"href":"/archives/2020-02","className":"hover:text-blue-500 transition-colors block","children":["2020年2月"," (",1,")"]}]}],["$","li","2020年1月",{"className":"mb-2 border-b border-dashed border-gray-200 pb-1 last:border-none","children":["$","$L6",null,{"href":"/archives/2020-01","className":"hover:text-blue-500 transition-colors block","children":["2020年1月"," (",1,")"]}]}],["$","li","2019年12月",{"className":"mb-2 border-b border-dashed border-gray-200 pb-1 last:border-none","children":["$","$L6",null,{"href":"/archives/2019-12","className":"hover:text-blue-500 transition-colors block","children":["2019年12月"," (",1,")"]}]}],["$","li","2019年11月",{"className":"mb-2 border-b border-dashed border-gray-200 pb-1 last:border-none","children":["$","$L6",null,{"href":"/archives/2019-11","className":"hover:text-blue-500 transition-colors block","children":["2019年11月"," (",2,")"]}]}],["$","li","2019年10月",{"className":"mb-2 border-b border-dashed border-gray-200 pb-1 last:border-none","children":["$","$L6",null,{"href":"/archives/2019-10","className":"hover:text-blue-500 transition-colors block","children":["2019年10月"," (",2,")"]}]}],["$","li","2019年9月",{"className":"mb-2 border-b border-dashed border-gray-200 pb-1 last:border-none","children":["$","$L6",null,{"href":"/archives/2019-09","className":"hover:text-blue-500 transition-colors block","children":["2019年9月"," (",1,")"]}]}],["$","li","2019年8月",{"className":"mb-2 border-b border-dashed border-gray-200 pb-1 last:border-none","children":["$","$L6",null,{"href":"/archives/2019-08","className":"hover:text-blue-500 transition-colors block","children":["2019年8月"," (",8,")"]}]}],["$","li","2019年7月",{"className":"mb-2 border-b border-dashed border-gray-200 pb-1 last:border-none","children":["$","$L6",null,{"href":"/archives/2019-07","className":"hover:text-blue-500 transition-colors block","children":["2019年7月"," (",1,")"]}]}],["$","li","2019年6月",{"className":"mb-2 border-b border-dashed border-gray-200 pb-1 last:border-none","children":["$","$L6",null,{"href":"/archives/2019-06","className":"hover:text-blue-500 transition-colors block","children":["2019年6月"," (",2,")"]}]}]]}]]}],["$","div",null,{"className":"bg-white p-6 rounded shadow-sm border","children":[["$","h3",null,{"className":"font-bold text-lg mb-4 text-[#494949] border-b pb-2","children":"タグ一覧"}],["$","div",null,{"className":"flex flex-wrap gap-2","children":[["$","$L6","データ分析",{"href":"/tags/データ分析","className":"bg-gray-100 hover:bg-blue-500 hover:text-white rounded px-2 py-1 text-sm transition-colors duration-200 text-gray-600","children":["データ分析"," (",18,")"]}],["$","$L6","自然言語処理",{"href":"/tags/自然言語処理","className":"bg-gray-100 hover:bg-blue-500 hover:text-white rounded px-2 py-1 text-sm transition-colors duration-200 text-gray-600","children":["自然言語処理"," (",16,")"]}],["$","$L6","SAS",{"href":"/tags/SAS","className":"bg-gray-100 hover:bg-blue-500 hover:text-white rounded px-2 py-1 text-sm transition-colors duration-200 text-gray-600","children":["SAS"," (",12,")"]}],["$","$L6","Kaggle",{"href":"/tags/Kaggle","className":"bg-gray-100 hover:bg-blue-500 hover:text-white rounded px-2 py-1 text-sm transition-colors duration-200 text-gray-600","children":["Kaggle"," (",3,")"]}],["$","$L6","雑談",{"href":"/tags/雑談","className":"bg-gray-100 hover:bg-blue-500 hover:text-white rounded px-2 py-1 text-sm transition-colors duration-200 text-gray-600","children":["雑談"," (",2,")"]}]]}]]}],["$","div",null,{"className":"bg-white p-6 rounded shadow-sm border","children":[["$","h3",null,{"className":"font-bold text-lg mb-4 text-[#494949] border-b pb-2","children":"広告枠"}],["$","div",null,{"className":"flex justify-center items-center","children":[["$","a",null,{"href":"https://px.a8.net/svt/ejp?a8mat=4AXI0F+CULTTE+348+6CWQP","rel":"nofollow","target":"_blank","children":["$","img",null,{"style":{"border":0},"width":"250","height":"250","alt":"","src":"https://www25.a8.net/svt/bgt?aid=260223855777&wid=001&eno=01&mid=s00000000404001068000&mc=1"}]}],["$","img",null,{"style":{"border":0},"width":"1","height":"1","src":"https://www17.a8.net/0.gif?a8mat=4AXI0F+CULTTE+348+6CWQP","alt":""}]]}]]}]]}]