{"id":5249,"date":"2024-08-21T17:11:04","date_gmt":"2024-08-21T08:11:04","guid":{"rendered":"https:\/\/blog.since2020.jp\/?p=5249"},"modified":"2024-08-26T09:45:39","modified_gmt":"2024-08-26T00:45:39","slug":"multiple_regression_multicollinearity","status":"publish","type":"post","link":"https:\/\/since2020.jp\/media\/multiple_regression_multicollinearity\/","title":{"rendered":"\u3010\u30c7\u30fc\u30bf\u5206\u6790\u3011\u91cd\u56de\u5e30\u5206\u6790\u306b\u304a\u3051\u308b\u591a\u91cd\u5171\u7dda\u6027\u3068\u305d\u306e\u5224\u5b9a\u6cd5\u306b\u3064\u3044\u3066"},"content":{"rendered":"\n

\u30c7\u30fc\u30bf\u5206\u6790\u306b\u304a\u3044\u3066\u3001\u91cd\u56de\u5e30\u5206\u6790\u306f\u5404\u8aac\u660e\u5909\u6570\u304c\u76ee\u7684\u5909\u6570\u306b\u5bfe\u3057\u3066\u3001\u3069\u308c\u304f\u3089\u3044\u5f71\u97ff\u3092\u4e0e\u3048\u308b\u306e\u304b\u3092\u7406\u89e3\u3059\u308b\u4e0a\u3067\u91cd\u8981\u306a\u6307\u6a19\u3067\u3059\u3002\u91cd\u56de\u5e30\u5206\u6790\u3067\u306f\u3001\u5206\u6790\u3092\u884c\u3046\u969b\u306b\u6ce8\u610f\u3059\u3079\u304d\u554f\u984c\u306e\uff11\u3064\u306b\u300c\u591a\u91cd\u5171\u7dda\u6027\u300d\u3068\u3044\u3046\u3082\u306e\u304c\u3042\u308a\u307e\u3059\u3002\u672c\u8a18\u4e8b\u3067\u306f\u3001\u91cd\u56de\u5e30\u5206\u6790\u306b\u304a\u3051\u308b\u591a\u91cd\u5171\u7dda\u6027\u306e\u554f\u984c\u3068\u305d\u306e\u5224\u5b9a\u6cd5\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002<\/p>\n\n\n

0.\u672c\u30d6\u30ed\u30b0\u306e\u8981\u7d04<\/h2>\n

\u6700\u521d\u306b\u672c\u30d6\u30ed\u30b0\u306e\u8981\u70b9\u3092\u30b7\u30f3\u30d7\u30eb\u306b\u304b\u3064\u30dd\u30c3\u30d7\u306b\u307e\u3068\u3081\u307e\u3059<\/p>\r\n

 <\/p>\r\n

\u2460\u91cd\u56de\u5e30\u5206\u6790\u2192\u30c7\u30fc\u30bf\u5206\u6790\u624b\u6cd5\u3060\u3088\u301c<\/p>\r\n

\u2461\u91cd\u56de\u5e30\u5206\u6790\u306b\u306f\u591a\u91cd\u5171\u7dda\u6027\u3063\u3066\u3082\u306e\u304c\u5b58\u5728\u3059\u308b\u3088\u30fc<\/p>\r\n

\u2462\u591a\u91cd\u5171\u7dda\u6027\u3063\u3066\u306a\u3093\u3067\u30c0\u30e1\u306a\u306e\u2192\u5404\u8aac\u660e\u5909\u6570\u306f\u91cd\u56de\u5e30\u5206\u6790\u3067\u306f\u300c\u4e92\u3044\u306b\u72ec\u7acb\u300d\u3063\u3066\u30eb\u30fc\u30eb\u306e\u3082\u3068\u3067\u5206\u6790\u304c\u884c\u308f\u308c\u3066\u3044\u308b\u3002\u2192\u5404\u5909\u6570\u9593\u306b\u76f8\u95a2\u304c\u3042\u3063\u305f\u3089\u3001\u30eb\u30fc\u30eb\u304c\u5d29\u308c\u3066\u5206\u6790\u304c\u304a\u304b\u3057\u304f\u306a\u308b\u3088\u306d<\/p>\r\n

\u2463\u591a\u91cd\u5171\u7dda\u6027\u3063\u3066\u3069\u3046\u3084\u3063\u3066\u30c1\u30a7\u30c3\u30af\u3059\u308b\u306e\u2192VIF\u3068\u76f8\u95a2\u884c\u5217<\/p>\r\n

\u2464\u591a\u91cd\u5171\u7dda\u6027\u3092\u898b\u3064\u3051\u305f\u3089\u2192\u5909\u6570\u524a\u9664or\u4e3b\u6210\u5206\u5206\u6790<\/p>\r\n

<\/p>\n\n

1.\u306f\u3058\u3081\u306b<\/h2>\n

\u30c7\u30fc\u30bf\u5206\u6790\u306b\u304a\u3044\u3066\u3001\u91cd\u56de\u5e30\u5206\u6790\u306f\u5404\u8aac\u660e\u5909\u6570\u304c\u76ee\u7684\u5909\u6570\u306b\u5bfe\u3057\u3066\u3001\u3069\u308c\u304f\u3089\u3044\u5f71\u97ff\u3092\u4e0e\u3048\u308b\u306e\u304b\u3092\u7406\u89e3\u3059\u308b\u4e0a\u3067\u91cd\u8981\u306a\u6307\u6a19\u3067\u3059\u3002\u91cd\u56de\u5e30\u5206\u6790\u3067\u306f\u3001\u5206\u6790\u3092\u884c\u3046\u969b\u306b\u6ce8\u610f\u3059\u3079\u304d\u554f\u984c\u306e\uff11\u3064\u306b\u300c\u591a\u91cd\u5171\u7dda\u6027\u300d\u3068\u3044\u3046\u3082\u306e\u304c\u3042\u308a\u307e\u3059\u3002\u672c\u8a18\u4e8b\u3067\u306f\u3001\u91cd\u56de\u5e30\u5206\u6790\u306b\u304a\u3051\u308b\u591a\u91cd\u5171\u7dda\u6027\u306e\u554f\u984c\u3068\u305d\u306e\u5224\u5b9a\u6cd5\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002<\/p>\n\n

2.\u91cd\u56de\u5e30\u5206\u6790<\/h2>\n

\u91cd\u56de\u5e30\u5206\u6790\u3068\u306f\u3001\u76ee\u7684\u5909\u6570(\u5f93\u5c5e\u5909\u6570\uff09\u3068\u8907\u6570\u306e\u8aac\u660e\u5909\u6570\uff08\u72ec\u7acb\u5909\u6570\uff09\u3068\u306e\u95a2\u4fc2\u3092\u30e2\u30c7\u30eb\u5316\u3059\u308b\u624b\u6cd5\u3067\u3059\u3002\u91cd\u56de\u5e30\u5206\u6790\u306e\u6570\u5f0f\u306f\u4e0b\u8a18\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\r\n

$$ \\widehat{Y} = \\beta_0 + \\beta_1 X_1 + \\beta_2 X_2 + \\dots + \\beta_n X_n $$<\/p>\r\n

\u3053\u306e\u6642\u3001\u5404\u8aac\u660e\u5909\u6570\uff08\u72ec\u7acb\u5909\u6570)\u306f\u300c\u4e92\u3044\u306b\u72ec\u7acb\u300d\u3068\u3044\u3046\u30eb\u30fc\u30eb\u304c\u3042\u308a\u3001\u3053\u306e\u30eb\u30fc\u30eb\u306e\u3082\u3068\u3067\u5206\u6790\u304c\u884c\u308f\u308c\u307e\u3059\u3002\u307e\u305f\u3001\u5404\u8aac\u660e\u5909\u6570\u304c\u3069\u308c\u3060\u3051\u76ee\u7684\u5909\u6570\u306b\u5f71\u97ff\u3092\u3057\u305f\u304b\u3092\u8003\u3048\u308b\u65b9\u6cd5\u3068\u3057\u3066\u306f\u3001\u3042\u308b\uff11\u3064\u306e\u5909\u6570\u304c\uff11\u5909\u5316\u3057\u305f\u6642\u306b\u76ee\u7684\u5909\u6570\u304c\u3069\u308c\u3060\u3051\u5909\u5316\u3057\u305f\u304b\u3092\u8003\u3048\u307e\u3059\u3002\u3053\u306e\u3068\u304d\u3001\u5404\u5909\u6570\u304c\u4e92\u3044\u306b\u72ec\u7acb\u3068\u3044\u3046\u30eb\u30fc\u30eb\u304c\u3044\u304d\u3066\u304d\u307e\u3059\u3002<\/p>\n\n

3.\u591a\u91cd\u5171\u7dda\u6027\u3068\u306f<\/h2>\n

\u591a\u91cd\u5171\u7dda\u6027\u3068\u306f\u3001\u8aac\u660e\u5909\u6570\u9593\u306b\u9ad8\u3044\u76f8\u95a2\u304c\u3042\u308b\u72b6\u614b\u3092\u8a00\u3044\u307e\u3059\u3002\uff08\u91cd\u56de\u5e30\u5206\u6790\u306e\u8aac\u660e\u3067\u306f\u3001\u5404\u8aac\u660e\u5909\u6570\u306f\u4e92\u3044\u306b\u72ec\u7acb\u3057\u3066\u3044\u308b\u3068\u8a00\u3044\u307e\u3057\u305f\u304c\u3001\u73fe\u5b9f\u306f\u3001\u591a\u5c11\u76f8\u95a2\u304c\u3042\u3063\u3066\u3082\u76f8\u95a2\u304c\u5927\u304d\u304f\u306a\u3051\u308c\u3070\u554f\u984c\u306a\u3044\u3067\u3059\u3002\uff09\u3053\u306e\u3088\u3046\u306a\u72b6\u614b\u304c\u767a\u751f\u3059\u308b\u3068\u3001\u30e2\u30c7\u30eb\u306e\u4fe1\u983c\u6027\u3068\u89e3\u91c8\u53ef\u80fd\u6027\u306b\u6df1\u523b\u306a\u5f71\u97ff\u3092\u4e0e\u3048\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002\u4ee5\u4e0b\u306b\u3001\u591a\u91cd\u5171\u7dda\u6027\u304c\u5f15\u304d\u8d77\u3053\u3059\u4e3b\u306a\u30c7\u30e1\u30ea\u30c3\u30c8\u3092\u7d39\u4ecb\u3057\u307e\u3059\u3002<\/p>\r\n

\u2460\u30e2\u30c7\u30eb\u306e\u89e3\u91c8\u304c\u56f0\u96e3\u306b\u306a\u308b<\/p>\r\n

\u91cd\u56de\u5e30\u5206\u6790\u306e\u57fa\u672c\u7684\u306a\u524d\u63d0\u3068\u3057\u3066\u3001\u5404\u8aac\u660e\u5909\u6570\u306f\u4e92\u3044\u306b\u72ec\u7acb\u3067\u3042\u308b\u3053\u3068\u304c\u6c42\u3081\u3089\u308c\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u8aac\u660e\u5909\u6570\u9593\u3067\u9ad8\u3044\u76f8\u95a2\u304c\u3042\u308b\u3068\u3001\u524d\u63d0\u6761\u4ef6\u304c\u5d29\u308c\u3066\u3057\u307e\u3044\u3001\u76ee\u7684\u5909\u6570\u306b\u5bc4\u4e0e\u3059\u308b\u8aac\u660e\u5909\u6570\u3092\u300c\u898b\u3064\u3051\u305a\u3089\u304f\u306a\u308a\u307e\u3059\u3002<\/p>\r\n

\u2461\u7d71\u8a08\u7684\u6709\u610f\u6027\u306e\u4f4e\u4e0b<\/p>\r\n

\u5404\u8aac\u660e\u5909\u6570\u306b\u5bfe\u3057\u3066\u3001\u76ee\u7684\u5909\u6570\u306b\u5bc4\u4e0e\u3057\u305f\u306e\u306f\u300c\u7d71\u8a08\u7684\u306b\u6709\u610f(\u5fc5\u7136\u7684\u3067\u3042\u308b\u306e\u304b\uff09\u306a\u306e\u304b\u300d\u3069\u3046\u304b\u5224\u65ad\u3059\u308b\u5834\u9762\u304c\u3042\u308a\u307e\u3059\u3002\u305d\u306e\u6642\u306b\u3001\u591a\u91cd\u5171\u7dda\u6027\u304c\u767a\u751f\u3057\u3066\u3044\u308b\u3068\u3001\u672c\u6765\u306f\u7d71\u8a08\u7684\u306b\u6709\u610f\u306a\u5909\u6570\u3082\u6709\u610f\u3067\u306a\u3044\u3068\u5224\u65ad\u3055\u308c\u3066\u3057\u307e\u3046\u5834\u5408\u304c\u3042\u308a\u307e\u3059\uff08\u9006\u3082\u3042\u308a\u307e\u3059\uff09\u3002<\/p>\r\n

<\/p>\n\n

4.\u591a\u91cd\u5171\u7dda\u6027\u306e\u5224\u5b9a\u6cd5<\/h2>\n

\u591a\u91cd\u5171\u7dda\u6027\u306e\u5224\u5b9a\u3092\u3059\u308b\u305f\u3081\u306b\u306f\u3001\u3044\u304f\u3064\u304b\u306e\u624b\u6cd5\u304c\u3042\u308a\u307e\u3059\u3002\u4eca\u56de\u306f\u3001\u305d\u306e\u4e2d\u3067\u3082\u6709\u540d\u306a\uff12\u3064\u306e\u624b\u6cd5\u3092\u7d39\u4ecb\u3057\u307e\u3059\u3002<\/p>\r\n

\u2460VIF(\u5206\u6563\u62e1\u5927\u8981\u56e0:Variance inflation factor)<\/p>\r\n

VIF\u306f\u7279\u5b9a\u306e\u8aac\u660e\u5909\u6570\u304c\u4ed6\u306e\u8aac\u660e\u5909\u6570\u306b\u5bfe\u3057\u3066\u3001\u3069\u306e\u7a0b\u5ea6\u76f8\u95a2\u3057\u3066\u3044\u308b\u304b\u3092\u793a\u3059\u6307\u6a19\u3067\u3042\u308a\u3001\u4e00\u822c\u7684\u306bVIF\u304c10\u3092\u8d85\u3048\u308b\u5834\u5408\u306f\u3001\u591a\u91cd\u5171\u7dda\u6027\u304c\u5f37\u3044\u3068\u5224\u65ad\u3055\u308c\u307e\u3059\u3002<\/p>\r\n

\u2461\u76f8\u95a2\u884c\u5217<\/p>\r\n

\u76f8\u95a2\u884c\u5217\u306f\u5404\u5909\u6570\u306e\u76f8\u95a2\u95a2\u4fc2\u3092\u307e\u3068\u3081\u305f\u8868\u306b\u306a\u308a\u307e\u3059\u3002\u8aac\u660e\u5909\u6570\u9593\u306e\u76f8\u95a2\u884c\u5217\u3092\u898b\u3066\u3001\u76f8\u95a2\u4fc2\u6570\u306e\u5024\u304c0.7\u4ee5\u4e0a\u306e\u5834\u5408\u3001\u591a\u91cd\u5171\u7dda\u6027\u306e\u53ef\u80fd\u6027\u304c\u9ad8\u3044\u3067\u3059\u3002\u305f\u3060\u3057\u3001\u76f8\u95a2\u884c\u5217\u3067\u306f2\u5909\u6570\u9593\u306e\u60c5\u5831\u3057\u304b\u898b\u308ct\u306a\u3044\u305f\u3081\u3001VIF\u3092\u4f7f\u3063\u305f\u65b9\u304c\u3088\u308a\u5b89\u5168\u3060\u3068\u8003\u3048\u3089\u308c\u307e\u3059\u3002<\/p>\r\n

\u500b\u4eba\u7684\u306b\u304a\u3059\u3059\u3081\u306a\u306e\u306f\u3001\u307e\u305aVIF\u3067\u591a\u91cd\u5171\u7dda\u6027\u3092\u8abf\u3079\u3001\u88dc\u52a9\u7684\u306a\u5f79\u5272\u3067\u76f8\u95a2\u884c\u5217\u3092\u898b\u3066\u3044\u3051\u3070\u826f\u3044\u306e\u3067\u306f\u306a\u3044\u304b\u3068\u601d\u3044\u307e\u3059\u3002\u307e\u305f\u3001\u591a\u91cd\u5171\u7dda\u6027\u306e\u539f\u56e0\u3068\u306a\u308b\u5909\u6570\u304c\u898b\u3064\u304b\u3063\u305f\u5834\u5408\u306f\u3001\u305d\u306e\u5909\u6570\u5909\u6570\u3092\u524a\u9664\u3057\u305f\u308a\u3001\u4e3b\u6210\u5206\u5206\u6790\u3067\u3001\u76f8\u95a2\u304c\u5f37\u3044\u5909\u6570\u3092\u307e\u3068\u3081\u308b\u306a\u3069\u306e\u5bfe\u51e6\u6cd5\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\r\n

<\/p>\n\n

5.\u307e\u3068\u3081<\/h2>\n

\u4eca\u56de\u306f\u3001\u91cd\u56de\u5e30\u5206\u6790\u306b\u304a\u3051\u308b\u591a\u91cd\u5171\u7dda\u6027\u3068\u591a\u91cd\u5171\u7dda\u6027\u306e\u5224\u5b9a\u6cd5\u306b\u3064\u3044\u3066\u3001\u307e\u3068\u3081\u307e\u3057\u305f\u3002\u591a\u91cd\u5171\u7dda\u6027\u3092\u8003\u616e\u3059\u308b\u3053\u3068\u3067\u3088\u308a\u3088\u308a\u3001\u5206\u6790\u3001\u30e2\u30c7\u30eb\u4f5c\u308a\u304c\u53ef\u80fd\u306b\u306a\u308b\u306e\u3067\u305c\u3072\u3084\u3063\u3066\u307f\u3066\u304f\u3060\u3055\u3044\u3002\u6700\u5f8c\u306b\u672c\u30da\u30fc\u30b8\u306e\u8981\u7d04\u3092\u3082\u3046\u4e00\u5ea6\u8f09\u305b\u3066\u7d42\u308f\u308a\u306b\u3057\u307e\u3059\u3002<\/p>\r\n

\u672c\u30d6\u30ed\u30b0\u306e\u8981\u7d04<\/p>\r\n

\u2460\u91cd\u56de\u5e30\u5206\u6790\u2192\u30c7\u30fc\u30bf\u5206\u6790\u624b\u6cd5\u3060\u3088\u301c<\/p>\r\n

\u2461\u91cd\u56de\u5e30\u5206\u6790\u306b\u306f\u591a\u91cd\u5171\u7dda\u6027\u3063\u3066\u3082\u306e\u304c\u5b58\u5728\u3059\u308b\u3088\u30fc<\/p>\r\n

\u2462\u591a\u91cd\u5171\u7dda\u6027\u3063\u3066\u306a\u3093\u3067\u30c0\u30e1\u306a\u306e\u2192\u5404\u8aac\u660e\u5909\u6570\u306f\u91cd\u56de\u5e30\u5206\u6790\u3067\u306f\u300c\u4e92\u3044\u306b\u72ec\u7acb\u300d\u3063\u3066\u30eb\u30fc\u30eb\u306e\u3082\u3068\u3067\u5206\u6790\u304c\u884c\u308f\u308c\u3066\u3044\u308b\u3002\u2192\u5404\u5909\u6570\u9593\u306b\u76f8\u95a2\u304c\u3042\u3063\u305f\u3089\u3001\u30eb\u30fc\u30eb\u304c\u5d29\u308c\u3066\u5206\u6790\u304c\u304a\u304b\u3057\u304f\u306a\u308b\u3088\u306d<\/p>\r\n

\u2463\u591a\u91cd\u5171\u7dda\u6027\u3063\u3066\u3069\u3046\u3084\u3063\u3066\u30c1\u30a7\u30c3\u30af\u3059\u308b\u306e\u2192VIF\u3068\u76f8\u95a2\u884c\u5217<\/p>\r\n

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