{"id":4753,"date":"2026-08-15T18:45:33","date_gmt":"2026-08-15T09:45:33","guid":{"rendered":"https:\/\/best-biostatistics.com\/toukei-er\/?p=4753"},"modified":"2026-08-15T18:45:34","modified_gmt":"2026-08-15T09:45:34","slug":"anova-is-not-just-for-comparing-means-the-real-reason-we-use-anova-for-model-selection-and-practical-fit-evaluation","status":"publish","type":"post","link":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/anova-is-not-just-for-comparing-means-the-real-reason-we-use-anova-for-model-selection-and-practical-fit-evaluation\/","title":{"rendered":"ANOVA\u306f\u300c\u5e73\u5747\u306e\u6bd4\u8f03\u300d\u3058\u3083\u306a\u3044\uff01\u56de\u5e30\u30e2\u30c7\u30eb\u306e\u6bd4\u8f03\u306b anova() \u3092\u4f7f\u3046\u672c\u5f53\u306e\u7406\u7531\u3068\u3042\u3066\u306f\u307e\u308a\u8a55\u4fa1\u306e\u5b9f\u8df5"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">\u300c\u5148\u751f\uff01\u30e2\u30c7\u30eb\u306b\u65b0\u3057\u3044\u30ea\u30b9\u30af\u56e0\u5b50\uff08$X_2$\uff09\u3092\u8ffd\u52a0\u3057\u3066\u307f\u305f\u306e\u3067\u3059\u304c\u3001\u3053\u306e\u5909\u6570\u3092\u8ffd\u52a0\u3057\u305f\u3053\u3068\u3067\u30e2\u30c7\u30eb\u306e\u3042\u3066\u306f\u307e\u308a\uff08\u8aac\u660e\u529b\uff09\u304c\u672c\u5f53\u306b\u826f\u304f\u306a\u3063\u305f\u306e\u304b\u3001\u5ba2\u89b3\u7684\u306b\u8a55\u4fa1\u3059\u308b\u65b9\u6cd5\u304c\u5206\u304b\u308a\u307e\u305b\u3093\u300d<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u300c\u305d\u308c\u306a\u3089\u3001\u30b7\u30f3\u30d7\u30eb\u306a\u30e2\u30c7\u30eb\uff08<code>model1<\/code>\uff09\u3068\u5909\u6570\u3092\u5897\u3084\u3057\u305f\u30e2\u30c7\u30eb\uff08<code>model2<\/code>\uff09\u3092\u4f5c\u3063\u3066\u3001R\u3067 <code>anova(model1, model2)<\/code> \u3092\u5b9f\u884c\u3057\u3066\u6bd4\u8f03\u3059\u308c\u3070\u826f\u3044\u3088\u300d<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u2026\u2026\u6307\u5c0e\u533b\u3084\u5148\u8f29\u304b\u3089\u305d\u3046\u30a2\u30c9\u30d0\u30a4\u30b9\u3055\u308c\u3066\u3001\u982d\u306e\u4e0a\u306b\u300c\uff1f\uff1f\uff1f\u300d\u304c\u6d6e\u304b\u3093\u3060\u7d4c\u9a13\u306f\u306a\u3044\u3060\u308d\u3046\u304b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u300c\u3048\u3063\uff1f ANOVA\uff08\u5206\u6563\u5206\u6790\uff09\u3063\u3066\u30013\u7fa4\u4ee5\u4e0a\u306e\u5e73\u5747\u5024\u3092\u6bd4\u8f03\u3059\u308b\u624b\u6cd5\u3058\u3083\u306a\u3044\u306e\uff1f \u4eca\u6bd4\u8f03\u3057\u305f\u3044\u306e\u306f\u56de\u5e30\u30e2\u30c7\u30eb\u306e\u300e\u3042\u3066\u306f\u307e\u308a\u306e\u826f\u3055\u300f\u3067\u3042\u3063\u3066\u3001\u5e73\u5747\u5024\u306a\u3093\u3066\u3069\u3053\u306b\u3082\u51fa\u3066\u3053\u306a\u3044\u306e\u306b\u3001\u306a\u305c <code>anova<\/code> \u95a2\u6570\u3092\u4f7f\u3046\u306e\uff1f\u300d<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5165\u9580\u66f8\u3067\u300ct\u691c\u5b9a\uff1d2\u7fa4\u306e\u5e73\u5747\u6bd4\u8f03\u300d\u300cANOVA\uff1d3\u7fa4\u4ee5\u4e0a\u306e\u5e73\u5747\u6bd4\u8f03\u300d\u300c\u56de\u5e30\u5206\u6790\uff1d\u95a2\u4fc2\u6027\u306e\u4e88\u6e2c\u300d\u3068\u5225\u3005\u306e\u30c4\u30fc\u30eb\u3068\u3057\u3066\u6697\u8a18\u3057\u3066\u3057\u307e\u3046\u3068\u3001\u3053\u306e\u5834\u9762\u3067\u6587\u8108\u304c\u5d29\u58ca\u3057\u3001\u5f37\u3044\u4e0d\u4fe1\u611f\u3068\u6df7\u4e71\u306b\u9665\u3063\u3066\u3057\u307e\u3046\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3057\u304b\u3057\u3001\u7d50\u8ad6\u304b\u3089\u8a00\u3048\u3070\u3001<strong>\u300c3\u7fa4\u4ee5\u4e0a\u306e\u5e73\u5747\u306e\u6bd4\u8f03\u300d\u3082\u300c\u56de\u5e30\u30e2\u30c7\u30eb\u306e\u3042\u3066\u306f\u307e\u308a\u6bd4\u8f03\u300d\u3082\u3001\u88cf\u3067\u3084\u3063\u3066\u3044\u308b\u8a08\u7b97\u306e\u672c\u8cea\u306f100%\u5b8c\u5168\u306b\u540c\u3058<\/strong>\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u672c\u8a18\u4e8b\u3067\u306f\u3001\u300cANOVA \uff1d \u5e73\u5747\u5024\u306e\u6bd4\u8f03\u300d\u3068\u3044\u3046\u4e38\u6697\u8a18\u306e\u7f60\u3092\u6253\u3061\u7834\u308a\u3001ANOVA\u306e\u672c\u8cea\u3067\u3042\u308b <strong>&#8220;Analysis of Variance&#8221;\uff08\u3070\u3089\u3064\u304d\/\u5206\u6563\u306e\u5206\u89e3\u3068\u6bd4\u8f03\uff09<\/strong> \u3092\u89e3\u304d\u660e\u304b\u3059\u3002\u3055\u3089\u306b\u3001\u30cd\u30b9\u30c8\u30e2\u30c7\u30eb\u306e\u8003\u3048\u65b9\u304b\u3089 <code>anova(model1, model2)<\/code> \u306eR\u3067\u306e\u5b9f\u8df5\u624b\u9806\u3001AIC\/BIC\u3068\u306e\u9069\u5207\u306a\u4f7f\u3044\u5206\u3051\u307e\u3067\u3092\u5fb9\u5e95\u89e3\u8aac\u3059\u308b\u3002<\/p>\n\n\n\n<!--more-->\n\n\n\n<h2 class=\"wp-block-heading\">1. \u300c\u5e73\u5747\u306e\u6bd4\u8f03\u306a\u306e\u306b\u3001\u306a\u305c\u30e2\u30c7\u30eb\u6bd4\u8f03\u3067 anova \u95a2\u6570\uff1f\u300d\u5b66\u7fd2\u8005\u304c\u9665\u308b\u6697\u8a18\u306e\u7f60<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u81e8\u5e8a\u7814\u7a76\u3084\u30c7\u30fc\u30bf\u89e3\u6790\u306e\u73fe\u5834\u3067\u3001\u30e2\u30c7\u30eb\u306b\u5909\u6570\u3084\u4ea4\u4e92\u4f5c\u7528\u9805\u3092\u8ffd\u52a0\u3057\u305f\u969b\u3001\u300c\u305d\u306e\u5909\u6570\u3092\u8ffd\u52a0\u3059\u308b\u4fa1\u5024\u304c\u672c\u5f53\u306b\u3042\u3063\u305f\u306e\u304b\uff08\u30e2\u30c7\u30eb\u306e\u3042\u3066\u306f\u307e\u308a\u304c\u6709\u610f\u306b\u5411\u4e0a\u3057\u305f\u304b\uff09\u300d\u3092\u5224\u5b9a\u3057\u305f\u3044\u5834\u9762\u306f\u983b\u7e41\u306b\u8a2a\u308c\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3053\u306e\u3068\u304dR\u30e6\u30fc\u30b6\u30fc\u304c\u5fc5\u305a\u51fa\u4f1a\u3046\u306e\u304c <code>anova(model1, model2)<\/code> \u3068\u3044\u3046\u30b3\u30fc\u30c9\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3057\u304b\u3057\u3001\u591a\u304f\u306e\u5b66\u7fd2\u8005\u306f\u3053\u3053\u3067\u632b\u6298\u3059\u308b\u3002\u300c\u81ea\u5206\u306f\u5e73\u5747\u5024\u306e\u6bd4\u8f03\u3092\u3057\u305f\u3044\u308f\u3051\u3067\u306f\u306a\u3044\u306e\u306b\u3001\u306a\u305cANOVA\u306a\u306e\u304b\uff1f\u300d\u3068\u3044\u3046\u7591\u554f\u304c\u62ed\u3048\u306a\u3044\u304b\u3089\u3060\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3053\u306e\u6df7\u4e71\u306e\u539f\u56e0\u306f\u3001\u65e5\u672c\u306e\u591a\u304f\u306e\u521d\u7d1a\u7d71\u8a08\u6559\u79d1\u66f8\u304c\u4ee5\u4e0b\u306e3\u3064\u3092\u300c\u307e\u3063\u305f\u304f\u5225\u306e\u9053\u5177\u300d\u3068\u3057\u3066\u6559\u3048\u8fbc\u3093\u3067\u3044\u308b\u70b9\u306b\u3042\u308b\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>t\u691c\u5b9a<\/strong>: 2\u3064\u306e\u30b0\u30eb\u30fc\u30d7\u306e\u5e73\u5747\u5024\u3092\u6bd4\u8f03\u3059\u308b<\/li>\n\n\n\n<li><strong>ANOVA\uff08\u5206\u6563\u5206\u6790\uff09<\/strong>: 3\u3064\u4ee5\u4e0a\u306e\u30b0\u30eb\u30fc\u30d7\u306e\u5e73\u5747\u5024\u3092\u6bd4\u8f03\u3059\u308b<\/li>\n\n\n\n<li><strong>\u5358\/\u591a\u5909\u91cf\u56de\u5e30\u5206\u6790<\/strong>: \u9023\u7d9a\u5909\u6570\u540c\u58eb\u306e\u76f4\u7dda\u95a2\u4fc2\u3084\u4e88\u6e2c\u3092\u884c\u3046<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">\u7d71\u8a08\u5b66\u306e\u6b74\u53f2\u7684\u7d4c\u7def\u306b\u3088\u308a\u540d\u524d\u3084\u4f7f\u3044\u65b9\u304c\u5206\u3051\u3089\u308c\u3066\u3044\u308b\u304c\u3001\u73fe\u4ee3\u306e\u7d71\u8a08\u5b66\u306b\u304a\u3044\u3066\u3053\u308c\u3089\u306f\u3059\u3079\u3066 <strong>\u4e00\u822c\u7dda\u5f62\u30e2\u30c7\u30eb\uff08General Linear Model: GLM\uff09<\/strong> \u3068\u3044\u30461\u3064\u306e\u5de8\u5927\u306a\u5358\u4e00\u30d5\u30ec\u30fc\u30e0\u30ef\u30fc\u30af\u306e\u4e2d\u3067\u5b8c\u5168\u306b\u7d71\u5408\u3055\u308c\u3066\u3044\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u300c\u5e73\u5747\u5024\u306e\u6bd4\u8f03\u300d\u3082\u300c\u30e2\u30c7\u30eb\u306e\u6bd4\u8f03\u300d\u3082\u3001\u672c\u8cea\u7684\u306b\u306f\u540c\u3058\u300c\u4e00\u822c\u7dda\u5f62\u30e2\u30c7\u30eb\u306e\u3042\u3066\u306f\u307e\u308a\u8a55\u4fa1\u300d\u3092\u884c\u3063\u3066\u3044\u308b\u306b\u904e\u304e\u306a\u3044\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">2. \u300c3\u7fa4\u4ee5\u4e0a\u306e\u5e73\u5747\u6bd4\u8f03\u300d\u3082\u5b9f\u306f\u56de\u5e30\u30e2\u30c7\u30eb\uff08\u30c0\u30df\u30fc\u5909\u6570\uff09\u3067\u3042\u308b<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u306a\u305c\u300c\u5e73\u5747\u5024\u306e\u6bd4\u8f03\u300d\u3068\u300c\u56de\u5e30\u30e2\u30c7\u30eb\u306e\u6bd4\u8f03\u300d\u304c\u540c\u3058\u306a\u306e\u304b\u3002\u305d\u306e\u7406\u7531\u3092\u66b4\u304f\u305f\u3081\u306b\u3001\u6700\u3082\u6a19\u6e96\u7684\u306a\u300c3\u7fa4\uff08A\u7fa4\u30fbB\u7fa4\u30fbC\u7fa4\uff09\u306e\u5e73\u5747\u5024\u306e\u6bd4\u8f03\uff081\u5143\u914d\u7f6e\u5206\u6563\u5206\u6790\uff09\u300d\u306e\u88cf\u5074\u3092\u898b\u3066\u307f\u3088\u3046\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A\u7fa4\u3092\u57fa\u6e96\uff08\u30ea\u30d5\u30a1\u30ec\u30f3\u30b9\uff09\u3068\u3057\u3001B\u7fa4\u30d5\u30e9\u30b0\uff08$\\text{GroupB}$\uff09\u3001C\u7fa4\u30d5\u30e9\u30b0\uff08$\\text{GroupC}$\uff09\u3068\u3044\u30462\u3064\u306e\u30c0\u30df\u30fc\u5909\u6570\u3092\u4f5c\u6210\u3059\u308b\u3068\u30013\u7fa4\u306e\u5e73\u5747\u5024\u6bd4\u8f03\u306f\u4ee5\u4e0b\u306e\u56de\u5e30\u30e2\u30c7\u30eb\u3068\u6570\u5b66\u7684\u306b\u5b8c\u5168\u4e00\u81f4\u3059\u308b\uff1a$$Y = \\beta_0 + \\beta_1 \\text{GroupB} + \\beta_2 \\text{GroupC} + \\epsilon$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3053\u3053\u3067\u3001\u305d\u308c\u305e\u308c\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u610f\u5473\u3092\u8003\u3048\u308b\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308b\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>$\\beta_0$: A\u7fa4\u306e\u5e73\u5747\u5024<\/li>\n\n\n\n<li>$\\beta_1$: A\u7fa4\u306b\u5bfe\u3059\u308bB\u7fa4\u306e\u5e73\u5747\u5024\u306e\u5dee<\/li>\n\n\n\n<li>$\\beta_2$: A\u7fa4\u306b\u5bfe\u3059\u308bC\u7fa4\u306e\u5e73\u5747\u5024\u306e\u5dee<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u3064\u307e\u308a\u3001\u5f93\u6765\u306e\u300c3\u7fa4\u306e\u5e73\u5747\u5024\u306b\u5dee\u304c\u3042\u308b\u304b\uff1f\u300d\u3068\u3044\u3046\u5206\u6563\u5206\u6790\uff08ANOVA\uff09\u306e\u5e30\u7121\u4eee\u8aac\uff08$H_0: \\mu_A = \\mu_B = \\mu_C$\uff09\u306f\u3001\u56de\u5e30\u30e2\u30c7\u30eb\u306e\u8a00\u8449\u3067\u8a00\u3044\u63db\u3048\u308b\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308b\uff1a<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\"><strong>\u300c\u30c0\u30df\u30fc\u5909\u6570\uff08<\/strong>$\\text{GroupB}, \\text{GroupC}$<strong>\uff09\u306e\u56de\u5e30\u4fc2\u6570\u304c\u3068\u3082\u306b<\/strong>$0$<strong>\u3067\u3042\u308b\uff08<\/strong>$\\beta_1 = \\beta_2 = 0$<strong>\uff09\u300d<\/strong><\/p>\n<\/blockquote>\n\n\n\n<p class=\"wp-block-paragraph\">\u3059\u306a\u308f\u3061\u30013\u7fa4\u6bd4\u8f03\u306eANOVA\u3068\u306f\u3001<strong>\u300c\u5207\u7247\u306e\u307f\u306e\u30b7\u30f3\u30d7\u30eb\u306a\u30e2\u30c7\u30eb\uff08<\/strong>$Y = \\beta_0$<strong>\uff09\u300d\u306b\u5bfe\u3057\u3066\u3001\u300c\u30b0\u30eb\u30fc\u30d7\u60c5\u5831\u3092\u52a0\u3048\u305f\u8907\u96d1\u306a\u30e2\u30c7\u30eb\uff08<\/strong>$Y = \\beta_0 + \\beta_1 \\text{GroupB} + \\beta_2 \\text{GroupC}$<strong>\uff09\u300d\u306e\u65b9\u304c\u3001\u30c7\u30fc\u30bf\u3092\u8aac\u660e\u3059\u308b\u80fd\u529b\uff08\u3042\u3066\u306f\u307e\u308a\uff09\u304c\u6709\u610f\u306b\u5411\u4e0a\u3057\u305f\u304b\u3092\u691c\u8a3c\u3057\u3066\u3044\u305f<\/strong>\u306e\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u300c\u5e73\u5747\u5024\u3092\u6bd4\u8f03\u3057\u3066\u3044\u305f\u300d\u3064\u3082\u308a\u304c\u3001\u79c1\u305f\u3061\u306f\u6700\u521d\u304b\u3089\u300c\u30e2\u30c7\u30eb\u306e\u6bd4\u8f03\u300d\u3092\u884c\u3063\u3066\u3044\u305f\u306e\u3060\u3002<\/p>\n\n\n\n<div id=\"biost-222633700\" class=\"biost- biost-entity-placement\"><p style=\"text-align: center;\"><span style=\"font-size: 20px;\"><strong><a href=\"https:\/\/best-biostatistics.com\/kmhl\">\uff1e\uff1e\u3082\u3046\u7d71\u8a08\u3067\u60a9\u3080\u306e\u306f\u7d42\u308f\u308a\u306b\u3057\u307e\u305b\u3093\u304b\uff1f\u00a0<\/a><\/strong><\/span><\/p>\r\n<a href=\"https:\/\/best-biostatistics.com\/kmhl\"><img class=\"aligncenter wp-image-2794 size-full\" src=\"https:\/\/best-biostatistics.com\/wp\/wp-content\/uploads\/2023\/11\/bn_r_03.png\" alt=\"\" width=\"500\" height=\"327\" \/><\/a>\r\n<p style=\"text-align: center;\"><span style=\"color: #ff0000; font-size: 20px;\"><strong><span class=\"marker2\">\u21911\u4e07\u4eba\u4ee5\u4e0a\u306e\u533b\u7642\u5f93\u4e8b\u8005\u304c\u8cfc\u8aad\u4e2d<\/span><\/strong><\/span><\/p><\/div><h2 class=\"wp-block-heading\">3. ANOVA\u306e\u672c\u8cea\u306f\u300c\u5206\u6563\uff08\u3070\u3089\u3064\u304d\uff09\u306e\u5206\u89e3\u3068\u6bd4\u8f03\u300d\u3067\u3042\u308b<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">ANOVA\u306e\u6b63\u5f0f\u540d\u79f0\u306f <strong>Analysis of Variance\uff08\u5206\u6563\u5206\u6790 \/ \u3070\u3089\u3064\u304d\u306e\u5206\u6790\uff09<\/strong> \u3067\u3042\u308b\u3002\u3053\u3053\u306b\u300c\u5e73\u5747\uff08Mean\uff09\u300d\u3068\u3044\u3046\u8a00\u8449\u306f\u4e00\u6587\u5b57\u3082\u5165\u3063\u3066\u3044\u306a\u3044\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">ANOVA\u306e\u672c\u8cea\u306f\u6587\u5b57\u901a\u308a\u3001<strong>\u30c7\u30fc\u30bf\u5168\u4f53\u304c\u6301\u3064\u3070\u3089\u3064\u304d\uff08\u5168\u5e73\u65b9\u548c \/ Total SS\uff09\u3092\u3001\u30e2\u30c7\u30eb\u3067\u8aac\u660e\u3067\u304d\u305f\u90e8\u5206\u3068\u8aac\u660e\u3067\u304d\u306a\u304b\u3063\u305f\u6b8b\u5dee\u306b\u5206\u89e3\u3057\u3001\u305d\u306e\u6bd4\u7387\uff08F\u5024\uff09\u3092\u898b\u308b\u3053\u3068<\/strong>\u306b\u3042\u308b\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3069\u3093\u306a\u8907\u96d1\u306a\u30e2\u30c7\u30eb\u3067\u3042\u3063\u3066\u3082\u3001\u30c7\u30fc\u30bf\u5168\u4f53\u306e\u3070\u3089\u3064\u304d\u306f\u5e38\u306b\u4ee5\u4e0b\u306e\u8db3\u3057\u7b97\u306b\u5206\u89e3\u3055\u308c\u308b\uff1a$$\\text{\u5168\u3070\u3089\u3064\u304d (Total SS)} = \\text{\u30e2\u30c7\u30eb\u3067\u8aac\u660e\u3067\u304d\u305f\u3070\u3089\u3064\u304d (Model SS)} + \\text{\u8aac\u660e\u3067\u304d\u306a\u304b\u3063\u305f\u6b8b\u5dee (Residual SS)}$$<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">F\u5024\uff08F-statistic\uff09\u306e\u76f4\u611f\u7684\u610f\u5473<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">ANOVA\u3067\u7b97\u51fa\u3055\u308c\u308b <strong>F\u5024<\/strong> \u3068\u306f\u3001\u300c\u30e2\u30c7\u30eb\u304c\u9811\u5f35\u3063\u3066\u8aac\u660e\u3057\u305f\u5206\u6563\u300d\u3068\u300c\u8aac\u660e\u3057\u304d\u308c\u305a\u306b\u6b8b\u3063\u305f\u6b8b\u5dee\u306e\u5206\u6563\u300d\u306e\u6bd4\u7387\uff08\u30b7\u30b0\u30ca\u30eb vs \u30ce\u30a4\u30ba\u306e\u6bd4\uff09\u3067\u3042\u308b\u3002$$F = \\frac{\\text{\u30e2\u30c7\u30eb\u304c\u8aac\u660e\u3067\u304d\u305f\u5e73\u5747\u5206\u6563 (Model MS)}}{\\text{\u8aac\u660e\u3057\u304d\u308c\u306a\u304b\u3063\u305f\u6b8b\u5dee\u306e\u5e73\u5747\u5206\u6563 (Residual MS)}}$$<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>F\u5024\u304c 1 \u8fd1\u3044<\/strong>: \u30e2\u30c7\u30eb\u306b\u5909\u6570\u3092\u8ffd\u52a0\u3057\u3066\u3082\u3001\u5f97\u3089\u308c\u305f\u8aac\u660e\u529b\u306f\u30ce\u30a4\u30ba\uff08\u5076\u7136\u306e\u8aa4\u5dee\uff09\u3068\u540c\u7b49\u30ec\u30d9\u30eb\u3002\u300c\u5909\u6570\u3092\u8ffd\u52a0\u3057\u305f\u610f\u5473\u304c\u306a\u3044\u300d\u3002<\/li>\n\n\n\n<li><strong>F\u5024\u304c\u5341\u5206\u306b\u5927\u304d\u3044 (<\/strong>$P &lt; 0.05$<strong>)<\/strong>: \u30e2\u30c7\u30eb\u306b\u5909\u6570\u3092\u8ffd\u52a0\u3057\u305f\u3053\u3068\u3067\u3001\u30ce\u30a4\u30ba\uff08\u5076\u7136\uff09\u3092\u8d85\u3048\u3066\u5727\u5012\u7684\u306b\u3070\u3089\u3064\u304d\u3092\u8aac\u660e\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u3063\u305f\u3002\u300c\u5909\u6570\u3092\u8ffd\u52a0\u3059\u308b\u4fa1\u5024\u304c\u3042\u308b\u300d\u3002<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u3064\u307e\u308a\u3001ANOVA\u3068\u306f\u300c\u5e73\u5747\u5024\u3092\u6bd4\u8f03\u3059\u308b\u8a08\u7b97\u300d\u3067\u306f\u306a\u304f\u3001<strong>\u300c\u30e2\u30c7\u30eb\u306b\u5909\u6570\u3092\u8ffd\u52a0\u3057\u305f\u3053\u3068\u3067\u3001\u6b8b\u5dee\uff08\u3070\u3089\u3064\u304d\uff09\u304c\u5076\u7136\u3092\u8d85\u3048\u3066\u6709\u610f\u306b\u6e1b\u3063\u305f\u304b\u3092\u5224\u5b9a\u3059\u308b\u8a08\u7b97\u300d<\/strong> \u306a\u306e\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">4. \u30cd\u30b9\u30c8\u30e2\u30c7\u30eb\u306e\u3042\u3066\u306f\u307e\u308a\u6bd4\u8f03\uff1a<code>anova(model1, model2)<\/code> \u304c\u3084\u3063\u3066\u3044\u308b\u3053\u3068<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u5909\u6570\u3092\u8ffd\u52a0\u3057\u305f\u969b\u306e\u30e2\u30c7\u30eb\u6bd4\u8f03\u3092\u884c\u3046\u306b\u3042\u305f\u308a\u3001\u6700\u3082\u91cd\u8981\u306a\u524d\u63d0\u6982\u5ff5\u304c <strong>\u30cd\u30b9\u30c8\u30e2\u30c7\u30eb\uff08Nested Models \/ \u5305\u542b\u95a2\u4fc2\u306b\u3042\u308b\u30e2\u30c7\u30eb\uff09<\/strong> \u3067\u3042\u308b\u3002<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<h3 class=\"wp-block-heading\">\u3010\u30b3\u30e9\u30e0\u3011\u76f4\u611f\u3067\u308f\u304b\u308b\u300c\u30cd\u30b9\u30c8\u30e2\u30c7\u30eb\uff08\u5305\u542b\u95a2\u4fc2\uff09\u300d\u3068\u306f\uff1f<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u7d71\u8a08\u5b66\u3067\u8a00\u3046\u300c\u30cd\u30b9\u30c8\uff08Nested\uff09\u300d\u3068\u306f\u3001<strong>\u30de\u30c8\u30ea\u30e7\u30fc\u30b7\u30ab\u4eba\u5f62\u306e\u3088\u3046\u306b\u3001\u30b7\u30f3\u30d7\u30eb\u306a\u30e2\u30c7\u30eb\u304c\u6301\u3064\u3059\u3079\u3066\u306e\u5909\u6570\u3092\u3001\u8907\u96d1\u306a\u30e2\u30c7\u30eb\u304c\u5b8c\u5168\u306b\u98f2\u307f\u8fbc\u3093\u3067\u3044\u308b\uff08\u542b\u3093\u3067\u3044\u308b\uff09\u95a2\u4fc2<\/strong>\u3092\u6307\u3059\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u30cd\u30b9\u30c8\u95a2\u4fc2\u304c\u6210\u7acb\u3059\u308b\u4f8b\uff08\u6bd4\u8f03\u53ef\u80fd\uff09<\/strong>:\n<ul class=\"wp-block-list\">\n<li><strong>Model 1\uff08Reduced \/ \u7e2e\u5c0f\u30e2\u30c7\u30eb\uff09<\/strong>: <code>y ~ age<\/code><\/li>\n\n\n\n<li><strong>Model 2\uff08Full \/ Perfect \/ \u5b8c\u5168\u30e2\u30c7\u30eb\uff09<\/strong>: <code>y ~ age + bmi<\/code><\/li>\n\n\n\n<li>$\\rightarrow$Model 1 \u306f Model 2 \u306b\u5b8c\u5168\u306b\u542b\u307e\u308c\u3066\u3044\u308b\uff08<code>age<\/code> \u304c\u5171\u901a\uff09\u3002\u3053\u306e\u5834\u5408\u3001<code>anova(model1, model2)<\/code> \u304c\u4f7f\u7528\u3067\u304d\u308b\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>\u30cd\u30b9\u30c8\u95a2\u4fc2\u304c\u6210\u7acb\u3057\u306a\u3044\u4f8b\uff08<code>anova<\/code> \u4e0d\u53ef\uff09<\/strong>:\n<ul class=\"wp-block-list\">\n<li><strong>Model A<\/strong>: <code>y ~ age<\/code><\/li>\n\n\n\n<li><strong>Model B<\/strong>: <code>y ~ bmi<\/code><\/li>\n\n\n\n<li>$\\rightarrow$\u4e92\u3044\u306b\u542b\u307e\u308c\u5408\u3063\u3066\u3044\u306a\u3044\uff08\u5171\u901a\u9805\u304c\u306a\u3044\u3001\u307e\u305f\u306f\u7247\u65b9\u306e\u5909\u6570\u304c\u6b20\u3051\u3066\u3044\u308b\uff09\u3002\u3053\u306e\u3088\u3046\u306a\u300c\u975e\u30cd\u30b9\u30c8\u30e2\u30c7\u30eb\u300d\u306e\u6bd4\u8f03\u306b\u306f <code>anova()<\/code> \u306f\u4f7f\u3048\u305a\u3001\u5f8c\u8ff0\u3059\u308b <strong>AIC \/ BIC<\/strong> \u3092\u4f7f\u7528\u3059\u308b\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/blockquote>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<h3 class=\"wp-block-heading\">\u3010\u5b9f\u52d9\u4e0a\u306e\u6ce8\u610f\u70b9\u3011\u6b20\u640d\u5024\uff08NA\uff09\u306b\u3088\u308b\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u306e\u76f8\u9055\u306b\u6ce8\u610f\uff01<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">R\u3067 <code>anova(model1, model2)<\/code> \u3092\u5b9f\u884c\u3059\u308b\u969b\u3001\u8ffd\u52a0\u3057\u305f\u5909\u6570\uff08\u4f8b: <code>bmi<\/code>\uff09\u306b\u6b20\u640d\u5024\uff08NA\uff09\u304c\u542b\u307e\u308c\u3066\u3044\u308b\u3068\u3001<code>model1<\/code> \u3068 <code>model2<\/code> \u3067\u89e3\u6790\u5bfe\u8c61\u3068\u306a\u308b\u60a3\u8005\u6570\uff08$N$\uff09\u304c\u5909\u5316\u3057\u3001\u300c<code>models were fitted to different numbers of observations<\/code>\u300d\u3068\u3044\u3046\u30a8\u30e9\u30fc\u304c\u767a\u751f\u3059\u308b\u3002 \u6bd4\u8f03\u3092\u884c\u3046\u524d\u306b\u3001\u3042\u3089\u304b\u3058\u3081\u89e3\u6790\u5bfe\u8c61\u30c7\u30fc\u30bf\u3092\u5b8c\u5168\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\uff08\u5b8c\u5168\u30b1\u30fc\u30b9\u89e3\u6790\uff09\u306b\u63c3\u3048\u308b\u304b\u3001\u5358\u4e00\u306e\u30c7\u30fc\u30bf\u30d5\u30ec\u30fc\u30e0\u306b\u7d5e\u3063\u3066\u304a\u304f\u3053\u3068\u304c\u5b9f\u52d9\u4e0a\u304d\u308f\u3081\u3066\u91cd\u8981\u3067\u3042\u308b\u3002<\/p>\n<\/blockquote>\n\n\n\n<h3 class=\"wp-block-heading\"><code>anova(model1, model2)<\/code> \u306e\u8a08\u7b97\u30e1\u30ab\u30cb\u30ba\u30e0<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u30cd\u30b9\u30c8\u95a2\u4fc2\u306b\u3042\u308b2\u3064\u306e\u30e2\u30c7\u30eb\uff08<code>model1<\/code> vs <code>model2<\/code>\uff09\u3092 <code>anova(model1, model2)<\/code> \u306b\u6295\u5165\u3057\u305f\u969b\u3001\u5185\u90e8\u3067\u306f\u4ee5\u4e0b\u306e\u8a08\u7b97\u304c\u884c\u308f\u308c\u3066\u3044\u308b\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u6b8b\u5dee\u5e73\u65b9\u548c\uff08RSS\uff09\u306e\u6e1b\u9000\u91cf\u3092\u8a08\u7b97<\/strong>:<code>model1<\/code>\uff08\u30b7\u30f3\u30d7\u30eb\uff09\u304b\u3089 <code>model2<\/code>\uff08\u8907\u96d1\uff09\u306b\u5909\u6570\u3092\u5897\u3084\u3057\u305f\u3053\u3068\u3067\u3001\u30e2\u30c7\u30eb\u304c\u4e88\u6e2c\u3092\u5916\u3057\u305f\u91cf\uff08\u6b8b\u5dee\u5e73\u65b9\u548c: Residual Sum of Squares\uff09\u304c\u3069\u308c\u3060\u3051\u6e1b\u5c11\u3057\u305f\u304b\uff08\uff1d\u3069\u308c\u3060\u3051\u3042\u3066\u306f\u307e\u308a\u304c\u826f\u304f\u306a\u3063\u305f\u304b\uff09\u3092\u6c42\u3081\u308b\u3002<\/li>\n\n\n\n<li><strong>F\u691c\u5b9a\uff08\u307e\u305f\u306f\u5c24\u5ea6\u6bd4\u691c\u5b9a\uff09\u3092\u5b9f\u884c<\/strong>:\u300c\u6e1b\u5c11\u3057\u305f\u6b8b\u5dee\uff08\u65b0\u5909\u6570\u304c\u8aac\u660e\u3057\u3066\u304f\u308c\u305f\u3070\u3089\u3064\u304d\uff09\u300d\u3092\u300c<code>model2<\/code> \u306e\u6b8b\u5dee\u300d\u3067\u5272\u308a\u7b97\u3057\u3001F\u5024\u3092\u7b97\u51fa\u3059\u308b\u3002<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">$$F = \\frac{(\\text{RSS}_1 &#8211; \\text{RSS}_2) \/ \\Delta df}{\\text{RSS}_2 \/ df_2}$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3053\u306e $P$ \u5024\uff08<code>Pr(&gt;F)<\/code>\uff09\u304c $0.05$ \u672a\u6e80\u3067\u3042\u308c\u3070\u3001<strong>\u300c\u5909\u6570\u3092\u8ffd\u52a0\u3057\u305f\u3053\u3068\u3067\u3001\u5358\u306a\u308b\u5076\u7136\u3092\u8d85\u3048\u3066\u30e2\u30c7\u30eb\u306e\u3042\u3066\u306f\u307e\u308a\uff08\u8aac\u660e\u529b\uff09\u304c\u7d71\u8a08\u5b66\u7684\u306b\u6709\u610f\u306b\u5411\u4e0a\u3057\u305f\u300d<\/strong> \u3068\u5ba2\u89b3\u7684\u306b\u7d50\u8ad6\u4ed8\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">5. \u3010\u5b9f\u8df5R\u30b3\u30fc\u30c9\u3011<code>lm()<\/code> \/ <code>glm()<\/code> \u3067\u306e\u30cd\u30b9\u30c8\u30e2\u30c7\u30eb\u6bd4\u8f03\u3068\u3042\u3066\u306f\u307e\u308a\u5224\u5b9a\uff08Step by Step\uff09<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u3053\u3053\u304b\u3089\u306f\u3001\u5b9f\u969b\u306bR\u3092\u7528\u3044\u30662\u3064\u306e\u56de\u5e30\u30e2\u30c7\u30eb\u3092\u69cb\u7bc9\u3057\u3001<code>anova()<\/code> \u3092\u7528\u3044\u3066\u30e2\u30c7\u30eb\u9078\u629e\uff08\u3042\u3066\u306f\u307e\u308a\u8a55\u4fa1\uff09\u3092\u884c\u3046\u624b\u9806\u3092 Step by Step \u3067\u89e3\u8aac\u3059\u308b\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: \u7591\u4f3c\u81e8\u5e8a\u30c7\u30fc\u30bf\u306e\u4f5c\u6210<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u60a3\u8005300\u4eba\u5206\u3001\u30a2\u30a6\u30c8\u30ab\u30e0 $Y$\uff08\u53ce\u7e2e\u671f\u8840\u5727\uff09\u3001\u57fa\u672c\u80cc\u666f $X_1$\uff08\u5e74\u9f62\uff09\u3001\u8a55\u4fa1\u3057\u305f\u3044\u8ffd\u52a0\u56e0\u5b50 $X_2$\uff08BMI\uff09\u306e\u30c7\u30fc\u30bf\u3092\u751f\u6210\u3059\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>library(tidyverse)\n\n# \u4e71\u6570\u30b7\u30fc\u30c9\u306e\u8a2d\u5b9a\nset.seed(123)\nn &lt;- 300\n\n# \u7591\u4f3c\u30c7\u30fc\u30bf\u306e\u751f\u6210\uff08BMI\u304c\u8840\u5727\u306b\u771f\u306e\u5f71\u97ff\u3092\u4e0e\u3048\u308b\u30c7\u30fc\u30bf\uff09\ndf_sim &lt;- tibble(\n  id = 1:n,\n  age = round(rnorm(n, mean = 60, sd = 10)),\n  bmi = round(rnorm(n, mean = 24, sd = 3), 1)\n) %&gt;% \n  mutate(\n    # \u53ce\u7e2e\u671f\u8840\u5727 Y \u306e\u751f\u6210\n    sbp = round(100 + 0.5 * age + 1.2 * bmi + rnorm(n, mean = 0, sd = 10), 1)\n  )\n\n# \u30c7\u30fc\u30bf\u306e\u78ba\u8a8d\nhead(df_sim)\n<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: 2\u3064\u306e\u30e2\u30c7\u30eb\uff08Reduced vs Full\uff09\u306e\u69cb\u7bc9<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u5e74\u9f62\u306e\u307f\u3092\u8abf\u6574\u3057\u305f\u30b7\u30f3\u30d7\u30eb\u306a\u30e2\u30c7\u30eb\uff08<code>model1<\/code>\uff09\u3068\u3001\u65b0\u305f\u306bBMI\u3092\u8ffd\u52a0\u3057\u305f\u30e2\u30c7\u30eb\uff08<code>model2<\/code>\uff09\u3092\u69cb\u7bc9\u3059\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code># Model 1: \u5e74\u9f62\u306e\u307f (Reduced Model)\nmodel1 &lt;- lm(sbp ~ age, data = df_sim)\n\n# Model 2: \u5e74\u9f62 + BMI (Full Model)\nmodel2 &lt;- lm(sbp ~ age + bmi, data = df_sim)\n\n# \u305d\u308c\u305e\u308c\u306e\u30e2\u30c7\u30eb\u306e\u6982\u8981\u78ba\u8a8d\nsummary(model1)$r.squared\nsummary(model2)$r.squared\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">\u30e2\u30c7\u30eb1\u306e $R^2$ \u3088\u308a\u30e2\u30c7\u30eb2\u306e $R^2$ \u306e\u65b9\u304c\u9ad8\u304f\u306a\u308b\u304c\u3001<strong>\u300c\u5909\u6570\u3092\u5897\u3084\u305b\u3070 <\/strong>$R^2$<strong> \u306f\u5fc5\u305a\u4e0a\u304c\u308b\uff08\u307e\u305f\u306f\u6a2a\u3070\u3044\uff09\u300d<\/strong> \u3068\u3044\u3046\u6027\u8cea\u304c\u3042\u308b\u305f\u3081\u3001$R^2$ \u306e\u4e0a\u6607\u3060\u3051\u3067\u300c\u30e2\u30c7\u30eb2\u304c\u826f\u3044\u300d\u3068\u7d50\u8ad6\u3065\u3051\u308b\u3053\u3068\u306f\u3067\u304d\u306a\u3044\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: <code>anova(model1, model2)<\/code> \u306e\u5b9f\u884c\u3068\u51fa\u529b\u7d50\u679c\u306e\u89e3\u91c8<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u3053\u3053\u3067 <code>anova()<\/code> \u3092\u5b9f\u884c\u3057\u3001\u3042\u3066\u306f\u307e\u308a\u306e\u5411\u4e0a\u304c\u7d71\u8a08\u5b66\u7684\u306b\u6709\u610f\u304b\u3092\u5224\u5b9a\u3059\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code># \u30cd\u30b9\u30c8\u30e2\u30c7\u30eb\u306e\u6bd4\u8f03 (F\u691c\u5b9a)\nanova_res &lt;- anova(model1, model2)\nprint(anova_res)\n<\/code><\/pre>\n\n\n\n<pre class=\"wp-block-code\"><code>> print(anova_res)\nAnalysis of Variance Table\n\nModel 1: sbp ~ age\nModel 2: sbp ~ age + bmi\n  Res.Df   RSS Df Sum of Sq      F    Pr(>F)    \n1    298 34730                                  \n2    297 31819  1    2911.5 27.176 3.486e-07 ***\n---\nSignif. codes:  0 \u2018***\u2019 0.001 \u2018**\u2019 0.01 \u2018*\u2019 0.05 \u2018.\u2019 0.1 \u2018 \u2019 1\n<\/code><\/pre>\n\n\n\n<h4 class=\"wp-block-heading\">\u51fa\u529b\u30c6\u30fc\u30d6\u30eb\u306e\u8aad\u307f\u65b9<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong><code>Res.Df<\/code> (\u6b8b\u5dee\u81ea\u7531\u5ea6)<\/strong>: \u30c7\u30fc\u30bf\u6570\u304b\u3089\u30d1\u30e9\u30e1\u30fc\u30bf\u6570\u3092\u5f15\u3044\u305f\u81ea\u7531\u5ea6\u3002\u5909\u6570\u30921\u3064\u8ffd\u52a0\u3057\u305f\u305f\u3081 <code>298<\/code> \u304b\u3089 <code>297<\/code> \u30781\u6e1b\u5c11\u3057\u3066\u3044\u308b\u3002<\/li>\n\n\n\n<li><strong><code>RSS<\/code> (\u6b8b\u5dee\u5e73\u65b9\u548c)<\/strong>: \u30e2\u30c7\u30eb\u304c\u4e88\u6e2c\u3092\u5916\u3057\u305f\u300c\u8aa4\u5dee\u306e\u4e8c\u4e57\u548c\u300d\u3002<code>34730<\/code> \u304b\u3089 <code>31819<\/code> \u3078\u6e1b\u5c11\u3057\u3001\u30e2\u30c7\u30eb\u306e\u3042\u3066\u306f\u307e\u308a\u304c\u826f\u304f\u306a\u3063\u305f\u3053\u3068\u3092\u793a\u3059\u3002<\/li>\n\n\n\n<li><strong><code>Sum of Sq<\/code> (\u6e1b\u5c11\u3057\u305f\u6b8b\u5dee)<\/strong>: BMI\u3092\u8ffd\u52a0\u3057\u305f\u3053\u3068\u3067\u65b0\u305f\u306b\u8aac\u660e\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u3063\u305f\u3070\u3089\u3064\u304d\uff08$34730 &#8211; 31819 = 2911.5$\uff09\u3002<\/li>\n\n\n\n<li><strong><code>F<\/code> \u5024 (<\/strong>$27.176$<strong>)<\/strong>: \u8ffd\u52a0\u3055\u308c\u305f\u8aac\u660e\u529b\uff08Sum of Sq\uff09\u3068\u6b8b\u5dee\u306e\u6bd4\u3002<\/li>\n\n\n\n<li><strong><code>Pr(>F)<\/code> (<\/strong>$3.486 \\times 10^{-7}$<strong>)<\/strong>: $P$ \u5024\u304c 3.486e-07\uff083.486 x 10\u306e\u30de\u30a4\u30ca\u30b97\u4e57\u3068\u3044\u3046\u610f\u5473\uff09\u3067\u3042\u3063\u3066\u3001$0.05$ \u3092\u4e0b\u56de\u3063\u3066\u3044\u308b\u3002$\\rightarrow$ <strong>\u7d50\u8ad6<\/strong>: \u300cBMI\u3092\u8ffd\u52a0\u3057\u305f\u3053\u3068\u3067\u3001\u30e2\u30c7\u30eb\u306e\u3042\u3066\u306f\u307e\u308a\uff08\u8aac\u660e\u529b\uff09\u304c\u5076\u7136\u3092\u8d85\u3048\u3066\u6709\u610f\u306b\u5411\u4e0a\u3057\u305f\u3002\u3057\u305f\u304c\u3063\u3066 <code>model2<\/code> \u3092\u63a1\u7528\u3059\u3079\u304d\u3067\u3042\u308b\u300d\u3068\u5ba2\u89b3\u7684\u306b\u5224\u65ad\u3067\u304d\u308b\u3002<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 4: \u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u56de\u5e30\uff08<code>glm<\/code>\uff09\u3067\u306e\u30e2\u30c7\u30eb\u6bd4\u8f03\u306e\u6ce8\u610f\u70b9<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e8c\u5024\u30a2\u30a6\u30c8\u30ab\u30e0\uff08\u6b7b\u4ea1\u306e\u6709\u7121\u306a\u3069\uff09\u3092\u6271\u3046\u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u56de\u5e30\uff08<code>glm<\/code>\uff09\u3084Cox\u6bd4\u4f8b\u30cf\u30b6\u30fc\u30c9\u30e2\u30c7\u30eb\uff08<code>coxph<\/code>\uff09\u3067\u30e2\u30c7\u30eb\u6bd4\u8f03\u3092\u884c\u3046\u5834\u5408\u306f\u3001F\u691c\u5b9a\u3067\u306f\u306a\u304f <strong>\u5c24\u5ea6\u6bd4\u691c\u5b9a\uff08Likelihood Ratio Test: <\/strong>$\\chi^2$<strong> \u691c\u5b9a\uff09<\/strong> \u3092\u6307\u5b9a\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code># \u7591\u4f3c\u30a2\u30a6\u30c8\u30ab\u30e0\uff08\u9ad8\u8840\u5727\u30d5\u30e9\u30b0: 1\/0\uff09\u306e\u4f5c\u6210\ndf_sim &lt;- df_sim %&gt;% mutate(htn = if_else(sbp &gt;= 140, 1, 0))\n\n# \u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u56de\u5e30\u30e2\u30c7\u30eb\u306e\u69cb\u7bc9\nglm1 &lt;- glm(htn ~ age, data = df_sim, family = binomial)\nglm2 &lt;- glm(htn ~ age + bmi, data = df_sim, family = binomial)\n\n# \u5c24\u5ea6\u6bd4\u691c\u5b9a (test = \"Chisq\" \u3092\u660e\u8a18\u3059\u308b)\nanova(glm1, glm2, test = \"Chisq\")\n<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\"><code>glm<\/code> \u306e\u5834\u5408\u306f <code>test = \"Chisq\"<\/code> \u30aa\u30d7\u30b7\u30e7\u30f3\u3092\u660e\u8a18\u3059\u308b\u3053\u3068\u3067\u3001Deviance\uff08\u9038\u8131\u5ea6\uff09\u306e\u6e1b\u5c11\u91cf\u3092\u30ab\u30a4\u4e8c\u4e57\u5206\u5e03\u3067\u691c\u5b9a\u3057\u3001\u9069\u5207\u306a\u30e2\u30c7\u30eb\u9078\u629e\u3092\u884c\u3046\u3053\u3068\u304c\u3067\u304d\u308b\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">6. \u3042\u3066\u306f\u307e\u308a\u8a55\u4fa1\u306e\u4f7f\u3044\u5206\u3051\uff1a<code>anova()<\/code>\uff08\u4eee\u8aac\u691c\u5b9a\uff09 vs <code>AIC\/BIC<\/code>\uff08\u60c5\u5831\u91cf\u63a8\u5b9a\u91cf\uff09<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u30e2\u30c7\u30eb\u306e\u300c\u3042\u3066\u306f\u307e\u308a\u300d\u3092\u8a55\u4fa1\u3059\u308b\u6307\u6a19\u3068\u3057\u3066\u3001<code>anova()<\/code> \u306e\u4ed6\u306b <strong>AIC\uff08\u8d64\u6c60\u60c5\u5831\u91cf\u898f\u6e96\uff09<\/strong> \u3084 <strong>BIC<\/strong> \u3082\u3088\u304f\u4f7f\u308f\u308c\u308b\u3002\u3053\u308c\u3089\u306f\u3069\u306e\u3088\u3046\u306b\u4f7f\u3044\u5206\u3051\u308b\u3079\u304d\u3060\u308d\u3046\u304b\uff1f<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u7d50\u8ad6\u306f<strong>\u300c\u30e2\u30c7\u30eb\u540c\u58eb\u306b\u30cd\u30b9\u30c8\u95a2\u4fc2\uff08\u5305\u542b\u95a2\u4fc2\uff09\u304c\u3042\u308b\u304b\u3069\u3046\u304b\u300d<\/strong>\u3067\u6c7a\u307e\u308b\u3002<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td><strong>\u6bd4\u8f03\u3059\u308b\u6761\u4ef6<\/strong><\/td><td><strong>\u4e3b\u306a\u624b\u6cd5<\/strong><\/td><td><strong>\u5224\u5b9a\u57fa\u6e96<\/strong><\/td><td><strong>\u7279\u5fb4\u30fb\u30e1\u30ea\u30c3\u30c8<\/strong><\/td><\/tr><tr><td><strong>\u30cd\u30b9\u30c8\u95a2\u4fc2\u3042\u308a<\/strong><br>(\u4f8b: <code>y ~ x1<\/code> vs <code>y ~ x1 + x2<\/code>)<\/td><td><strong><code>anova()<\/code><\/strong><br>(F\u691c\u5b9a \/ \u5c24\u5ea6\u6bd4\u691c\u5b9a)<\/td><td>$P &lt; 0.05$ \u306a\u3089\u8907\u96d1\u306a\u30e2\u30c7\u30eb\u3092\u63a1\u7528<\/td><td>\u660e\u78ba\u306a $P$ \u5024\u3067\u300c\u5909\u6570\u3092\u5897\u3084\u3059\u7d71\u8a08\u5b66\u7684\u4fa1\u5024\u304c\u3042\u308b\u304b\u300d\u3092\u53b3\u683c\u306b\u5224\u5b9a\u3067\u304d\u308b\uff08\u4eee\u8aac\u691c\u5b9a\uff09\u3002<\/td><\/tr><tr><td><strong>\u30cd\u30b9\u30c8\u95a2\u4fc2\u306a\u3057<\/strong><br>(\u4f8b: <code>y ~ x1 + x2<\/code> vs <code>y ~ x3 + x4<\/code>)<\/td><td><strong>AIC \/ BIC<\/strong><\/td><td><strong>AIC\u304c\u5c0f\u3055\u3044<\/strong>\u65b9\u306e\u30e2\u30c7\u30eb\u3092\u63a1\u7528<\/td><td>\u5305\u542b\u95a2\u4fc2\u304c\u306a\u3044\u5168\u304f\u7570\u306a\u308b\u5909\u6570\u30bb\u30c3\u30c8\u3084\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u3082\u6bd4\u8f03\u53ef\u80fd\u3002\u8907\u96d1\u3055\uff08\u5909\u6570\u5897\uff09\u3078\u306e\u30da\u30ca\u30eb\u30c6\u30a3\u3092\u542b\u3080\u3002<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u30cd\u30b9\u30c8\u95a2\u4fc2\u306b\u3042\u308b\u30e2\u30c7\u30eb\u306e\u6bd4\u8f03\u306b\u304a\u3044\u3066\u306f\u3001\u307e\u305a <strong><code>anova()<\/code> \u306b\u3088\u308b\u4eee\u8aac\u691c\u5b9a<\/strong> \u3092\u884c\u3046\u306e\u304c\u533b\u5b66\u30fb\u751f\u7269\u7d71\u8a08\u306b\u304a\u3051\u308b\u6b63\u653b\u6cd5\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">7. \u307e\u3068\u3081\uff06\u4e00\u62ec\u30b3\u30d4\u30da\u7528R\u30b9\u30af\u30ea\u30d7\u30c8<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">\u672c\u8a18\u4e8b\u306e\u30dd\u30a4\u30f3\u30c8\u304a\u3055\u3089\u3044<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>ANOVA\u306e\u672c\u8cea\u306f\u5206\u6563\u306e\u5206\u89e3<\/strong>: \u300c\u5e73\u5747\u5024\u306e\u6bd4\u8f03\u300d\u3082\u300c\u56de\u5e30\u30e2\u30c7\u30eb\u306e\u3042\u3066\u306f\u307e\u308a\u6bd4\u8f03\u300d\u3082\u3001\u3084\u3063\u3066\u3044\u308b\u8a08\u7b97\u306f\u300c\u8aac\u660e\u3067\u304d\u305f\u5206\u6563 vs \u6b8b\u5dee\u306e\u5206\u6563\u300d\u306e\u6bd4\uff08F\u5024\uff09\u3092\u898b\u308b\u540c\u3058\u30a2\u30d7\u30ed\u30fc\u30c1\u3067\u3042\u308b\u3002<\/li>\n\n\n\n<li><strong>\u30cd\u30b9\u30c8\u30e2\u30c7\u30eb\u306b\u306f <code>anova(model1, model2)<\/code><\/strong>: \u5909\u6570\u3092\u8ffd\u52a0\u3057\u305f\u3053\u3068\u3067\u6b8b\u5dee\u5e73\u65b9\u548c\uff08RSS\uff09\u304c\u6709\u610f\u306b\u6e1b\u3063\u305f\u304b\u3092\u691c\u5b9a\u3057\u3001\u5909\u6570\u306e\u5fc5\u8981\u6027\u3092\u5ba2\u89b3\u7684\u306b\u5224\u5b9a\u3067\u304d\u308b\u3002<\/li>\n\n\n\n<li><strong><code>glm<\/code> \u3084 <code>coxph<\/code> \u3067\u306f <code>test = \"Chisq\"<\/code><\/strong>: \u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u56de\u5e30\u306a\u3069\u3067\u306f\u5c24\u5ea6\u6bd4\u691c\u5b9a\uff08\u30ab\u30a4\u4e8c\u4e57\u691c\u5b9a\uff09\u3092\u6307\u5b9a\u3059\u308b\u3002<\/li>\n\n\n\n<li><strong>\u30cd\u30b9\u30c8\u306a\u3057\u306a\u3089 AIC<\/strong>: \u5305\u542b\u95a2\u4fc2\u304c\u306a\u3044\u30e2\u30c7\u30eb\u540c\u58eb\u306e\u6bd4\u8f03\u306b\u306f <code>anova()<\/code> \u306f\u4f7f\u3048\u305a\u3001AIC\/BIC \u3092\u4f7f\u7528\u3059\u308b\u3002<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">\u4e00\u62ec\u5b9f\u884c\u7528R\u30b9\u30af\u30ea\u30d7\u30c8<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u4ee5\u4e0b\u306e\u30b3\u30fc\u30c9\u3092\u30b3\u30d4\u30fc\uff06\u30da\u30fc\u30b9\u30c8\u3059\u308b\u3053\u3068\u3067\u3001\u7591\u4f3c\u30c7\u30fc\u30bf\u4f5c\u6210\u304b\u3089 <code>lm<\/code> \/ <code>glm<\/code> \u3067\u306e\u30e2\u30c7\u30eb\u69cb\u7bc9\u3001<code>anova()<\/code> \u306b\u3088\u308b\u30cd\u30b9\u30c8\u30e2\u30c7\u30eb\u6bd4\u8f03\uff08F\u691c\u5b9a\u30fb\u5c24\u5ea6\u6bd4\u691c\u5b9a\uff09\u3001AIC\u6bd4\u8f03\u307e\u3067\u3092\u4e00\u6c17\u901a\u8cab\u3067\u8d70\u3089\u305b\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code># ==============================================================================\n# \u56de\u5e30\u30e2\u30c7\u30eb\u306e\u3042\u3066\u306f\u307e\u308a\u8a55\u4fa1\u3068 anova() \u30e2\u30c7\u30eb\u9078\u629e \u4e00\u62ec\u5b9f\u884c\u30b9\u30af\u30ea\u30d7\u30c8\n# ==============================================================================\n\nif (!requireNamespace(\"tidyverse\", quietly = TRUE)) install.packages(\"tidyverse\")\nlibrary(tidyverse)\n\n# 1. \u7591\u4f3c\u81e8\u5e8a\u30c7\u30fc\u30bf\u306e\u4f5c\u6210\nset.seed(123)\nn &lt;- 300\n\ndf_sim &lt;- tibble(\n  id = 1:n,\n  age = round(rnorm(n, mean = 60, sd = 10)),\n  bmi = round(rnorm(n, mean = 24, sd = 3), 1)\n) %&gt;% \n  mutate(\n    sbp = round(100 + 0.5 * age + 1.2 * bmi + rnorm(n, mean = 0, sd = 10), 1),\n    htn = if_else(sbp &gt;= 140, 1, 0)\n  )\n\n# 2. \u7dda\u5f62\u56de\u5e30\u30e2\u30c7\u30eb(lm)\u306e\u6bd4\u8f03 (F\u691c\u5b9a)\ncat(\"\\n=================== 1. \u9023\u7d9a\u30a2\u30a6\u30c8\u30ab\u30e0 (lm) \u3067\u306e anova() \u6bd4\u8f03 ===================\\n\")\nlm_reduced &lt;- lm(sbp ~ age, data = df_sim)\nlm_full    &lt;- lm(sbp ~ age + bmi, data = df_sim)\n\n# anova() \u306b\u3088\u308b\u30cd\u30b9\u30c8\u30e2\u30c7\u30eb\u6bd4\u8f03\nprint(anova(lm_reduced, lm_full))\n\n# 3. \u30ed\u30b8\u30b9\u30c6\u30a3\u30c3\u30af\u56de\u5e30(glm)\u306e\u6bd4\u8f03 (\u5c24\u5ea6\u6bd4\u691c\u5b9a: Chisq)\ncat(\"\\n================ 2. \u4e8c\u5024\u30a2\u30a6\u30c8\u30ab\u30e0 (glm) \u3067\u306e anova() \u6bd4\u8f03 =================\\n\")\nglm_reduced &lt;- glm(htn ~ age, data = df_sim, family = binomial)\nglm_full    &lt;- glm(htn ~ age + bmi, data = df_sim, family = binomial)\n\n# anova() \u3067 test = \"Chisq\" \u3092\u6307\u5b9a\nprint(anova(glm_reduced, glm_full, test = \"Chisq\"))\n\n# 4. AIC\u306b\u3088\u308b\u30e2\u30c7\u30eb\u6bd4\u8f03\u53c2\u8003\ncat(\"\\n========================= 3. AIC \u306b\u3088\u308b\u30e2\u30c7\u30eb\u6bd4\u8f03 =========================\\n\")\ncat(sprintf(\"LM Reduced AIC: %.2f | LM Full AIC: %.2f\\n\", AIC(lm_reduced), AIC(lm_full)))\ncat(sprintf(\"GLM Reduced AIC: %.2f | GLM Full AIC: %.2f\\n\", AIC(glm_reduced), AIC(glm_full)))\n<\/code><\/pre>\n\n\n\n<h2 class=\"wp-block-heading\">\u304a\u3059\u3059\u3081\u66f8\u7c4d<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/amzn.to\/461zmy5\">\u8ab0\u3082\u6559\u3048\u3066\u304f\u308c\u306a\u304b\u3063\u305f\u3000\u533b\u7642\u7d71\u8a08\u306e\u4f7f\u3044\u5206\u3051\u301c\u8ff7\u3044\u3084\u3059\u3044\u89e3\u6790\u624b\u6cd5\u306e\u9078\u3073\u65b9\u304c\uff0cR\u3067\u5b9f\u611f\u3057\u306a\u304c\u3089\u308f\u304b\u308b\uff01<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u300c\u5148\u751f\uff01\u30e2\u30c7\u30eb\u306b\u65b0\u3057\u3044\u30ea\u30b9\u30af\u56e0\u5b50\uff08$X_2$\uff09\u3092\u8ffd\u52a0\u3057\u3066\u307f\u305f\u306e\u3067\u3059\u304c\u3001\u3053\u306e\u5909\u6570\u3092\u8ffd\u52a0\u3057\u305f\u3053\u3068\u3067\u30e2\u30c7\u30eb\u306e\u3042\u3066\u306f\u307e\u308a\uff08\u8aac\u660e\u529b\uff09\u304c\u672c\u5f53\u306b\u826f\u304f\u306a\u3063\u305f\u306e\u304b\u3001\u5ba2\u89b3\u7684\u306b\u8a55\u4fa1\u3059\u308b\u65b9\u6cd5\u304c\u5206\u304b\u308a\u307e\u305b\u3093\u300d \u300c\u305d\u308c\u306a\u3089\u3001\u30b7\u30f3\u30d7\u30eb\u306a\u30e2\u30c7\u30eb\uff08mod [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":4755,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"swell_btn_cv_data":"","_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"jetpack_post_was_ever_published":false},"categories":[58],"tags":[],"class_list":["post-4753","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-58"],"jetpack_publicize_connections":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2026\/08\/ANOVA\u3067\u5f53\u3066\u306f\u307e\u308a\u6bd4\u8f03-scaled.jpeg","_links":{"self":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/4753","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/comments?post=4753"}],"version-history":[{"count":2,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/4753\/revisions"}],"predecessor-version":[{"id":4756,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/4753\/revisions\/4756"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/media\/4755"}],"wp:attachment":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/media?parent=4753"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/categories?post=4753"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/tags?post=4753"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}