{"id":11426,"date":"2026-09-24T09:00:00","date_gmt":"2026-09-24T00:00:00","guid":{"rendered":"https:\/\/triumphmind.com\/cfa\/?p=11426"},"modified":"2026-09-29T09:01:25","modified_gmt":"2026-09-29T00:01:25","slug":"cfa-l2-quants-formulas","status":"publish","type":"post","link":"https:\/\/triumphmind.com\/cfa\/2026\/09\/24\/cfa-l2-quants-formulas\/","title":{"rendered":"\u3010CFA\u00ae\ufe0e L2 Quants \u516c\u5f0f\u96c6\u3011Quantitative Methods \u306e\u91cd\u8981\u516c\u5f0f16\u672c\uff5c\u8a18\u53f7\u306e\u610f\u5473\u3068\u4f7f\u3044\u3069\u3053\u308d\u3092\u5358\u5143\u5225\u306b\u6574\u7406"},"content":{"rendered":"<link rel=\"stylesheet\" href=\"https:\/\/cdn.jsdelivr.net\/npm\/katex@0.18.9\/dist\/katex.min.css\">\n<style> .cfagl-nav{background:#f6f7fb;border-radius:6px;padding:1em 1.2em;margin:1em 0;line-height:1.9;word-break:normal;overflow-wrap:anywhere} .cfagl-nav a{display:block;margin:.15em 0} .cfagl-lm{font-size:.9em;margin:.2em 0 1em} .cfagl-t{border:1px solid #d5d9e3;border-left:4px solid #172152;border-radius:4px;padding:.75em 1em;margin:0 0 .8em;background:#fff} .cfagl-t .en{display:block;font-weight:bold;color:#172152;line-height:1.5;word-break:normal;overflow-wrap:anywhere} .cfagl-t .ja{display:block;font-size:.9em;color:#555;margin:.15em 0 .4em;line-height:1.5} .cfagl-t .df{display:block;line-height:1.75} .cfafm-c{border:1px solid #d5d9e3;border-top:4px solid #172152;border-radius:4px;padding:.9em 1em;margin:0 0 1.2em;background:#fff} .cfafm-c .nm{display:block;font-weight:bold;color:#172152;line-height:1.5} .cfafm-c .ne{display:block;font-size:.85em;color:#667;margin-bottom:.5em;word-break:normal;overflow-wrap:anywhere} .cfafm-x{background:#f6f7fb;border-radius:4px;padding:.6em .8em;margin:.4em 0 .7em;overflow-x:auto;overflow-y:hidden;-webkit-overflow-scrolling:touch} .cfafm-x .katex-display{margin:.3em 0!important} .cfafm-lg{margin:.3em 0 .6em;padding:0;font-size:.92em} .cfafm-lg div{display:flex;gap:.8em;padding:.25em 0;border-bottom:1px dotted #d5d9e3;line-height:1.6} .cfafm-lg .s{flex:0 0 auto;min-width:4.5em;max-width:45%;overflow-x:auto} .cfafm-lg .d{flex:1 1 auto} .cfafm-x .katex-display+.katex-display{margin-top:.2em!important} @media (max-width:600px){.cfafm-x .katex-display>.katex{font-size:.9em}.cfafm-lg div{flex-wrap:wrap;gap:.1em .8em}.cfafm-lg .s{max-width:100%}} .cfafm-u{display:block;line-height:1.75;font-size:.95em} .cfafm-u b{color:#172152} .cfahub-g{display:grid;grid-template-columns:repeat(auto-fill,minmax(250px,1fr));gap:.8em;margin:1em 0} .cfahub-g a{display:block;border:1px solid #d5d9e3;border-left:4px solid #172152;border-radius:4px;padding:.8em 1em;background:#fff;text-decoration:none;color:#172152;line-height:1.5} .cfahub-g a .n{display:block;font-weight:bold} .cfahub-g a .j{display:block;font-size:.88em;color:#555} .cfagl-t p:empty,.cfafm-c p:empty,.cfahub-g p:empty,.cfagl-nav p:empty{display:none} .cfagl-lsc{border:2px solid #c9a227;background:#fffbea;border-radius:6px;padding:.9em 1.1em;margin:1em 0 1.4em;line-height:1.75} .cfagl-lsc b{display:block;color:#8a6d1d;margin-bottom:.3em} .cfagl-lsc a{display:inline-block;margin-top:.4em;font-weight:bold} .cfahub-g a .c{display:block;font-size:.82em;color:#8a6d1d;margin-top:.3em} <\/style>\n<div class=\"box05\">CFA\u00ae\ufe0e Level 2\u300cQuantitative Methods\uff08\u6570\u91cf\u5206\u6790\uff09\u300d\u306e\u91cd\u8981\u516c\u5f0f16\u672c\u3092\u3001\u5b66\u7fd2\u5358\u5143\uff08Learning Module\uff09\u3054\u3068\u306b\u6574\u7406\u3057\u307e\u3057\u305f\u3002\u516c\u5f0f\u3054\u3068\u306b<strong>\u6570\u5f0f\u30fb\u8a18\u53f7\u306e\u610f\u5473\u30fb\u4f7f\u3044\u3069\u3053\u308d<\/strong>\u3092\u307e\u3068\u3081\u3066\u3044\u307e\u3059\u3002\u6570\u5f0f\u304c\u6a2a\u306b\u9577\u3044\u5834\u5408\u306f\u3001\u6a2a\u306b\u30b9\u30af\u30ed\u30fc\u30eb\u3057\u3066\u3054\u89a7\u304f\u3060\u3055\u3044\u3002<\/div>\n<div class=\"cfagl-lsc\"><b>Leveraged Support Course \u3092\u3054\u5229\u7528\u306e\u65b9\u3078<\/b>FA-Academy \u306e Leveraged Support Course\uff08LSC\uff09\u3092\u3054\u5229\u7528\u306e\u65b9\u306b\u306f\u3001\u3053\u306e\u7528\u8a9e\u96c6\u3068\u516c\u5f0f\u96c6\u3092\u30ec\u30d9\u30eb\u5225\u306b\u6574\u7406\u3057\u305f\u8cc7\u6599\uff08PDF\uff09\u3092\u304a\u6e21\u3057\u3057\u3066\u3044\u307e\u3059\u3002\u30aa\u30d5\u30e9\u30a4\u30f3\u3067\u306e\u78ba\u8a8d\u3084\u8a66\u9a13\u76f4\u524d\u306e\u898b\u76f4\u3057\u306b\u3054\u6d3b\u7528\u304f\u3060\u3055\u3044\u3002<a href=\"https:\/\/triumphmind.com\/cfa\/side_by_side\/\">Level 2 Leveraged Support Course \u306e\u8a73\u7d30\u3092\u898b\u308b<\/a><\/div>\n<h2>\u5358\u5143\uff08LM\uff09\u4e00\u89a7<\/h2>\n<div class=\"cfagl-nav\"><a href=\"#l2-quants-f-lm2\">LM2 \u56de\u5e30\u30e2\u30c7\u30eb\u306e\u5f53\u3066\u306f\u307e\u308a\u3068\u7d50\u679c\u306e\u89e3\u91c8<\/a><a href=\"#l2-quants-f-lm3\">LM3 \u30e2\u30c7\u30eb\u306e\u8aa4\u7279\u5b9a<\/a><a href=\"#l2-quants-f-lm4\">LM4 \u91cd\u56de\u5e30\u306e\u62e1\u5f35<\/a><a href=\"#l2-quants-f-lm5\">LM5 \u6642\u7cfb\u5217\u5206\u6790<\/a><a href=\"#l2-quants-f-lm7\">LM7 \u30d3\u30c3\u30b0\u30c7\u30fc\u30bf\u30fb\u30d7\u30ed\u30b8\u30a7\u30af\u30c8<\/a><\/div>\n<h2>Quants \u306e\u91cd\u8981\u516c\u5f0f\uff08LM\u5225\uff09<\/h2>\n<h3 id=\"l2-quants-f-lm2\">LM2 Evaluating Regression Model Fit and Interpreting Model Results\uff08\u56de\u5e30\u30e2\u30c7\u30eb\u306e\u5f53\u3066\u306f\u307e\u308a\u3068\u7d50\u679c\u306e\u89e3\u91c8\uff09<\/h3>\n<div class=\"cfagl-lm\">\u3053\u306e\u5358\u5143\u306e\u8981\u70b9\u89e3\u8aac\uff1a<a href=\"https:\/\/triumphmind.com\/cfa\/2026\/09\/22\/cfa-l2-quants-lm2\/\">LM2 \u56de\u5e30\u30e2\u30c7\u30eb\u306e\u5f53\u3066\u306f\u307e\u308a\u3068\u7d50\u679c\u306e\u89e3\u91c8<\/a><\/div>\n<div class=\"cfafm-c\">\n<div class=\"nm\">1. \u91cd\u56de\u5e30\u306b\u3088\u308b\u4e88\u6e2c\u5024<\/div>\n<div class=\"ne\">Predicted Value from Multiple Regression<\/div>\n<div class=\"cfafm-x\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.9468em;\"><\/span><span class=\"mord katex-accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.9468em;\"><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.2222em;\">Y<\/span><\/span><span style=\"top:-3.2523em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"accent-body\" style=\"left:-0.25em;\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1.1079em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord katex-accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.9579em;\"><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord mathnormal\">b<\/span><\/span><span style=\"top:-3.2634em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"accent-body\" style=\"left:-0.25em;\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1.1079em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord katex-accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.9579em;\"><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord mathnormal\">b<\/span><\/span><span style=\"top:-3.2634em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"accent-body\" style=\"left:-0.25em;\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.0785em;\">X<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1.1079em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord katex-accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.9579em;\"><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord mathnormal\">b<\/span><\/span><span style=\"top:-3.2634em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"accent-body\" style=\"left:-0.25em;\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.0785em;\">X<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6667em;vertical-align:-0.0833em;\"><\/span><span class=\"minner\">\u22ef<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1.1079em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord katex-accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.9579em;\"><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord mathnormal\">b<\/span><\/span><span style=\"top:-3.2634em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"accent-body\" style=\"left:-0.25em;\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3361em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.0315em;\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.0785em;\">X<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3361em;\"><span style=\"top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.0315em;\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/div>\n<div class=\"cfafm-lg\">\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.9468em;\"><\/span><span class=\"mord katex-accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.9468em;\"><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.2222em;\">Y<\/span><\/span><span style=\"top:-3.2523em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"accent-body\" style=\"left:-0.25em;\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u5f93\u5c5e\u5909\u6570\u306e\u4e88\u6e2c\u5024<\/span><\/div>\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1.1079em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord katex-accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.9579em;\"><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord mathnormal\">b<\/span><\/span><span style=\"top:-3.2634em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"accent-body\" style=\"left:-0.25em;\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u5207\u7247\u306e\u63a8\u5b9a\u5024<\/span><\/div>\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1.244em;vertical-align:-0.2861em;\"><\/span><span class=\"mord\"><span class=\"mord katex-accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.9579em;\"><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord mathnormal\">b<\/span><\/span><span style=\"top:-3.2634em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"accent-body\" style=\"left:-0.25em;\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3117em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.0572em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2861em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u7b2cj\u72ec\u7acb\u5909\u6570\uff08j = 1, \u2026, k\uff09\u306e\u50be\u304d\u4fc2\u6570\u306e\u63a8\u5b9a\u5024<\/span><\/div>\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.9694em;vertical-align:-0.2861em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.0785em;\">X<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3117em;\"><span style=\"top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.0572em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2861em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u7b2cj\u72ec\u7acb\u5909\u6570\u306e\u5024<\/span><\/div>\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6944em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k<\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u72ec\u7acb\u5909\u6570\u306e\u6570<\/span><\/div>\n<\/div>\n<div class=\"cfafm-u\"><b>\u4f7f\u3044\u3069\u3053\u308d\uff1a<\/b>\u63a8\u5b9a\u3057\u305f\u56de\u5e30\u4fc2\u6570\u306b\u5404\u72ec\u7acb\u5909\u6570\u306e\u60f3\u5b9a\u5024\u3092\u4ee3\u5165\u3057\u3001\u5207\u7247\u3092\u52a0\u3048\u3066\u5f93\u5c5e\u5909\u6570\u306e\u4e88\u6e2c\u5024\u3092\u6c42\u3081\u308b\u5f0f\u3002<\/div>\n<\/div>\n<div class=\"cfafm-c\">\n<div class=\"nm\">2. \u81ea\u7531\u5ea6\u8abf\u6574\u6e08\u307f\u6c7a\u5b9a\u4fc2\u6570<\/div>\n<div class=\"ne\">Adjusted R-Squared<\/div>\n<div class=\"cfafm-x\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8641em;\"><\/span><span class=\"mord\"><span class=\"mord katex-accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8201em;\"><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0077em;\">R<\/span><\/span><span style=\"top:-3.2523em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"accent-body\" style=\"left:-0.1667em;\"><span class=\"mord\">\u02c9<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8641em;\"><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.7278em;vertical-align:-0.0833em;\"><\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:2.4em;vertical-align:-0.95em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\"><span class=\"delimsizing size3\">(<\/span><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.3214em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">n<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">n<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7693em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\"><span class=\"delimsizing size3\">)<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1.1141em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.0077em;\">R<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8641em;\"><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/div>\n<div class=\"cfafm-lg\">\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8201em;\"><\/span><span class=\"mord\"><span class=\"mord katex-accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8201em;\"><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0077em;\">R<\/span><\/span><span style=\"top:-3.2523em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"accent-body\" style=\"left:-0.1667em;\"><span class=\"mord\">\u02c9<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8141em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u8abf\u6574\u6e08\u307f\u6c7a\u5b9a\u4fc2\u6570<\/span><\/div>\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8141em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.0077em;\">R<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8141em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u901a\u5e38\u306e\u6c7a\u5b9a\u4fc2\u6570<\/span><\/div>\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.4306em;\"><\/span><span class=\"mord mathnormal\">n<\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u89b3\u6e2c\u6570<\/span><\/div>\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6944em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k<\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u72ec\u7acb\u5909\u6570\u306e\u6570<\/span><\/div>\n<\/div>\n<div class=\"cfafm-u\"><b>\u4f7f\u3044\u3069\u3053\u308d\uff1a<\/b>\u6a19\u672c\u6570\u3068\u72ec\u7acb\u5909\u6570\u306e\u6570\u3067\u81ea\u7531\u5ea6\u3092\u8abf\u6574\u3057\u305f\u6c7a\u5b9a\u4fc2\u6570\u3002\u72ec\u7acb\u5909\u6570\u306e\u6570\u304c\u7570\u306a\u308b\u91cd\u56de\u5e30\u30e2\u30c7\u30eb\u306e\u5f53\u3066\u306f\u307e\u308a\u3092\u6bd4\u3079\u308b\u5834\u9762\u3067\u4f7f\u3046\u3002<\/div>\n<\/div>\n<div class=\"cfafm-c\">\n<div class=\"nm\">3. \u5168\u4f53\u306eF\u691c\u5b9a(\u30e2\u30c7\u30eb\u306e\u6709\u610f\u6027)<\/div>\n<div class=\"ne\">Overall F-Test (Model Significance)<\/div>\n<div class=\"cfafm-x\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6833em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">F<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:2.0463em;vertical-align:-0.686em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.3603em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord text\"><span class=\"mord\">MSE<\/span><\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord text\"><span class=\"mord\">MSR<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.686em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:2.363em;vertical-align:-0.936em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.427em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord text\"><span class=\"mord\">SSE<\/span><\/span><span class=\"mord\">\/<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord\">1<\/span><span class=\"mclose\">)<\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord text\"><span class=\"mord\">SSR<\/span><\/span><span class=\"mord\">\/<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.936em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/div>\n<div class=\"cfafm-lg\">\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6833em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">F<\/span><\/span><\/span><\/span><\/span><span class=\"d\">F\u7d71\u8a08\u91cf\uff08F\u5206\u5e03\u3067\u8a55\u4fa1\u3059\u308b\u691c\u5b9a\u7d71\u8a08\u91cf\uff09<\/span><\/div>\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6833em;\"><\/span><span class=\"mord text\"><span class=\"mord\">MSR<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u56de\u5e30\u306e\u5e73\u5747\u5e73\u65b9\uff08Mean Square Regression\uff09= SSR\/k<\/span><\/div>\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6833em;\"><\/span><span class=\"mord text\"><span class=\"mord\">MSE<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u8aa4\u5dee\u306e\u5e73\u5747\u5e73\u65b9\uff08Mean Squared Error\uff09= SSE\/(n\u2212k\u22121)<\/span><\/div>\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6833em;\"><\/span><span class=\"mord text\"><span class=\"mord\">SSR<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u56de\u5e30\u5e73\u65b9\u548c\uff08Sum of Squares Regression\uff09\uff1a\u30e2\u30c7\u30eb\u3067\u8aac\u660e\u3067\u304d\u305f\u5909\u52d5<\/span><\/div>\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6833em;\"><\/span><span class=\"mord text\"><span class=\"mord\">SSE<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u6b8b\u5dee\u5e73\u65b9\u548c\uff08Sum of Squared Errors\uff09\uff1a\u8aac\u660e\u3067\u304d\u306a\u304b\u3063\u305f\u5909\u52d5<\/span><\/div>\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6944em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k<\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u72ec\u7acb\u5909\u6570\u306e\u6570\uff08\u5206\u5b50\u306e\u81ea\u7531\u5ea6\uff09<\/span><\/div>\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.4306em;\"><\/span><span class=\"mord mathnormal\">n<\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u89b3\u6e2c\u6570<\/span><\/div>\n<\/div>\n<div class=\"cfafm-u\"><b>\u4f7f\u3044\u3069\u3053\u308d\uff1a<\/b>\u3059\u3079\u3066\u306e\u50be\u304d\u4fc2\u6570\u304c\u540c\u6642\u306b\u30bc\u30ed\u304b\u3092\u691c\u5b9a\u3059\u308bF\u7d71\u8a08\u91cf\u3002\u56de\u5e30\u30e2\u30c7\u30eb\u5168\u4f53\u306b\u8aac\u660e\u529b\u304c\u3042\u308b\u304b\u3092\u5224\u65ad\u3059\u308b\u5834\u9762\u3067\u4f7f\u3046\u3002<\/div>\n<\/div>\n<div class=\"cfafm-c\">\n<div class=\"nm\">4. \u5165\u308c\u5b50\u30e2\u30c7\u30eb\u306e\u7d50\u5408F\u691c\u5b9a(\u90e8\u5206F\u691c\u5b9a)<\/div>\n<div class=\"ne\">Joint (Partial) F-Test for Nested Models<\/div>\n<div class=\"cfafm-x\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6833em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">F<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:2.363em;vertical-align:-0.936em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.427em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord text\"><span class=\"mord\">SSE<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3283em;\"><span style=\"top:-2.55em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.109em;\">U<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\/<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord\">1<\/span><span class=\"mclose\">)<\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord text\"><span class=\"mord\">SSE<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3283em;\"><span style=\"top:-2.55em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.0077em;\">R<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord\"><span class=\"mord text\"><span class=\"mord\">SSE<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3283em;\"><span style=\"top:-2.55em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.109em;\">U<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mord\">\/<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">q<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.936em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/div>\n<div class=\"cfafm-lg\">\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6833em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">F<\/span><\/span><\/span><\/span><\/span><span class=\"d\">F\u7d71\u8a08\u91cf<\/span><\/div>\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8333em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord text\"><span class=\"mord\">SSE<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3283em;\"><span style=\"top:-2.55em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.0077em;\">R<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u5236\u7d04\u30e2\u30c7\u30eb\uff08\u5909\u6570\u3092\u9664\u3044\u305f\u30e2\u30c7\u30eb\uff09\u306e\u6b8b\u5dee\u5e73\u65b9\u548c\uff08SSE = Sum of Squared Errors\u3002R = Restricted\uff09<\/span><\/div>\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8333em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord text\"><span class=\"mord\">SSE<\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3283em;\"><span style=\"top:-2.55em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.109em;\">U<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u975e\u5236\u7d04\u30e2\u30c7\u30eb\uff08\u5168\u5909\u6570\u3092\u542b\u3080\u30e2\u30c7\u30eb\uff09\u306e\u6b8b\u5dee\u5e73\u65b9\u548c\uff08U = Unrestricted\uff09<\/span><\/div>\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">q<\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u5236\u7d04\u6570\uff08\u9664\u3044\u305f\u5909\u6570\u306e\u6570\uff09<\/span><\/div>\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.4306em;\"><\/span><span class=\"mord mathnormal\">n<\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u89b3\u6e2c\u6570<\/span><\/div>\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6944em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k<\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u975e\u5236\u7d04\u30e2\u30c7\u30eb\u306e\u72ec\u7acb\u5909\u6570\u306e\u6570<\/span><\/div>\n<\/div>\n<div class=\"cfafm-u\"><b>\u4f7f\u3044\u3069\u3053\u308d\uff1a<\/b>\u5236\u7d04\u4ed8\u304d\u30e2\u30c7\u30eb\u3068\u5236\u7d04\u306a\u3057\u30e2\u30c7\u30eb\u306e\u6b8b\u5dee\u5e73\u65b9\u548c\u3092\u6bd4\u3079\u3001\u9664\u5916\u3057\u305f\u8907\u6570\u306e\u5909\u6570\u304c\u307e\u3068\u3081\u3066\u8aac\u660e\u529b\u3092\u3082\u3064\u304b\u3092\u691c\u5b9a\u3059\u308b\u5f0f\u3002<\/div>\n<\/div>\n<div class=\"cfafm-c\">\n<div class=\"nm\">5. \u56de\u5e30\u4fc2\u6570\u306et\u7d71\u8a08\u91cf<\/div>\n<div class=\"ne\">t-Statistic for a Regression Coefficient<\/div>\n<div class=\"cfafm-x\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6151em;\"><\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:2.8439em;vertical-align:-1.209em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.6349em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3448em;\"><span style=\"top:-2.3743em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord katex-accent mtight\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.9579em;\"><span style=\"top:-2.7em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"mord mathnormal mtight\">b<\/span><\/span><span style=\"top:-2.9634em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"accent-body\" style=\"left:-0.25em;\"><span class=\"mord mtight\">^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3281em;\"><span style=\"top:-2.357em;margin-left:0em;margin-right:0.0714em;\"><span class=\"pstrut\" style=\"height:2.5em;\"><\/span><span class=\"katex-sizing reset-size3 size1 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.0572em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2819em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.523em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord katex-accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.9579em;\"><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord mathnormal\">b<\/span><\/span><span style=\"top:-3.2634em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"accent-body\" style=\"left:-0.25em;\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3117em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.0572em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2861em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">b<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3117em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.0572em;\">j<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2861em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.209em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/div>\n<div class=\"cfafm-lg\">\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6151em;\"><\/span><span class=\"mord mathnormal\">t<\/span><\/span><\/span><\/span><\/span><span class=\"d\">t\u7d71\u8a08\u91cf\uff08t\u5206\u5e03\u3067\u8a55\u4fa1\u3059\u308b\u691c\u5b9a\u7d71\u8a08\u91cf\uff09<\/span><\/div>\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1.244em;vertical-align:-0.2861em;\"><\/span><span class=\"mord\"><span class=\"mord katex-accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.9579em;\"><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord mathnormal\">b<\/span><\/span><span style=\"top:-3.2634em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"accent-body\" style=\"left:-0.25em;\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3117em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.0572em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2861em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u7b2cj\u72ec\u7acb\u5909\u6570\u306e\u4fc2\u6570\u306e\u63a8\u5b9a\u5024<\/span><\/div>\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.9805em;vertical-align:-0.2861em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">b<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3117em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.0572em;\">j<\/span><span class=\"mpunct mtight\">,<\/span><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2861em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u5e30\u7121\u4eee\u8aac\u3067\u7f6e\u304f\u4fc2\u6570\u306e\u5024\uff08\u901a\u5e380\uff09<\/span><\/div>\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.9536em;vertical-align:-0.523em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">s<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3448em;\"><span style=\"top:-2.3743em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord katex-accent mtight\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.9579em;\"><span style=\"top:-2.7em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"mord mathnormal mtight\">b<\/span><\/span><span style=\"top:-2.9634em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"accent-body\" style=\"left:-0.25em;\"><span class=\"mord mtight\">^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3281em;\"><span style=\"top:-2.357em;margin-left:0em;margin-right:0.0714em;\"><span class=\"pstrut\" style=\"height:2.5em;\"><\/span><span class=\"katex-sizing reset-size3 size1 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.0572em;\">j<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2819em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.523em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u4fc2\u6570\u306e\u63a8\u5b9a\u5024\u306e\u6a19\u6e96\u8aa4\u5dee<\/span><\/div>\n<\/div>\n<div class=\"cfafm-u\"><b>\u4f7f\u3044\u3069\u3053\u308d\uff1a<\/b>\u500b\u3005\u306e\u56de\u5e30\u4fc2\u6570\u304c\u4eee\u8aac\u5024\uff08\u901a\u5e38\u306f\u30bc\u30ed\uff09\u3068\u6709\u610f\u306b\u7570\u306a\u308b\u304b\u3092\u691c\u5b9a\u3059\u308bt\u7d71\u8a08\u91cf\u3002\u5404\u72ec\u7acb\u5909\u6570\u306e\u6709\u610f\u6027\u3092\u5224\u65ad\u3059\u308b\u5834\u9762\u3067\u4f7f\u3046\u3002<\/div>\n<\/div>\n<h3 id=\"l2-quants-f-lm3\">LM3 Model Misspecification\uff08\u30e2\u30c7\u30eb\u306e\u8aa4\u7279\u5b9a\uff09<\/h3>\n<div class=\"cfagl-lm\">\u3053\u306e\u5358\u5143\u306e\u8981\u70b9\u89e3\u8aac\uff1a<a href=\"https:\/\/triumphmind.com\/cfa\/2026\/09\/22\/cfa-l2-quants-lm3\/\">LM3 \u30e2\u30c7\u30eb\u306e\u8aa4\u7279\u5b9a<\/a><\/div>\n<div class=\"cfafm-c\">\n<div class=\"nm\">6. \u4e0d\u5747\u4e00\u5206\u6563\u306eBreusch\u2013Pagan\u691c\u5b9a<\/div>\n<div class=\"ne\">Breusch\u2013Pagan Test for Heteroskedasticity<\/div>\n<div class=\"cfafm-x\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6833em;\"><\/span><span class=\"mord text\"><span class=\"mord\">BP<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1.1111em;vertical-align:-0.247em;\"><\/span><span class=\"mord mathnormal\">n<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.0077em;\">R<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8641em;\"><span style=\"top:-2.453em;margin-left:-0.0077em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">resid<\/span><\/span><\/span><\/span><\/span><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.247em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">\u223c<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1.1111em;vertical-align:-0.247em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03c7<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8641em;\"><span style=\"top:-2.453em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.0315em;\">k<\/span><\/span><\/span><\/span><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.247em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/div>\n<div class=\"cfafm-lg\">\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6833em;\"><\/span><span class=\"mord text\"><span class=\"mord\">BP<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"d\">Breusch\u2013Pagan\u691c\u5b9a\u7d71\u8a08\u91cf<\/span><\/div>\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.4306em;\"><\/span><span class=\"mord mathnormal\">n<\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u89b3\u6e2c\u6570<\/span><\/div>\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1.0972em;vertical-align:-0.2831em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.0077em;\">R<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8141em;\"><span style=\"top:-2.4169em;margin-left:-0.0077em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord text mtight\"><span class=\"mord mtight\">resid<\/span><\/span><\/span><\/span><\/span><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2831em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u6b8b\u5dee\u306e\u4e8c\u4e57\u3092\u72ec\u7acb\u5909\u6570\u306b\u56de\u5e30\u3057\u305f\u969b\u306e\u6c7a\u5b9a\u4fc2\u6570\uff08resid = residual\u3001\u6b8b\u5dee\uff09<\/span><\/div>\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1.0972em;vertical-align:-0.2831em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">\u03c7<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8141em;\"><span style=\"top:-2.4169em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.0315em;\">k<\/span><\/span><\/span><\/span><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2831em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u81ea\u7531\u5ea6k\u306e\u30ab\u30a4\u4e8c\u4e57\u5206\u5e03\uff08\u691c\u5b9a\u7d71\u8a08\u91cf\u304c\u5f93\u3046\u5206\u5e03\uff09<\/span><\/div>\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6944em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0315em;\">k<\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u72ec\u7acb\u5909\u6570\u306e\u6570\uff08\u30ab\u30a4\u4e8c\u4e57\u5206\u5e03\u306e\u81ea\u7531\u5ea6\uff09<\/span><\/div>\n<\/div>\n<div class=\"cfafm-u\"><b>\u4f7f\u3044\u3069\u3053\u308d\uff1a<\/b>\u6b8b\u5dee\u306e2\u4e57\u3092\u72ec\u7acb\u5909\u6570\u306b\u56de\u5e30\u3057\u305f\u6c7a\u5b9a\u4fc2\u6570\u304b\u3089\u3001\u6761\u4ef6\u4ed8\u304d\u4e0d\u5747\u4e00\u5206\u6563\u306e\u6709\u7121\u3092\u691c\u5b9a\u3059\u308b\u7d71\u8a08\u91cf\u3002\u30ab\u30a4\u4e8c\u4e57\u5206\u5e03\u3067\u8a55\u4fa1\u3059\u308b\u3002<\/div>\n<\/div>\n<h3 id=\"l2-quants-f-lm4\">LM4 Extensions of Multiple Regression\uff08\u91cd\u56de\u5e30\u306e\u62e1\u5f35\uff09<\/h3>\n<div class=\"cfagl-lm\">\u3053\u306e\u5358\u5143\u306e\u8981\u70b9\u89e3\u8aac\uff1a<a href=\"https:\/\/triumphmind.com\/cfa\/2026\/09\/22\/cfa-l2-quants-lm4\/\">LM4 \u91cd\u56de\u5e30\u306e\u62e1\u5f35<\/a><\/div>\n<div class=\"cfafm-c\">\n<div class=\"nm\">7. \u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u56de\u5e30\u306e\u4e8b\u8c61\u78ba\u7387<\/div>\n<div class=\"ne\">Logistic Regression (Logit) Event Probability<\/div>\n<div class=\"cfafm-x\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6833em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">P<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:2.1088em;vertical-align:-0.7873em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.3214em;\"><span style=\"top:-2.296em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.814em;\"><span style=\"top:-2.989em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">\u2212<\/span><span class=\"mopen mtight\">(<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">b<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3173em;\"><span style=\"top:-2.357em;margin-left:0em;margin-right:0.0714em;\"><span class=\"pstrut\" style=\"height:2.5em;\"><\/span><span class=\"katex-sizing reset-size3 size1 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.143em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin mtight\">+<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">b<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3173em;\"><span style=\"top:-2.357em;margin-left:0em;margin-right:0.0714em;\"><span class=\"pstrut\" style=\"height:2.5em;\"><\/span><span class=\"katex-sizing reset-size3 size1 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.143em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.0785em;\">X<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3173em;\"><span style=\"top:-2.357em;margin-left:-0.0785em;margin-right:0.0714em;\"><span class=\"pstrut\" style=\"height:2.5em;\"><\/span><span class=\"katex-sizing reset-size3 size1 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.143em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin mtight\">+<\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">b<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3173em;\"><span style=\"top:-2.357em;margin-left:0em;margin-right:0.0714em;\"><span class=\"pstrut\" style=\"height:2.5em;\"><\/span><span class=\"katex-sizing reset-size3 size1 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.143em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.0785em;\">X<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3173em;\"><span style=\"top:-2.357em;margin-left:-0.0785em;margin-right:0.0714em;\"><span class=\"pstrut\" style=\"height:2.5em;\"><\/span><span class=\"katex-sizing reset-size3 size1 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.143em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose mtight\">)<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7873em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:2.4em;vertical-align:-0.95em;\"><\/span><span class=\"mop\">ln<\/span><span class=\"mspace\" style=\"margin-right:-0.1667em;\"><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top:0em;\"><span class=\"delimsizing size3\">(<\/span><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.3603em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">P<\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">P<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7693em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mclose delimcenter\" style=\"top:0em;\"><span class=\"delimsizing size3\">)<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8444em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">b<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8444em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">b<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.0785em;\">X<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8444em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">b<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.0785em;\">X<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/div>\n<div class=\"cfafm-lg\">\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6833em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">P<\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u4e8b\u8c61\uff08\u4f8b\uff1a\u30c7\u30d5\u30a9\u30eb\u30c8\uff09\u306e\u767a\u751f\u78ba\u7387<\/span><\/div>\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.4306em;\"><\/span><span class=\"mord mathnormal\">e<\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u81ea\u7136\u5bfe\u6570\u306e\u5e95\uff08\u2248 2.718\uff09<\/span><\/div>\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8444em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">b<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u5207\u7247<\/span><\/div>\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">b<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\">\u00a0<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">b<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u50be\u304d\u4fc2\u6570<\/span><\/div>\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8778em;vertical-align:-0.1944em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.0785em;\">X<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\">\u00a0<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.0785em;\">X<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u72ec\u7acb\u5909\u6570\u306e\u5024<\/span><\/div>\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mop\">ln<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">P<\/span><span class=\"mord\">\/<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">P<\/span><span class=\"mclose\">))<\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u30ed\u30b0\u30aa\u30c3\u30ba\uff08\u7dda\u5f62\u90e8\u5206\u306b\u7b49\u3057\u3044\uff09<\/span><\/div>\n<\/div>\n<div class=\"cfafm-u\"><b>\u4f7f\u3044\u3069\u3053\u308d\uff1a<\/b>\u30ed\u30b0\u30fb\u30aa\u30c3\u30ba\u3092\u72ec\u7acb\u5909\u6570\u306e\u7dda\u5f62\u95a2\u6570\u3067\u8868\u3057\u3001\u305d\u308c\u3092\u78ba\u7387\u306b\u5909\u63db\u3059\u308b\u5f0f\u3002\u30c7\u30d5\u30a9\u30eb\u30c8\u306e\u6709\u7121\u306a\u3069\u4e8c\u5024\u4e8b\u8c61\u306e\u767a\u751f\u78ba\u7387\u3092\u63a8\u5b9a\u3059\u308b\u5834\u9762\u3067\u4f7f\u3046\u3002<\/div>\n<\/div>\n<h3 id=\"l2-quants-f-lm5\">LM5 Time-Series Analysis\uff08\u6642\u7cfb\u5217\u5206\u6790\uff09<\/h3>\n<div class=\"cfagl-lm\">\u3053\u306e\u5358\u5143\u306e\u8981\u70b9\u89e3\u8aac\uff1a<a href=\"https:\/\/triumphmind.com\/cfa\/2026\/09\/22\/cfa-l2-quants-lm5\/\">LM5 \u6642\u7cfb\u5217\u5206\u6790<\/a><\/div>\n<div class=\"cfafm-c\">\n<div class=\"nm\">8. \u5bfe\u6570\u7dda\u5f62\u30c8\u30ec\u30f3\u30c9\u30e2\u30c7\u30eb\u306e\u4e88\u6e2c<\/div>\n<div class=\"ne\">Log-Linear Trend Model Forecast<\/div>\n<div class=\"cfafm-x\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mop\">ln<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord katex-accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.6944em;\"><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">y<\/span><\/span><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"accent-body\" style=\"left:-0.1944em;\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1944em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1.1079em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord katex-accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.9579em;\"><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord mathnormal\">b<\/span><\/span><span style=\"top:-3.2634em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"accent-body\" style=\"left:-0.25em;\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1.1079em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord katex-accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.9579em;\"><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord mathnormal\">b<\/span><\/span><span style=\"top:-3.2634em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"accent-body\" style=\"left:-0.25em;\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">\u21d2<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\"><\/span><span class=\"mord\"><span class=\"mord katex-accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.6944em;\"><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">y<\/span><\/span><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"accent-body\" style=\"left:-0.1944em;\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1944em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1.0835em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.0835em;\"><span style=\"top:-3.113em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord katex-accent mtight\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.9579em;\"><span style=\"top:-2.7em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"mord mathnormal mtight\">b<\/span><\/span><span style=\"top:-2.9634em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"accent-body\" style=\"left:-0.25em;\"><span class=\"mord mtight\">^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3173em;\"><span style=\"top:-2.357em;margin-left:0em;margin-right:0.0714em;\"><span class=\"pstrut\" style=\"height:2.5em;\"><\/span><span class=\"katex-sizing reset-size3 size1 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.143em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin mtight\">+<\/span><span class=\"mord mtight\"><span class=\"mord katex-accent mtight\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.9579em;\"><span style=\"top:-2.7em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"mord mathnormal mtight\">b<\/span><\/span><span style=\"top:-2.9634em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"accent-body\" style=\"left:-0.25em;\"><span class=\"mord mtight\">^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3173em;\"><span style=\"top:-2.357em;margin-left:0em;margin-right:0.0714em;\"><span class=\"pstrut\" style=\"height:2.5em;\"><\/span><span class=\"katex-sizing reset-size3 size1 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.143em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/div>\n<div class=\"cfafm-lg\">\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\"><\/span><span class=\"mord\"><span class=\"mord katex-accent\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.6944em;\"><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0359em;\">y<\/span><\/span><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"accent-body\" style=\"left:-0.1944em;\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1944em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u6642\u70b9t\u306e\u4e88\u6e2c\u6c34\u6e96<\/span><\/div>\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1.1079em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord katex-accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.9579em;\"><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord mathnormal\">b<\/span><\/span><span style=\"top:-3.2634em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"accent-body\" style=\"left:-0.25em;\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u5207\u7247<\/span><\/div>\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1.1079em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord katex-accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.9579em;\"><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord mathnormal\">b<\/span><\/span><span style=\"top:-3.2634em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"accent-body\" style=\"left:-0.25em;\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u30c8\u30ec\u30f3\u30c9\u4fc2\u6570\uff08\u2252\u671f\u9593\u3042\u305f\u308a\u6210\u9577\u7387\uff09<\/span><\/div>\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6151em;\"><\/span><span class=\"mord mathnormal\">t<\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u6642\u9593\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\uff08\u671f\u306e\u756a\u53f7\uff09<\/span><\/div>\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.4306em;\"><\/span><span class=\"mord mathnormal\">e<\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u81ea\u7136\u5bfe\u6570\u306e\u5e95\uff08\u2248 2.718\uff09<\/span><\/div>\n<\/div>\n<div class=\"cfafm-u\"><b>\u4f7f\u3044\u3069\u3053\u308d\uff1a<\/b>\u4e00\u5b9a\u306e\u7387\u3067\u6210\u9577\u3059\u308b\u6642\u7cfb\u5217\u306b\u3064\u3044\u3066\u3001\u5bfe\u6570\u7dda\u5f62\u30c8\u30ec\u30f3\u30c9\u306e\u63a8\u5b9a\u5f0f\u304b\u3089\u6307\u6570\u3092\u3068\u3063\u3066\u6c34\u6e96\u306e\u4e88\u6e2c\u5024\u3092\u6c42\u3081\u308b\u5f0f\u3002<\/div>\n<\/div>\n<div class=\"cfafm-c\">\n<div class=\"nm\">9. AR(1)\u30e2\u30c7\u30eb\u306e\u5e73\u5747\u56de\u5e30\u6c34\u6e96<\/div>\n<div class=\"ne\">AR(1) Mean-Reverting Level<\/div>\n<div class=\"cfafm-x\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.5806em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:2.2074em;vertical-align:-0.836em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.3714em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">b<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\">b<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.836em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/div>\n<div class=\"cfafm-lg\">\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.5806em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u5e73\u5747\u56de\u5e30\u6c34\u6e96\uff08\u6642\u7cfb\u5217\u304c\u9577\u671f\u7684\u306b\u5411\u304b\u3046\u6c34\u6e96\uff09<\/span><\/div>\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8444em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">b<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"d\">AR(1)\u306e\u5207\u7247\uff08AR = \u81ea\u5df1\u56de\u5e30\u3001Autoregressive\uff09<\/span><\/div>\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8444em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">b<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"d\">AR(1)\u306e\u50be\u304d\u4fc2\u6570\uff081\u671f\u524d\u306e\u5024\u306b\u304b\u304b\u308b\u4fc2\u6570\uff09<\/span><\/div>\n<\/div>\n<div class=\"cfafm-u\"><b>\u4f7f\u3044\u3069\u3053\u308d\uff1a<\/b>AR(1)\u30e2\u30c7\u30eb\u306e\u6642\u7cfb\u5217\u304c\u9577\u671f\u7684\u306b\u5411\u304b\u3046\u6c34\u6e96\u3092\u6c42\u3081\u308b\u5f0f\u3002\u73fe\u5728\u5024\u3068\u306e\u6bd4\u8f03\u3067\u3001\u4e88\u6e2c\u5024\u304c\u4e0a\u6607\u3059\u308b\u304b\u4f4e\u4e0b\u3059\u308b\u304b\u3092\u5224\u65ad\u3059\u308b\u3002<\/div>\n<\/div>\n<div class=\"cfafm-c\">\n<div class=\"nm\">10. AR(1)\u306e\u591a\u671f\u5148\u4e88\u6e2c(\u9023\u9396\u5247)<\/div>\n<div class=\"ne\">Multiperiod AR(1) Forecast (Chain Rule)<\/div>\n<div class=\"cfafm-x\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.9028em;vertical-align:-0.2083em;\"><\/span><span class=\"mord\"><span class=\"mord katex-accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.6944em;\"><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"accent-body\" style=\"left:-0.2222em;\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mbin mtight\">+<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2083em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1.1079em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord katex-accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.9579em;\"><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord mathnormal\">b<\/span><\/span><span style=\"top:-3.2634em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"accent-body\" style=\"left:-0.25em;\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1.1079em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord katex-accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.9579em;\"><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord mathnormal\">b<\/span><\/span><span style=\"top:-3.2634em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"accent-body\" style=\"left:-0.25em;\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.9028em;vertical-align:-0.2083em;\"><\/span><span class=\"mord\"><span class=\"mord katex-accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.6944em;\"><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"accent-body\" style=\"left:-0.2222em;\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mbin mtight\">+<\/span><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2083em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1.1079em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord katex-accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.9579em;\"><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord mathnormal\">b<\/span><\/span><span style=\"top:-3.2634em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"accent-body\" style=\"left:-0.25em;\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1.1662em;vertical-align:-0.2083em;\"><\/span><span class=\"mord\"><span class=\"mord katex-accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.9579em;\"><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord mathnormal\">b<\/span><\/span><span style=\"top:-3.2634em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"accent-body\" style=\"left:-0.25em;\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord katex-accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.6944em;\"><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"accent-body\" style=\"left:-0.2222em;\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mbin mtight\">+<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2083em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/div>\n<div class=\"cfafm-lg\">\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.9028em;vertical-align:-0.2083em;\"><\/span><span class=\"mord\"><span class=\"mord katex-accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.6944em;\"><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"accent-body\" style=\"left:-0.2222em;\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mbin mtight\">+<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2083em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"d\">1\u671f\u5148\u4e88\u6e2c<\/span><\/div>\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.9028em;vertical-align:-0.2083em;\"><\/span><span class=\"mord\"><span class=\"mord katex-accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.6944em;\"><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord mathnormal\">x<\/span><\/span><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"accent-body\" style=\"left:-0.2222em;\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mbin mtight\">+<\/span><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2083em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"d\">2\u671f\u5148\u4e88\u6e2c<\/span><\/div>\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.5806em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u73fe\u5728\uff08\u6642\u70b9t\uff09\u306e\u5b9f\u6e2c\u5024<\/span><\/div>\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1.1523em;vertical-align:-0.1944em;\"><\/span><span class=\"mord\"><span class=\"mord katex-accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.9579em;\"><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord mathnormal\">b<\/span><\/span><span style=\"top:-3.2634em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"accent-body\" style=\"left:-0.25em;\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\">\u00a0<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord katex-accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.9579em;\"><span style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord mathnormal\">b<\/span><\/span><span style=\"top:-3.2634em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"accent-body\" style=\"left:-0.25em;\"><span class=\"mord\">^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"d\">AR(1)\uff08\u81ea\u5df1\u56de\u5e30\u30e2\u30c7\u30eb\uff09\u306e\u5207\u7247\u30fb\u50be\u304d\u306e\u63a8\u5b9a\u5024<\/span><\/div>\n<\/div>\n<div class=\"cfafm-u\"><b>\u4f7f\u3044\u3069\u3053\u308d\uff1a<\/b>AR(1)\u30e2\u30c7\u30eb\u30671\u671f\u5148\u306e\u4e88\u6e2c\u5024\u3092\u6c42\u3081\u3001\u305d\u308c\u3092\u518d\u3073\u5f0f\u306b\u4ee3\u5165\u3057\u30662\u671f\u5148\u4ee5\u964d\u3092\u4e88\u6e2c\u3059\u308b\u9023\u9396\u5247\u306e\u5f0f\u3002<\/div>\n<\/div>\n<div class=\"cfafm-c\">\n<div class=\"nm\">11. 1\u968e\u5dee\u5206AR(2)\u30e2\u30c7\u30eb\u306e\u4e88\u6e2c<\/div>\n<div class=\"ne\">First-Differenced AR(2) Forecast<\/div>\n<div class=\"cfafm-x\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8333em;vertical-align:-0.15em;\"><\/span><span class=\"mord\">\u0394<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8444em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">b<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.9028em;vertical-align:-0.2083em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">b<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u0394<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2083em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.9028em;vertical-align:-0.2083em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">b<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u0394<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2083em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right:1em;\"><\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\">\u0394<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.7333em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6389em;vertical-align:-0.2083em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2083em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/div>\n<div class=\"cfafm-lg\">\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8333em;vertical-align:-0.15em;\"><\/span><span class=\"mord\">\u0394<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u6642\u70b9t\u306e\u6c34\u6e96\u306e1\u968e\u5dee\u5206\uff08x_t \u2212 x_{t\u22121}\uff09<\/span><\/div>\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8917em;vertical-align:-0.2083em;\"><\/span><span class=\"mord\">\u0394<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2083em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\">\u00a0<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\">\u0394<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2083em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"d\">1\u671f\u524d\u30fb2\u671f\u524d\u306e1\u968e\u5dee\u5206\uff08\u30e9\u30b01\u30fb\u30e9\u30b02\uff09<\/span><\/div>\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8444em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">b<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u5207\u7247<\/span><\/div>\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">b<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\">\u00a0<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">b<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u5dee\u5206\u7cfb\u5217\u306e\u30e9\u30b01\u30fb\u30e9\u30b02\u306e\u4fc2\u6570<\/span><\/div>\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6389em;vertical-align:-0.2083em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2806em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">t<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\">\u00a0<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">t<\/span><span class=\"mbin mtight\">\u2212<\/span><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2083em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u6642\u70b9t\u30fb1\u671f\u524d\u306e\u6c34\u6e96\uff08\u5dee\u5206\u304b\u3089\u5fa9\u5143\u3059\u308b\u5143\u306e\u7cfb\u5217\uff09<\/span><\/div>\n<\/div>\n<div class=\"cfafm-u\"><b>\u4f7f\u3044\u3069\u3053\u308d\uff1a<\/b>\u5358\u4f4d\u6839\u3092\u3082\u3064\u7cfb\u5217\u30921\u968e\u306e\u968e\u5dee\u3067\u5b9a\u5e38\u5316\u3057\u3066\u81ea\u5df1\u56de\u5e30\uff08AR\uff09\u30e2\u30c7\u30eb\u3092\u5f53\u3066\u306f\u3081\u308b\u5f0f\u3002\u968e\u5dee\u306e\u4e88\u6e2c\u5024\u306b\u76f4\u8fd1\u306e\u6c34\u6e96\u3092\u52a0\u3048\u3066\u5143\u306e\u7cfb\u5217\u306e\u4e88\u6e2c\u306b\u623b\u3059\u3002<\/div>\n<\/div>\n<div class=\"cfafm-c\">\n<div class=\"nm\">12. \u4e8c\u4e57\u5e73\u5747\u5e73\u65b9\u6839\u8aa4\u5dee(RMSE)<\/div>\n<div class=\"ne\">Root Mean Squared Error (RMSE)<\/div>\n<div class=\"cfafm-x\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6833em;\"><\/span><span class=\"mord text\"><span class=\"mord\">RMSE<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:2.44em;vertical-align:-0.7036em;\"><\/span><span class=\"mord sqrt\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.7364em;\"><span class=\"svg-align\" style=\"top:-4.4em;\"><span class=\"pstrut\" style=\"height:4.4em;\"><\/span><span class=\"mord\" style=\"padding-left:1em;\"><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.4911em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">m<\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8141em;\"><span style=\"top:-2.4519em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2481em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8141em;\"><span style=\"top:-2.4519em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.2481em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"minner\">\u22ef<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8141em;\"><span style=\"top:-2.453em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">m<\/span><\/span><\/span><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.247em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.686em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><span style=\"top:-3.6964em;\"><span class=\"pstrut\" style=\"height:4.4em;\"><\/span><span class=\"hide-tail\" style=\"min-width:1.02em;height:2.48em;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"400em\" height=\"2.48em\" viewBox=\"0 0 400000 2592\" preserveAspectRatio=\"xMinYMin slice\"><path d=\"M424,2478\nc-1.3,-0.7,-38.5,-172,-111.5,-514c-73,-342,-109.8,-513.3,-110.5,-514\nc0,-2,-10.7,14.3,-32,49c-4.7,7.3,-9.8,15.7,-15.5,25c-5.7,9.3,-9.8,16,-12.5,20\ns-5,7,-5,7c-4,-3.3,-8.3,-7.7,-13,-13s-13,-13,-13,-13s76,-122,76,-122s77,-121,77,-121\ns209,968,209,968c0,-2,84.7,-361.7,254,-1079c169.3,-717.3,254.7,-1077.7,256,-1081\nl0 -0c4,-6.7,10,-10,18,-10 H400000\nv40H1014.6\ns-87.3,378.7,-272.6,1166c-185.3,787.3,-279.3,1182.3,-282,1185\nc-2,6,-10,9,-24,9\nc-8,0,-12,-0.7,-12,-2z M1001 80\nh400000v40h-400000z\"\/><\/svg><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7036em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/div>\n<div class=\"cfafm-lg\">\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6833em;\"><\/span><span class=\"mord text\"><span class=\"mord\">RMSE<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u4e8c\u4e57\u5e73\u5747\u5e73\u65b9\u6839\u8aa4\u5dee\uff08Root Mean Squared Error\uff09<\/span><\/div>\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\">\u00a0<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\">\u00a0<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"minner\">\u2026<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\">\u00a0<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">e<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1514em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">m<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u7b2c1\u671f\u30fb\u7b2c2\u671f\u2026\u7b2cm\u671f\u306e\u4e88\u6e2c\u8aa4\u5dee\uff08\u5b9f\u6e2c\u2212\u4e88\u6e2c\uff09<\/span><\/div>\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.4306em;\"><\/span><span class=\"mord mathnormal\">m<\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u6a19\u672c\u5916\u4e88\u6e2c\u306e\u671f\u9593\u6570<\/span><\/div>\n<\/div>\n<div class=\"cfafm-u\"><b>\u4f7f\u3044\u3069\u3053\u308d\uff1a<\/b>\u4e88\u6e2c\u8aa4\u5dee\u306e2\u4e57\u5e73\u5747\u306e\u5e73\u65b9\u6839\u3002\u8907\u6570\u306e\u6642\u7cfb\u5217\u30e2\u30c7\u30eb\u306e\u30b5\u30f3\u30d7\u30eb\u5916\u4e88\u6e2c\u7cbe\u5ea6\u3092\u6bd4\u3079\u308b\u57fa\u6e96\u3067\u3001\u5024\u304c\u5c0f\u3055\u3044\u307b\u3069\u7cbe\u5ea6\u304c\u9ad8\u3044\u3002<\/div>\n<\/div>\n<div class=\"cfafm-c\">\n<div class=\"nm\">13. \u30c0\u30fc\u30d3\u30f3\u30fb\u30ef\u30c8\u30bd\u30f3\u7d71\u8a08\u91cf<\/div>\n<div class=\"ne\">Durbin\u2013Watson Statistic<\/div>\n<div class=\"cfafm-x\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6833em;\"><\/span><span class=\"mord text\"><span class=\"mord\">DW<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">\u2248<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\">2<\/span><span class=\"mspace\" style=\"margin-right:0.1667em;\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:1em;vertical-align:-0.25em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">r<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/div>\n<div class=\"cfafm-lg\">\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6833em;\"><\/span><span class=\"mord text\"><span class=\"mord\">DW<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u30c0\u30fc\u30d3\u30f3\u30fb\u30ef\u30c8\u30bd\u30f3\u7d71\u8a08\u91cf\uff08Durbin\u2013Watson\uff09\u30020\u301c4\u306e\u5024\u3092\u3068\u308b<\/span><\/div>\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.5806em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.0278em;\">r<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3011em;\"><span style=\"top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u6b8b\u5dee\u306e1\u6b21\u81ea\u5df1\u76f8\u95a2<\/span><\/div>\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8444em;vertical-align:-0.15em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">d<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3361em;\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"><\/span><span class=\"katex-sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\" style=\"margin-right:0.0197em;\">l<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"d\">\uff08\u95a2\u9023\uff09\u4e0b\u5074\u81e8\u754c\u5024\uff08DW\u304c\u3053\u308c\u3092\u4e0b\u56de\u308b\u3068\u6b63\u306e\u7cfb\u5217\u76f8\u95a2\u3068\u5224\u65ad\uff09<\/span><\/div>\n<\/div>\n<div class=\"cfafm-u\"><b>\u4f7f\u3044\u3069\u3053\u308d\uff1a<\/b>\u30c8\u30ec\u30f3\u30c9\u30fb\u30e2\u30c7\u30eb\u306a\u3069\u306e\u6b8b\u5dee\u306b1\u6b21\u306e\u7cfb\u5217\u76f8\u95a2\u304c\u3042\u308b\u304b\u3092\u5224\u5b9a\u3059\u308b\u7d71\u8a08\u91cf\u3002\u5024\u304c2\u306b\u8fd1\u3051\u308c\u3070\u7cfb\u5217\u76f8\u95a2\u306f\u306a\u3044\u3068\u307f\u306a\u3059\u3002<\/div>\n<\/div>\n<h3 id=\"l2-quants-f-lm7\">LM7 Big Data Projects\uff08\u30d3\u30c3\u30b0\u30c7\u30fc\u30bf\u30fb\u30d7\u30ed\u30b8\u30a7\u30af\u30c8\uff09<\/h3>\n<div class=\"cfagl-lm\">\u3053\u306e\u5358\u5143\u306e\u8981\u70b9\u89e3\u8aac\uff1a<a href=\"https:\/\/triumphmind.com\/cfa\/2026\/09\/22\/cfa-l2-quants-lm7\/\">LM7 \u30d3\u30c3\u30b0\u30c7\u30fc\u30bf\u30fb\u30d7\u30ed\u30b8\u30a7\u30af\u30c8<\/a><\/div>\n<div class=\"cfafm-c\">\n<div class=\"nm\">14. \u5206\u985e\u306e\u6b63\u89e3\u7387(Accuracy)<\/div>\n<div class=\"ne\">Classification Accuracy<\/div>\n<div class=\"cfafm-x\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8778em;vertical-align:-0.1944em;\"><\/span><span class=\"mord text\"><span class=\"mord\">Accuracy<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:2.1297em;vertical-align:-0.7693em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.3603em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord text\"><span class=\"mord\">TP<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord text\"><span class=\"mord\">FP<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord text\"><span class=\"mord\">TN<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord text\"><span class=\"mord\">FN<\/span><\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord text\"><span class=\"mord\">TP<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord text\"><span class=\"mord\">TN<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7693em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/div>\n<div class=\"cfafm-lg\">\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.8778em;vertical-align:-0.1944em;\"><\/span><span class=\"mord text\"><span class=\"mord\">Accuracy<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u6b63\u89e3\u7387\uff1a\u5168\u4ef6\u306e\u3046\u3061\u6b63\u3057\u304f\u5206\u985e\u3067\u304d\u305f\u5272\u5408<\/span><\/div>\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6833em;\"><\/span><span class=\"mord text\"><span class=\"mord\">TP<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u771f\u967d\u6027\uff08True Positive\uff09\uff1a\u6b63\u3057\u304f1\u3068\u4e88\u6e2c<\/span><\/div>\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6833em;\"><\/span><span class=\"mord text\"><span class=\"mord\">TN<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u771f\u9670\u6027\uff08True Negative\uff09\uff1a\u6b63\u3057\u304f0\u3068\u4e88\u6e2c<\/span><\/div>\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6833em;\"><\/span><span class=\"mord text\"><span class=\"mord\">FP<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u507d\u967d\u6027\uff08False Positive\uff09\uff1a\u8aa4\u3063\u30661\u3068\u4e88\u6e2c\uff08\u30bf\u30a4\u30d7I\u30a8\u30e9\u30fc\uff09<\/span><\/div>\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6833em;\"><\/span><span class=\"mord text\"><span class=\"mord\">FN<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u507d\u9670\u6027\uff08False Negative\uff09\uff1a\u8aa4\u3063\u30660\u3068\u4e88\u6e2c\uff08\u30bf\u30a4\u30d7II\u30a8\u30e9\u30fc\uff09<\/span><\/div>\n<\/div>\n<div class=\"cfafm-u\"><b>\u4f7f\u3044\u3069\u3053\u308d\uff1a<\/b>\u6df7\u540c\u884c\u5217\u304b\u3089\u3001\u5168\u4ef6\u306e\u3046\u3061\u6b63\u3057\u304f\u5206\u985e\u3067\u304d\u305f\u5272\u5408\u3092\u6c42\u3081\u308b\u5f0f\u3002\u5206\u985e\u30e2\u30c7\u30eb\u306e\u5168\u4f53\u7684\u306a\u6b63\u78ba\u3055\u3092\u8a55\u4fa1\u3059\u308b\u5834\u9762\u3067\u4f7f\u3046\u3002<\/div>\n<\/div>\n<div class=\"cfafm-c\">\n<div class=\"nm\">15. \u9069\u5408\u7387(Precision)\u3068\u518d\u73fe\u7387(Recall)<\/div>\n<div class=\"ne\">Precision and Recall<\/div>\n<div class=\"cfafm-x\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6833em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">P<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:2.1297em;vertical-align:-0.7693em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.3603em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord text\"><span class=\"mord\">TP<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord text\"><span class=\"mord\">FP<\/span><\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord text\"><span class=\"mord\">TP<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7693em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6833em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0077em;\">R<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:2.1297em;vertical-align:-0.7693em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.3603em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord text\"><span class=\"mord\">TP<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord text\"><span class=\"mord\">FN<\/span><\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord text\"><span class=\"mord\">TP<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7693em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/div>\n<div class=\"cfafm-lg\">\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6833em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">P<\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u9069\u5408\u7387\uff08Precision\uff09\uff1a\u967d\u6027\u3068\u4e88\u6e2c\u3057\u305f\u3046\u3061\u6b63\u3057\u3044\u5272\u5408<\/span><\/div>\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6833em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0077em;\">R<\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u518d\u73fe\u7387\uff08Recall\uff09\/\u611f\u5ea6\uff1a\u5b9f\u969b\u306e\u967d\u6027\u3092\u6349\u3048\u305f\u5272\u5408<\/span><\/div>\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6833em;\"><\/span><span class=\"mord text\"><span class=\"mord\">TP<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u771f\u967d\u6027\uff08True Positive\uff09<\/span><\/div>\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6833em;\"><\/span><span class=\"mord text\"><span class=\"mord\">FP<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u507d\u967d\u6027\uff08False Positive\uff09<\/span><\/div>\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6833em;\"><\/span><span class=\"mord text\"><span class=\"mord\">FN<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u507d\u9670\u6027\uff08False Negative\uff09<\/span><\/div>\n<\/div>\n<div class=\"cfafm-u\"><b>\u4f7f\u3044\u3069\u3053\u308d\uff1a<\/b>\u9069\u5408\u7387\u306f\u967d\u6027\u4e88\u6e2c\u306e\u3046\u3061\u6b63\u89e3\u306e\u5272\u5408\u3001\u518d\u73fe\u7387\u306f\u5b9f\u969b\u306e\u967d\u6027\u306e\u3046\u3061\u691c\u51fa\u3067\u304d\u305f\u5272\u5408\u3092\u8868\u3059\u3002\u507d\u967d\u6027\u3068\u507d\u9670\u6027\u306e\u3069\u3061\u3089\u3092\u91cd\u8996\u3059\u308b\u304b\u3067\u4f7f\u3044\u5206\u3051\u308b\u3002<\/div>\n<\/div>\n<div class=\"cfafm-c\">\n<div class=\"nm\">16. F1\u30b9\u30b3\u30a2<\/div>\n<div class=\"ne\">F1 Score<\/div>\n<div class=\"cfafm-x\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6833em;\"><\/span><span class=\"mord text\"><span class=\"mord\">F1<\/span><\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><span class=\"mrel\">=<\/span><span class=\"mspace\" style=\"margin-right:0.2778em;\"><\/span><\/span><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:2.1297em;vertical-align:-0.7693em;\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.3603em;\"><span style=\"top:-2.314em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">P<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">+<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0077em;\">R<\/span><\/span><\/span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"><\/span><\/span><span style=\"top:-3.677em;\"><span class=\"pstrut\" style=\"height:3em;\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">P<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mbin\">\u00d7<\/span><span class=\"mspace\" style=\"margin-right:0.2222em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0077em;\">R<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7693em;\"><span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><\/span><\/span><\/span><\/span><\/div>\n<div class=\"cfafm-lg\">\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6833em;\"><\/span><span class=\"mord text\"><span class=\"mord\">F1<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"d\">F1\u30b9\u30b3\u30a2\uff1a\u9069\u5408\u7387\u3068\u518d\u73fe\u7387\u306e\u8abf\u548c\u5e73\u5747<\/span><\/div>\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6833em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">P<\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u9069\u5408\u7387\uff08Precision\uff09= TP\/(TP+FP)\u3002TP = \u771f\u967d\u6027\u3001FP = \u507d\u967d\u6027<\/span><\/div>\n<div><span class=\"s\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"katex-base\"><span class=\"katex-strut\" style=\"height:0.6833em;\"><\/span><span class=\"mord mathnormal\" style=\"margin-right:0.0077em;\">R<\/span><\/span><\/span><\/span><\/span><span class=\"d\">\u518d\u73fe\u7387\uff08Recall\uff09= TP\/(TP+FN)\u3002FN = \u507d\u9670\u6027<\/span><\/div>\n<\/div>\n<div class=\"cfafm-u\"><b>\u4f7f\u3044\u3069\u3053\u308d\uff1a<\/b>\u9069\u5408\u7387\u3068\u518d\u73fe\u7387\u306e\u8abf\u548c\u5e73\u5747\u3002\u30af\u30e9\u30b9\u304c\u4e0d\u5747\u8861\u306a\u30c7\u30fc\u30bf\u3067\u5206\u985e\u30e2\u30c7\u30eb\u306e\u6027\u80fd\u30921\u3064\u306e\u6570\u5024\u3067\u8a55\u4fa1\u3059\u308b\u5834\u9762\u3067\u4f7f\u3046\u3002<\/div>\n<\/div>\n<h2>\u3042\u308f\u305b\u3066\u4f7f\u3044\u305f\u3044\u30da\u30fc\u30b8<\/h2>\n<ul>\n<li><a href=\"https:\/\/triumphmind.com\/cfa\/2026\/09\/24\/cfa-l2-quants-glossary\/\">CFA\u00ae\ufe0e Level 2 Quants \u7528\u8a9e\u96c6\uff08\u82f1\u8a9e\u30fb\u65e5\u672c\u8a9e\u8a33\u30fb\u610f\u5473\uff09<\/a><\/li>\n<li><a href=\"https:\/\/triumphmind.com\/cfa\/cfa-level2-formulas\/\">CFA\u00ae\ufe0e Level 2 \u516c\u5f0f\u96c6\uff08\u5168\u79d1\u76ee\u306e\u4e00\u89a7\uff09<\/a><\/li>\n<li><a href=\"https:\/\/triumphmind.com\/cfa\/cfa-curriculum\/#l2-quants\">CFA\u00ae\ufe0e \u5b66\u7fd2\u5185\u5bb9\u306e\u76ee\u6b21\uff08Level 2 Quantitative Methods\uff09<\/a><\/li>\n<\/ul>\n<h2>\u52b9\u7387\u3088\u304f\u5b66\u3076\u306b\u306f FA-Academy<\/h2>\n<p>CFA\u00ae\ufe0e\u306e\u5354\u4f1a\u30c6\u30ad\u30b9\u30c8\u306f\u82f1\u8a9e\u3067\u5206\u91cf\u3082\u591a\u304f\u3001\u7528\u8a9e\u3084\u516c\u5f0f\u3092\u82f1\u8a9e\u3060\u3051\u3067\u7406\u89e3\u3057\u3066\u3044\u304f\u306e\u306f\u5927\u304d\u306a\u8ca0\u62c5\u3067\u3059\u3002<\/p>\n<p>FA-Academy\uff08Financial Analyst Academy\uff09\u306f\u3001<strong>\u65e5\u672c\u8a9e\u3067\u5b66\u3079\u308b\u6570\u5c11\u306a\u3044CFA\u00ae\ufe0e\u8a66\u9a13\u30b5\u30dd\u30fc\u30c8<\/strong>\u3067\u3059\u3002\u3053\u308c\u307e\u3067 Level 1 \u304b\u3089 Level 3 \u307e\u3067\u591a\u304f\u306e\u5408\u683c\u8005\u3092\u8f29\u51fa\u3057\u3066\u304a\u308a\u3001\u5408\u683c\u8005\u306e\u65b9\u3005\u3068\u306e\u5bfe\u8ac7\u3082\u6570\u591a\u304f\u516c\u958b\u3057\u3066\u3044\u307e\u3059\u3002\u3069\u3093\u306a\u65b9\u304c\u3001\u3069\u306e\u3088\u3046\u306b\u5408\u683c\u3055\u308c\u305f\u306e\u304b\u306f<a href=\"https:\/\/triumphmind.com\/cfa\/category\/gokaku\/\" target=\"_blank\" rel=\"noopener\">\u5408\u683c\u8005\u5bfe\u8ac7\u30fb\u5408\u683c\u4f53\u9a13\u8ac7\u306e\u4e00\u89a7<\/a>\u304b\u3089\u3054\u89a7\u3044\u305f\u3060\u3051\u307e\u3059\u3002<\/p>\n<ul>\n<li><a href=\"https:\/\/triumphmind.com\/cfa\/present1\/\" target=\"_blank\" rel=\"noopener\">Level 1 \u65e5\u672c\u8a9e\u8981\u70b9\u96c6\u306e\u7121\u6599\u30b5\u30f3\u30d7\u30eb\u3092\u53d7\u3051\u53d6\u308b\uff087\u65e5\u9593\u30e1\u30fc\u30eb\u8b1b\u5ea7\uff09<\/a><\/li>\n<li><a href=\"https:\/\/timerex.net\/s\/cfa.tips.slack_2a23\/e72e883e\/\" target=\"_blank\" rel=\"noopener\">\u7121\u6599\u500b\u5225\u9762\u8ac7\u3092\u4e88\u7d04\u3059\u308b\uff08\u5b66\u7fd2\u8a08\u753b\u306e\u3054\u76f8\u8ac7\uff09<\/a><\/li>\n<li><a href=\"https:\/\/triumphmind.com\/cfa\/course\/\" target=\"_blank\" rel=\"noopener\">\u53d7\u8b1b\u6848\u5185\uff08\u30b3\u30fc\u30b9\u4e00\u89a7\u30fb\u53d7\u8b1b\u6599\uff09\u3092\u898b\u308b<\/a><\/li>\n<li><a href=\"https:\/\/triumphmind.com\/cfa\/side_by_side\/\" target=\"_blank\" rel=\"noopener\">Level 2 Leveraged Support Course\uff08\u7528\u8a9e\u96c6\u30fb\u516c\u5f0f\u96c6\u306e\u6574\u7406\u8cc7\u6599\u3064\u304d\uff09\u3092\u898b\u308b<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>CFA\u00ae\ufe0e Level 2 Quantitative Methods\uff08\u6570\u91cf\u5206\u6790\uff09\u306e\u91cd\u8981\u516c\u5f0f16\u672c\u3092\u3001\u6700\u65b0\u7248\u30ab\u30ea\u30ad\u30e5\u30e9\u30e0\u306e\u5358\u5143\uff08LM\uff09\u5225\u306b\u3001\u6570\u5f0f\u30fb\u8a18\u53f7\u306e\u610f\u5473\u30fb\u4f7f\u3044\u3069\u3053\u308d\u3068\u3042\u308f\u305b\u3066\u6574\u7406\u3057\u305f\u516c\u5f0f\u96c6\u3067\u3059\u3002<\/p>\n","protected":false},"author":1,"featured_media":11625,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jin_ogp_image_url":"","_jin_last_featured_id":0,"footnotes":""},"categories":[102],"tags":[],"class_list":["post-11426","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-formulas"],"_links":{"self":[{"href":"https:\/\/triumphmind.com\/cfa\/wp-json\/wp\/v2\/posts\/11426","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/triumphmind.com\/cfa\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/triumphmind.com\/cfa\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/triumphmind.com\/cfa\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/triumphmind.com\/cfa\/wp-json\/wp\/v2\/comments?post=11426"}],"version-history":[{"count":5,"href":"https:\/\/triumphmind.com\/cfa\/wp-json\/wp\/v2\/posts\/11426\/revisions"}],"predecessor-version":[{"id":11929,"href":"https:\/\/triumphmind.com\/cfa\/wp-json\/wp\/v2\/posts\/11426\/revisions\/11929"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/triumphmind.com\/cfa\/wp-json\/wp\/v2\/media\/11625"}],"wp:attachment":[{"href":"https:\/\/triumphmind.com\/cfa\/wp-json\/wp\/v2\/media?parent=11426"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/triumphmind.com\/cfa\/wp-json\/wp\/v2\/categories?post=11426"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/triumphmind.com\/cfa\/wp-json\/wp\/v2\/tags?post=11426"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}