{"id":3140,"date":"2023-07-19T00:50:54","date_gmt":"2023-07-19T00:50:54","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e5%90%91%e5%89%8d%e9%80%89%e6%8b%a9\/"},"modified":"2023-07-19T00:50:54","modified_gmt":"2023-07-19T00:50:54","slug":"%e5%90%91%e5%89%8d%e9%80%89%e6%8b%a9","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e5%90%91%e5%89%8d%e9%80%89%e6%8b%a9\/","title":{"rendered":"\u4ec0\u4e48\u662f\u76f4\u63a5\u9009\u62e9\uff1f \uff08\u5b9a\u4e49&amp;#038\uff1b\u793a\u4f8b\uff09"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">\u5728\u7edf\u8ba1\u5b66\u4e2d\uff0c<strong>\u9010\u6b65\u9009\u62e9<\/strong>\u662f\u4e00\u79cd\u8fc7\u7a0b\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u5b83\u4ece\u4e00\u7ec4\u9884\u6d4b\u53d8\u91cf\u6784\u5efa<a href=\"https:\/\/statorials.org\/cn\/\u591a\u5143\u7ebf\u6027\u56de\u5f52-1\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u56de\u5f52\u6a21\u578b<\/a>\uff0c\u65b9\u6cd5\u662f\u5728\u6a21\u578b\u4e2d\u9010\u6b65\u8f93\u5165\u548c\u5220\u9664\u9884\u6d4b\u53d8\u91cf\uff0c\u76f4\u5230\u4e0d\u518d\u6709\u7edf\u8ba1\u4e0a\u6709\u6548\u7684\u7406\u7531\u8f93\u5165\u4e3a\u6b62\u6216\u5220\u9664\u66f4\u591a\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u9010\u6b65\u9009\u62e9\u7684\u76ee\u6807\u662f\u521b\u5efa\u4e00\u4e2a\u56de\u5f52\u6a21\u578b\uff0c\u5176\u4e2d\u5305\u62ec\u4e0e<a href=\"https:\/\/statorials.org\/cn\/\u53d8\u91cf\u89e3\u91ca\u6027\u53cd\u5e94\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u54cd\u5e94\u53d8\u91cf<\/a>\u5728\u7edf\u8ba1\u4e0a\u663e\u7740\u76f8\u5173\u7684\u6240\u6709\u9884\u6d4b\u53d8\u91cf\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\"><span style=\"color: #000000;\">\u6700\u5e38\u7528\u7684\u9010\u6b65\u9009\u62e9\u65b9\u6cd5\u4e4b\u4e00\u79f0\u4e3a<strong>\u76f4\u63a5\u9009\u62e9<\/strong>\uff0c\u5176\u5de5\u4f5c\u539f\u7406\u5982\u4e0b\uff1a<\/span><\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>\u6b65\u9aa4 1\uff1a<\/strong>\u62df\u5408\u6ca1\u6709\u9884\u6d4b\u53d8\u91cf\u7684\u4ec5\u622a\u8ddd\u56de\u5f52\u6a21\u578b\u3002\u8ba1\u7b97\u6a21\u578b\u7684 AIC <strong>*<\/strong>\u503c\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>\u6b65\u9aa4 2\uff1a<\/strong>\u62df\u5408\u6240\u6709\u53ef\u80fd\u7684\u5355\u9884\u6d4b\u56de\u5f52\u6a21\u578b\u3002\u786e\u5b9a\u4ea7\u751f\u6700\u4f4e AIC \u7684\u6a21\u578b\uff0c\u5e76\u4e14\u4e0e\u4ec5\u62e6\u622a\u6a21\u578b\u76f8\u6bd4\uff0cAIC \u5728\u7edf\u8ba1\u4e0a\u663e\u7740\u964d\u4f4e\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>\u6b65\u9aa4 3\uff1a<\/strong>\u5c06\u6240\u6709\u56de\u5f52\u6a21\u578b\u62df\u5408\u5230\u4e24\u4e2a\u53ef\u80fd\u7684\u9884\u6d4b\u53d8\u91cf\u3002\u786e\u5b9a\u4ea7\u751f\u6700\u4f4e AIC \u4e14\u4e0e\u5355\u9884\u6d4b\u53d8\u91cf\u6a21\u578b\u76f8\u6bd4 AIC \u663e\u7740\u964d\u4f4e\u7684\u6a21\u578b\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u91cd\u590d\u6b64\u8fc7\u7a0b\uff0c\u76f4\u5230\u7528\u66f4\u591a\u9884\u6d4b\u53d8\u91cf\u62df\u5408\u56de\u5f52\u6a21\u578b\u4e0d\u518d\u5bfc\u81f4 AIC \u51fa\u73b0\u7edf\u8ba1\u4e0a\u663e\u7740\u7684\u964d\u4f4e\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>*<\/strong>\u60a8\u53ef\u4ee5\u4f7f\u7528\u591a\u79cd\u6307\u6807\u6765\u8ba1\u7b97\u56de\u5f52\u6a21\u578b\u7684\u62df\u5408\u4f18\u5ea6\uff0c\u5305\u62ec\u4ea4\u53c9\u9a8c\u8bc1\u9884\u6d4b\u8bef\u5dee\u3001Cp\u3001BIC\u3001AIC \u6216\u8c03\u6574\u540e\u7684<sup>R2<\/sup> \u3002<\/span><span style=\"color: #000000;\">\u5728\u4e0b\u9762\u7684\u793a\u4f8b\u4e2d\uff0c\u6211\u4eec\u9009\u62e9\u4f7f\u7528 AIC\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4ee5\u4e0b\u793a\u4f8b\u5c55\u793a\u4e86\u5982\u4f55\u5728 R \u4e2d\u6267\u884c\u76f4\u63a5\u9009\u62e9\u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u793a\u4f8b\uff1aR \u4e2d\u7684\u76f4\u63a5\u9009\u62e9<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">\u5bf9\u4e8e\u6b64\u793a\u4f8b\uff0c\u6211\u4eec\u5c06\u4f7f\u7528 R \u4e2d\u5185\u7f6e\u7684<a href=\"https:\/\/statorials.org\/cn\/mtcars-r-\u6570\u636e\u96c6\/\" target=\"_blank\" rel=\"noopener\">mtcars \u6570\u636e\u96c6<\/a>\uff1a<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#view first six rows of <em>mtcars\n<\/em><\/span>head(mtcars)\n\n                   mpg cyl disp hp drat wt qsec vs am gear carb\nMazda RX4 21.0 6 160 110 3.90 2.620 16.46 0 1 4 4\nMazda RX4 Wag 21.0 6 160 110 3.90 2.875 17.02 0 1 4 4\nDatsun 710 22.8 4 108 93 3.85 2.320 18.61 1 1 4 1\nHornet 4 Drive 21.4 6 258 110 3.08 3.215 19.44 1 0 3 1\nHornet Sportabout 18.7 8 360 175 3.15 3.440 17.02 0 0 3 2\nValiant 18.1 6 225 105 2.76 3,460 20.22 1 0 3 1\n<\/strong><\/pre>\n<p><span style=\"color: #000000;\">\u6211\u4eec\u5c06\u4f7f\u7528<em>mpg<\/em> \uff08\u82f1\u91cc\/\u52a0\u4ed1\uff09\u4f5c\u4e3a\u54cd\u5e94\u53d8\u91cf\uff0c\u5e76\u4f7f\u7528\u6570\u636e\u96c6\u4e2d\u7684\u5176\u4ed6 10 \u4e2a\u53d8\u91cf\u4f5c\u4e3a\u6f5c\u5728\u7684\u9884\u6d4b\u53d8\u91cf\u6765\u62df\u5408\u591a\u5143\u7ebf\u6027\u56de\u5f52\u6a21\u578b\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4ee5\u4e0b\u4ee3\u7801\u6f14\u793a\u4e86\u5982\u4f55\u9010\u6b65\u6267\u884c\u9009\u62e9\uff1a<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#define intercept-only model\n<\/span>intercept_only &lt;- lm(mpg ~ 1, data=mtcars)\n\n<span style=\"color: #008080;\">#define model with all predictors\n<\/span>all &lt;- lm(mpg ~ ., data=mtcars)\n\n<span style=\"color: #008080;\">#perform forward stepwise regression\n<\/span>forward &lt;- step(intercept_only, direction=' <span style=\"color: #008000;\">forward<\/span> ', scope= <span style=\"color: #3366ff;\">formula<\/span> (all), trace= <span style=\"color: #008000;\">0<\/span> )\n\n<span style=\"color: #008080;\">#view results of forward stepwise regression<\/span>\nforward$anova\n\n   Step Df Deviance Resid. Df Resid. Dev AIC\n1 NA NA 31 1126.0472 115.94345\n2 + wt -1 847.72525 30 278.3219 73.21736\n3 + cyl -1 87.14997 29 191.1720 63.19800\n4 + hp -1 14.55145 28 176.6205 62.66456\n\n<span style=\"color: #008080;\">#view final model\n<\/span>forward$coefficients\n\n(Intercept) wt cyl hp \n 38.7517874 -3.1669731 -0.9416168 -0.0180381 \n<\/strong><\/pre>\n<p><span style=\"color: #000000;\">\u4ee5\u4e0b\u662f\u5982\u4f55\u89e3\u91ca\u7ed3\u679c\uff1a<\/span><\/p>\n<p><span style=\"color: #000000;\">\u9996\u5148\uff0c\u6211\u4eec\u62df\u5408\u4ec5\u622a\u8ddd\u6a21\u578b\u3002\u8be5\u6a21\u578b\u7684 AIC \u4e3a<strong>115.94345<\/strong> \u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u7136\u540e\u6211\u4eec\u5c06\u6240\u6709\u53ef\u80fd\u7684\u6a21\u578b\u62df\u5408\u5230\u9884\u6d4b\u5668\u3002\u4e0e\u4f7f\u7528<em>wt<\/em>\u9884\u6d4b\u5668\u7684\u4ec5\u622a\u8ddd\u6a21\u578b\u76f8\u6bd4\uff0c\u4ea7\u751f\u6700\u4f4e AIC \u5e76\u4e14 AIC \u4e5f\u5177\u6709\u7edf\u8ba1\u663e\u7740\u6027\u964d\u4f4e\u7684\u6a21\u578b\u3002\u8be5\u6a21\u578b\u7684 AIC \u4e3a<strong>73.21736<\/strong> \u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u7528\u4e24\u4e2a\u9884\u6d4b\u53d8\u91cf\u62df\u5408\u6240\u6709\u53ef\u80fd\u7684\u6a21\u578b\u3002\u4e0e\u6dfb\u52a0\u4e86<em>cyl<\/em>\u9884\u6d4b\u5668\u7684\u5355\u9884\u6d4b\u5668\u6a21\u578b\u76f8\u6bd4\uff0c\u4ea7\u751f\u6700\u4f4e AIC \u4e14 AIC \u5177\u6709\u7edf\u8ba1\u663e\u7740\u6027\u964d\u4f4e\u7684\u6a21\u578b\u3002\u8be5\u6a21\u578b\u7684 AIC \u4e3a<strong>63.19800<\/strong> \u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u5c06\u6240\u6709\u53ef\u80fd\u7684\u6a21\u578b\u62df\u5408\u5230\u4e09\u4e2a\u9884\u6d4b\u53d8\u91cf\u3002\u4e0e\u6dfb\u52a0\u4e86<em>hp<\/em>\u9884\u6d4b\u5668\u7684\u53cc\u9884\u6d4b\u5668\u6a21\u578b\u76f8\u6bd4\uff0c\u4ea7\u751f\u6700\u4f4e AIC \u4e14 AIC \u5177\u6709\u7edf\u8ba1\u663e\u7740\u6027\u964d\u4f4e\u7684\u6a21\u578b\u3002\u8be5\u6a21\u578b\u7684 AIC \u4e3a<strong>62.66456<\/strong> \u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u5c06\u6240\u6709\u53ef\u80fd\u7684\u6a21\u578b\u62df\u5408\u5230\u56db\u4e2a\u9884\u6d4b\u53d8\u91cf\u3002\u4e8b\u5b9e\u8bc1\u660e\uff0c\u8fd9\u4e9b\u6a21\u578b\u90fd\u6ca1\u6709\u663e\u7740\u964d\u4f4e AIC\uff0c\u56e0\u6b64\u6211\u4eec\u505c\u6b62\u4e86\u8be5\u8fc7\u7a0b\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u56e0\u6b64\uff0c\u6700\u7ec8\u6a21\u578b\u662f\uff1a<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>mpg = 38.75 \u2013 3.17*\u91cd\u91cf \u2013 0.94*\u7f38\u6570 \u2013 0.02*hyp<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u4e8b\u5b9e\u8bc1\u660e\uff0c\u5c1d\u8bd5\u5411\u6a21\u578b\u4e2d\u6dfb\u52a0\u66f4\u591a\u9884\u6d4b\u53d8\u91cf\u5e76\u4e0d\u4f1a\u5bfc\u81f4 AIC \u5728\u7edf\u8ba1\u4e0a\u663e\u7740\u964d\u4f4e\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u56e0\u6b64\uff0c\u6211\u4eec\u5f97\u51fa\u7684\u7ed3\u8bba\u662f\uff0c\u6700\u597d\u7684\u6a21\u578b\u662f\u5177\u6709\u4e09\u4e2a\u9884\u6d4b\u53d8\u91cf\u7684\u6a21\u578b\uff1awt\u3001cyl \u548c hp\u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u4f7f\u7528AIC\u7684\u6ce8\u610f\u4e8b\u9879<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">\u5728\u524d\u9762\u7684\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u9009\u62e9\u4f7f\u7528AIC\u4f5c\u4e3a\u8861\u91cf\u5404\u79cd\u56de\u5f52\u6a21\u578b\u62df\u5408\u5ea6\u7684\u6307\u6807\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\">AIC \u4ee3\u8868<strong>\u8d64\u6c60\u4fe1\u606f\u51c6\u5219<\/strong>\uff0c\u8ba1\u7b97\u516c\u5f0f\u5982\u4e0b\uff1a<\/span><\/p>\n<p> <span style=\"color: #000000;\">AIC = 2K \u2013 2 <em>ln<\/em> (L)<\/span><\/p>\n<p><span style=\"color: #000000;\">\u91d1\u5b50\uff1a<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>K\uff1a<\/strong>\u6a21\u578b\u53c2\u6570\u7684\u6570\u91cf\u3002<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong><em>ln<\/em> (L)<\/strong> \uff1a\u6a21\u578b\u7684\u5bf9\u6570\u4f3c\u7136\u3002\u8fd9\u544a\u8bc9\u6211\u4eec\u6a21\u578b\u57fa\u4e8e\u6570\u636e\u7684\u53ef\u80fd\u6027\u6709\u591a\u5927\u3002<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u4f46\u662f\uff0c\u60a8\u53ef\u4ee5\u9009\u62e9\u4f7f\u7528\u5176\u4ed6\u6307\u6807\u6765\u8bc4\u4f30\u56de\u5f52\u6a21\u578b\u7684\u62df\u5408\u5ea6\uff0c\u5305\u62ec\u4ea4\u53c9\u9a8c\u8bc1\u9884\u6d4b\u8bef\u5dee\u3001Cp\u3001BIC\u3001AIC \u6216\u8c03\u6574\u540e\u7684<sup>R2<\/sup> \u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u5e78\u8fd0\u7684\u662f\uff0c\u5927\u591a\u6570\u7edf\u8ba1\u8f6f\u4ef6\u90fd\u5141\u8bb8\u60a8\u5728\u76f4\u63a5\u9009\u62e9\u65f6\u6307\u5b9a\u8981\u4f7f\u7528\u54ea\u4e2a\u6307\u6807\u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u5176\u4ed6\u8d44\u6e90<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">\u4ee5\u4e0b\u6559\u7a0b\u63d0\u4f9b\u6709\u5173\u56de\u5f52\u6a21\u578b\u7684\u5176\u4ed6\u4fe1\u606f\uff1a<\/span><\/p>\n<p><a href=\"https:\/\/statorials.org\/cn\/\u591a\u91cd\u5171\u7ebf\u6027\u56de\u5f52\/\" target=\"_blank\" rel=\"noopener\">\u56de\u5f52\u4e2d\u7684\u591a\u91cd\u5171\u7ebf\u6027\u548c VIF \u6307\u5357<\/a><br \/><a href=\"https:\/\/statorials.org\/cn\" target=\"_blank\" rel=\"noopener\">\u4ec0\u4e48\u88ab\u8ba4\u4e3a\u662f\u826f\u597d\u7684 AIC \u503c\uff1f<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5728\u7edf\u8ba1\u5b66\u4e2d\uff0c\u9010\u6b65\u9009\u62e9\u662f\u4e00\u79cd\u8fc7\u7a0b\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u5b83\u4ece\u4e00\u7ec4\u9884\u6d4b\u53d8\u91cf\u6784\u5efa\u56de\u5f52\u6a21\u578b\uff0c\u65b9\u6cd5\u662f\u5728\u6a21\u578b\u4e2d\u9010\u6b65\u8f93\u5165\u548c\u5220\u9664\u9884\u6d4b\u53d8\u91cf [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"class_list":["post-3140","post","type-post","status-publish","format-standard","hentry","category-11"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u4ec0\u4e48\u662f\u76f4\u63a5\u9009\u62e9\uff1f \uff08\u5b9a\u4e49\u548c\u793a\u4f8b\uff09- \u9759\u6001<\/title>\n<meta name=\"description\" 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