{"id":4472,"date":"2025-12-20T20:54:00","date_gmt":"2025-12-20T11:54:00","guid":{"rendered":"https:\/\/best-biostatistics.com\/toukei-er\/?p=4472"},"modified":"2025-12-20T20:54:03","modified_gmt":"2025-12-20T11:54:03","slug":"the-linear-regression-trap-why-normality-of-data-is-not-a-requirement","status":"publish","type":"post","link":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/the-linear-regression-trap-why-normality-of-data-is-not-a-requirement\/","title":{"rendered":"\u7dda\u5f62\u56de\u5e30\u306e\u7f60\uff1a\u306a\u305c\u300c\u30c7\u30fc\u30bf\u306e\u6b63\u898f\u6027\u300d\u306f\u5fc5\u9808\u3067\u306f\u306a\u3044\u306e\u304b"},"content":{"rendered":"\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p>\u7d71\u8a08\u5b66\u3084\u30c7\u30fc\u30bf\u5206\u6790\u306e\u521d\u5b66\u8005\u304c\u7dda\u5f62\u56de\u5e30\u3092\u5b66\u3076\u969b\u3001\u6700\u521d\u306b\u3064\u307e\u305a\u304f\u30dd\u30a4\u30f3\u30c8\u304c\u3042\u308b\u3002\u305d\u308c\u304c\u300c\u6b63\u898f\u6027\u306e\u4eee\u5b9a\u300d\u3060\u3002\u300c\u5206\u6790\u5bfe\u8c61\u306e\u30c7\u30fc\u30bf\uff08\u76ee\u7684\u5909\u6570\uff09\u304c\u6b63\u898f\u5206\u5e03\u3057\u3066\u3044\u306a\u3051\u308c\u3070\u3001\u56de\u5e30\u5206\u6790\u306f\u4f7f\u3048\u306a\u3044\u300d\u3068\u601d\u3044\u8fbc\u307f\u3001\u5206\u6790\u3092\u65ad\u5ff5\u3057\u305f\u308a\u3001\u7121\u7406\u306a\u30c7\u30fc\u30bf\u5909\u63db\u3092\u7e70\u308a\u8fd4\u3057\u305f\u308a\u3059\u308b\u30b1\u30fc\u30b9\u306f\u5c11\u306a\u304f\u306a\u3044\u3002<\/p>\n\n\n\n<p>\u3057\u304b\u3057\u3001\u7d50\u8ad6\u304b\u3089\u8a00\u3048\u3070\u3001<strong>\u76ee\u7684\u5909\u6570\u305d\u306e\u3082\u306e\u304c\u6b63\u898f\u5206\u5e03\u3057\u3066\u3044\u308b\u5fc5\u8981\u306f\u306a\u3044\u3002<\/strong> \u672c\u8a18\u4e8b\u3067\u306f\u3001\u3053\u306e\u8aa4\u89e3\u306e\u6b63\u4f53\u3092\u89e3\u304d\u660e\u304b\u3057\u3001\u5b9f\u52d9\u306b\u304a\u3044\u3066\u771f\u306b\u30c1\u30a7\u30c3\u30af\u3059\u3079\u304d\u30dd\u30a4\u30f3\u30c8\u3092\u89e3\u8aac\u3059\u308b\u3002<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<!--more-->\n\n\n\n<h2 class=\"wp-block-heading\">\u76ee\u7684\u5909\u6570\u306e\u6b63\u898f\u6027\u304c\u5fc5\u9808\u3068\u3044\u3046\u8aa4\u89e3\u306f\u3069\u3053\u304b\u3089\u6765\u308b\u306e\u304b<\/h2>\n\n\n\n<p>\u300c\u76ee\u7684\u5909\u6570\u304c\u6b63\u898f\u5206\u5e03\u3057\u3066\u3044\u308b\u5fc5\u8981\u304c\u3042\u308b\u300d\u3068\u3044\u3046\u8aa4\u89e3\u304c\u5e83\u307e\u3063\u3066\u3044\u308b\u80cc\u666f\u306b\u306f\u3001\u7d71\u8a08\u6559\u80b2\u306e\u30d7\u30ed\u30bb\u30b9\u3068\u3001\u4ed6\u306e\u624b\u6cd5\u3068\u306e\u6df7\u540c\u304c\u3042\u308b\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>t\u691c\u5b9a\u306a\u3069\u306e\u5370\u8c61:<\/strong> \u7d71\u8a08\u5b66\u306e\u57fa\u790e\u3067\u5b66\u3076\u300ct\u691c\u5b9a\u300d\u3084\u300cANOVA\uff08\u5206\u6563\u5206\u6790\uff09\u300d\u3067\u306f\u3001\u6bcd\u96c6\u56e3\u306e\u6b63\u898f\u6027\u304c\u524d\u63d0\u3068\u3055\u308c\u308b\u3053\u3068\u304c\u591a\u3044\u3002\u305d\u306e\u30a4\u30e1\u30fc\u30b8\u304c\u56de\u5e30\u5206\u6790\u306b\u3082\u7121\u6279\u5224\u306b\u6301\u3061\u8fbc\u307e\u308c\u3066\u3044\u308b\u3002<\/li>\n\n\n\n<li><strong>\u6559\u79d1\u66f8\u306e\u5358\u7d14\u5316:<\/strong> \u5165\u9580\u66f8\u3067\u306f\u3001\u7406\u89e3\u3092\u52a9\u3051\u308b\u305f\u3081\u306b\u300c\u7dba\u9e97\u306b\u30d9\u30eb\u30ab\u30fc\u30d6\u3092\u63cf\u304f\u30c7\u30fc\u30bf\u300d\u3092\u4f8b\u984c\u306b\u4f7f\u3046\u3002\u3053\u308c\u304c\u300c\u6b63\u898f\u5206\u5e03\u3057\u3066\u3044\u306a\u3051\u308c\u3070\u306a\u3089\u306a\u3044\u300d\u3068\u3044\u3046\u30eb\u30fc\u30eb\u3068\u3057\u3066\u8aa4\u8a8d\u3055\u308c\u3066\u3057\u307e\u3046\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u5b9f\u969b\u306b\u306f\u3001\u76ee\u7684\u5909\u6570\u304c\u3069\u306e\u3088\u3046\u306a\u5206\u5e03\u3067\u3042\u3063\u3066\u3082\u3001\u8aac\u660e\u5909\u6570\u306b\u3088\u3063\u3066\u305d\u306e\u5909\u52d5\u304c\u8aac\u660e\u3055\u308c\u3001\u6b8b\u3063\u305f\u8aa4\u5dee\u304c\u9069\u5207\u3067\u3042\u308c\u3070\u7dda\u5f62\u56de\u5e30\u306f\u6210\u7acb\u3059\u308b\u3002<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\u6b8b\u5dee\u306e\u6b63\u898f\u6027\u306b\u3064\u3044\u3066<\/h2>\n\n\n\n<p>\u7dda\u5f62\u56de\u5e30\u306b\u304a\u3044\u3066\u771f\u306b\u91cd\u8981\u306a\u306e\u306f\u3001\u30c7\u30fc\u30bf\u305d\u306e\u3082\u306e\u306e\u5206\u5e03\u3067\u306f\u306a\u304f\u3001\u30e2\u30c7\u30eb\u3092\u5f53\u3066\u306f\u3081\u305f\u5f8c\u306b\u6b8b\u308b<span class=\"swl-marker mark_orange\">\u300c\u6b8b\u5dee\uff08\u3056\u3093\u3055\uff09\u300d\u306e\u5206\u5e03<\/span>\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<p>\u7dda\u5f62\u56de\u5e30\u30e2\u30c7\u30eb\u306f\u6570\u5f0f\u3067\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3055\u308c\u308b\u3002<\/p>\n\n\n\n<p>$$y = \\beta_0 + \\beta_1x + \\epsilon$$<\/p>\n\n\n\n<p>\u3053\u3053\u3067\u6700\u3082\u91cd\u8981\u306a\u4eee\u5b9a\u306f\u3001$\\epsilon$\uff08\u8aa4\u5dee\u9805\uff09\u304c\u5e73\u5747 0\u3001\u5206\u6563 $\\sigma^2$ \u306e\u6b63\u898f\u5206\u5e03\u306b\u5f93\u3046\u3053\u3068\uff08$\\epsilon \\sim N(0, \\sigma^2)$\uff09\u3067\u3042\u308b\u3002\u6b8b\u5dee\u304c\u3053\u306e\u6761\u4ef6\u3092\u6e80\u305f\u3057\u3066\u3044\u308b\u3053\u3068\u3067\u3001\u521d\u3081\u3066\u4fc2\u6570\u306e\u6709\u610f\u6027\uff08p\u5024\uff09\u3084\u4fe1\u983c\u533a\u9593\u304c\u7d71\u8a08\u7684\u306b\u610f\u5473\u3092\u6301\u3064\u3002<\/p>\n\n\n\n<p>\u3064\u307e\u308a\u3001\u5143\u306e\u30c7\u30fc\u30bf\u304c\u3069\u308c\u307b\u3069\u6b6a\u3093\u3067\u3044\u3066\u3082\u3001\u30e2\u30c7\u30eb\u304c\u305d\u306e\u6b6a\u307f\u3092\u8aac\u660e\u3057\u304d\u308c\u3066\u304a\u308a\u3001\u4e88\u6e2c\u304b\u3089\u5916\u308c\u305f\u90e8\u5206\uff08\u6b8b\u5dee\uff09\u304c\u30e9\u30f3\u30c0\u30e0\u3067\u5de6\u53f3\u5bfe\u79f0\u3067\u3042\u308c\u3070\u3001\u7dda\u5f62\u56de\u5e30\u30e2\u30c7\u30eb\u3068\u3057\u3066\u59a5\u5f53\u3068\u8a00\u3048\u308b\u3002<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<div id=\"biost-3122335052\" 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\">\u6b63\u898f\u6027\u306e\u78ba\u8a8d\u65b9\u6cd5<\/h2>\n\n\n\n<p>\u6b8b\u5dee\u306e\u6b63\u898f\u6027\u3092\u78ba\u8a8d\u3059\u308b\u624b\u6cd5\u306f\u3001\u4e3b\u306b\u4ee5\u4e0b\u306e2\u3064\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u2460 Q-Q\u30d7\u30ed\u30c3\u30c8\u306b\u3088\u308b\u8996\u899a\u7684\u78ba\u8a8d<\/h3>\n\n\n\n<p>\u6700\u3082\u5b9f\u7528\u7684\u3067\u63a8\u5968\u3055\u308c\u308b\u65b9\u6cd5\u3067\u3042\u308b\u3002\u7406\u8ad6\u4e0a\u306e\u6b63\u898f\u5206\u5e03\u3068\u5b9f\u969b\u306e\u6b8b\u5dee\u3092\u6bd4\u8f03\u3057\u305f\u6563\u5e03\u56f3\u3092\u78ba\u8a8d\u3059\u308b\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u59a5\u5f53\u306a\u72b6\u614b:<\/strong> \u70b9\u304c\u5bfe\u89d2\u7dda\uff0845\u5ea6\u7dda\uff09\u4e0a\u306b\u307b\u307c\u91cd\u306a\u3063\u3066\u3044\u308b\u3002<\/li>\n\n\n\n<li><strong>\u554f\u984c\u304c\u3042\u308b\u72b6\u614b:<\/strong> 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\u5909\u63db\uff09\u3059\u308b\u3053\u3068\u3067\u3001\u6b8b\u5dee\u306e\u5206\u5e03\u3092\u6b63\u898f\u5206\u5e03\u306b\u8fd1\u3065\u3051\u308b\u3002\u7279\u306b\u304a\u91d1\u3084\u4eba\u53e3\u306a\u3069\u3001\u88fe\u306e\u9577\u3044\u30c7\u30fc\u30bf\u306b\u6709\u52b9\u3067\u3042\u308b\u3002<\/li>\n\n\n\n<li><strong>\u5916\u308c\u5024\u306e\u7cbe\u67fb:<\/strong> \u7279\u5b9a\u306e\u6570\u70b9\u304c\u6b63\u898f\u6027\u3092\u8457\u3057\u304f\u640d\u306a\u3063\u3066\u3044\u308b\u5834\u5408\u3001\u305d\u306e\u30c7\u30fc\u30bf\u304c\u5165\u529b\u30df\u30b9\u3084\u7570\u5e38\u5024\u3067\u306a\u3044\u304b\u3092\u78ba\u8a8d\u3057\u3001\u9664\u5916\u306e\u662f\u975e\u3092\u691c\u8a0e\u3059\u308b\u3002<\/li>\n\n\n\n<li><strong>\u4e00\u822c\u5316\u7dda\u5f62\u30e2\u30c7\u30eb\uff08GLM\uff09\u3078\u306e\u79fb\u884c:<\/strong> 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