{"id":508,"date":"2023-07-29T16:29:54","date_gmt":"2023-07-29T16:29:54","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e5%a6%82%e4%bd%95%e4%bd%bf%e7%94%a8%e5%ba%93%e5%85%8b%e8%b7%9d%e7%a6%bb%e8%af%86%e5%88%ab%e6%9c%89%e5%bd%b1%e5%93%8d%e7%9a%84%e6%95%b0%e6%8d%ae%e7%82%b9\/"},"modified":"2023-07-29T16:29:54","modified_gmt":"2023-07-29T16:29:54","slug":"%e5%a6%82%e4%bd%95%e4%bd%bf%e7%94%a8%e5%ba%93%e5%85%8b%e8%b7%9d%e7%a6%bb%e8%af%86%e5%88%ab%e6%9c%89%e5%bd%b1%e5%93%8d%e7%9a%84%e6%95%b0%e6%8d%ae%e7%82%b9","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e5%a6%82%e4%bd%95%e4%bd%bf%e7%94%a8%e5%ba%93%e5%85%8b%e8%b7%9d%e7%a6%bb%e8%af%86%e5%88%ab%e6%9c%89%e5%bd%b1%e5%93%8d%e7%9a%84%e6%95%b0%e6%8d%ae%e7%82%b9\/","title":{"rendered":"\u5982\u4f55\u4f7f\u7528\u5e93\u514b\u8ddd\u79bb\u8bc6\u522b\u6709\u5f71\u54cd\u529b\u7684\u6570\u636e\u70b9"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>\u5e93\u514b\u8ddd\u79bb<\/strong>\uff08\u901a\u5e38\u8868\u793a\u4e3a<sub>Di\uff09<\/sub>\u5728<a href=\"https:\/\/statorials.org\/cn\/\u591a\u5143\u7ebf\u6027\u56de\u5f52-1\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u56de\u5f52\u5206\u6790<\/a>\u4e2d\u7528\u4e8e\u8bc6\u522b\u53ef\u80fd\u5bf9\u56de\u5f52\u6a21\u578b\u4ea7\u751f\u8d1f\u9762\u5f71\u54cd\u7684\u6709\u5f71\u54cd\u529b\u7684\u6570\u636e\u70b9\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u5e93\u514b\u8ddd\u79bb\u7684\u516c\u5f0f\u4e3a\uff1a<\/span><\/p>\n<p style=\"text-align: center;\"> <span style=\"color: #000000;\"><strong>d <sub>i<\/sub><\/strong> = (r <sub>i<\/sub> <sup>2<\/sup> \/ p*MSE) * (h <sub>ii<\/sub> \/ (1-h <sub>ii<\/sub> ) <sup>2<\/sup> )<\/span><\/p>\n<p><span style=\"color: #000000;\">\u91d1\u5b50\uff1a<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>r<\/strong> <sub><strong>i<\/strong><\/sub>\u662f\u7b2c i<sup>\u4e2a<\/sup>\u6b8b\u57fa<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong>p<\/strong>\u662f\u56de\u5f52\u6a21\u578b\u4e2d\u7684\u7cfb\u6570\u6570\u91cf<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong>MSE<\/strong>\u662f\u5747\u65b9\u8bef\u5dee<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong>h<\/strong> <sub>ii<\/sub>\u4e3a<sup>\u7b2c i<\/sup>\u4e2a\u6760\u6746\u503c<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u5c3d\u7ba1\u8fd9\u4e2a\u516c\u5f0f\u770b\u8d77\u6765\u6709\u70b9\u590d\u6742\uff0c\u4f46\u597d\u6d88\u606f\u662f\u5927\u591a\u6570\u7edf\u8ba1\u8f6f\u4ef6\u90fd\u53ef\u4ee5\u8f7b\u677e\u5730\u4e3a\u60a8\u8ba1\u7b97\u51fa\u6765\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u672c\u8d28\u4e0a\uff0c\u5e93\u514b\u8ddd\u79bb\u505a\u4e86\u4e00\u4ef6\u4e8b\uff1a<strong>\u5b83\u6d4b\u91cf\u5f53\u7b2c i<sup>\u4e2a<\/sup>\u6570\u636e\u70b9\u88ab\u5220\u9664\u65f6\uff0c\u6240\u6709\u6a21\u578b\u7684\u62df\u5408\u503c\u53d1\u751f\u4e86\u591a\u5c11\u53d8\u5316\u3002<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u5e93\u514b\u8ddd\u79bb\u503c\u8f83\u9ad8\u7684\u6570\u636e\u70b9\u8868\u660e\u5b83\u5bf9\u62df\u5408\u503c\u5f71\u54cd\u5f88\u5927\u3002\u4e00\u822c\u89c4\u5219\u662f\uff0c\u5e93\u514b\u8ddd\u79bb\u5927\u4e8e 4\/n\uff08<em>\u5176\u4e2d n \u662f\u6570\u636e\u70b9\u603b\u6570<\/em>\uff09\u7684\u4efb\u4f55\u70b9\u90fd\u88ab\u89c6\u4e3a\u5f02\u5e38\u503c\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u5e93\u514b\u8ddd\u79bb\u901a\u5e38\u7528\u4e8e<em>\u8bc6\u522b<\/em>\u6709\u5f71\u54cd\u529b\u7684\u6570\u636e\u70b9\u3002\u4ec5\u4ec5\u56e0\u4e3a\u4e00\u4e2a\u6570\u636e\u70b9\u6709\u5f71\u54cd\u529b\u5e76\u4e0d\u4e00\u5b9a\u610f\u5473\u7740\u5b83\u5e94\u8be5\u88ab\u5220\u9664\u3002\u60a8\u5e94\u8be5\u9996\u5148\u68c0\u67e5\u6570\u636e\u70b9\u662f\u5426\u53ea\u662f\u9519\u8bef\u8bb0\u5f55\uff0c\u6216\u8005\u6570\u636e\u70b9\u662f\u5426\u5b58\u5728\u53ef\u80fd\u8868\u660e\u6709\u8da3\u53d1\u73b0\u7684\u5947\u602a\u60c5\u51b5\u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u5982\u4f55\u8ba1\u7b97R\u4e2d\u7684\u5e93\u514b\u8ddd\u79bb<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">\u4ee5\u4e0b\u793a\u4f8b\u8bf4\u660e\u4e86\u5982\u4f55\u8ba1\u7b97 R \u4e2d\u7684\u5e93\u514b\u8ddd\u79bb\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u9996\u5148\uff0c\u6211\u4eec\u5c06\u52a0\u8f7d\u672c\u793a\u4f8b\u6240\u9700\u7684\u4e24\u4e2a\u5e93\uff1a<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong>library(ggplot2)\nlibrary(gridExtra)<\/strong><\/pre>\n<p><span style=\"color: #000000;\">\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u5c06\u5b9a\u4e49\u4e24\u4e2a\u6570\u636e\u6846\uff1a\u4e00\u4e2a\u6709\u4e24\u4e2a\u5f02\u5e38\u503c\uff0c\u4e00\u4e2a\u6ca1\u6709\u5f02\u5e38\u503c\u3002<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#create data frame with no outliers<\/span>\nno_outliers &lt;- data.frame(x = c(1, 2, 2, 3, 4, 5, 7, 3, 2, 12, 11, 15, 14, 17, 22),\n                          y = c(22, 23, 24, 23, 19, 34, 35, 36, 36, 34, 32, 38, 41,\n                                42, 44))\n\n<span style=\"color: #008080;\">#create data frame with two outliers\n<\/span>outliers &lt;- data.frame(x = c(1, 2, 2, 3, 4, 5, 7, 3, 2, 12, 11, 15, 14, 17, 22),\n                       y = c( <span style=\"color: #800080;\">190<\/span> , 23, 24, 23, 19, 34, 35, 36, 36, 34, 32, 38, 41,\n                             42, <span style=\"color: #800080;\">180<\/span> ))<\/strong><\/pre>\n<p><span style=\"color: #000000;\">\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u5c06\u521b\u5efa\u4e00\u4e2a\u6563\u70b9\u56fe\u6765\u5e76\u6392\u663e\u793a\u4e24\u4e2a\u6570\u636e\u6846\uff1a<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#create scatterplot for data frame with no outliers\n<\/span>no_outliers_plot &lt;- ggplot(data = no_outliers, aes(x = x, y = y)) +\n  geom_point() +\n  geom_smooth(method = lm) +\n  ylim(0, 200) +\n  ggtitle(\"No Outliers\")\n\n<span style=\"color: #008080;\">#create scatterplot for data frame with outliers\n<\/span>outliers_plot &lt;- ggplot(data = outliers, aes(x = x, y = y)) +\n  geom_point() +\n  geom_smooth(method = lm) +\n  ylim(0, 200) +\n  ggtitle(\"With Outliers\")\n\n<span style=\"color: #008080;\">#plot the two scatterplots side by side\n<\/span>gridExtra::grid.arrange(no_outliers_plot, outliers_plot, ncol=2)<\/strong><\/pre>\n<p><span style=\"color: #000000;\">\u6211\u4eec\u53ef\u4ee5\u770b\u5230\u5f02\u5e38\u503c\u5982\u4f55\u5bf9\u7b2c\u4e8c\u5f20\u56fe\u4e2d\u56de\u5f52\u7ebf\u7684\u62df\u5408\u4ea7\u751f\u8d1f\u9762\u5f71\u54cd\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4e3a\u4e86\u8bc6\u522b\u7b2c\u4e8c\u4e2a\u6570\u636e\u96c6\u4e2d\u7684\u5f71\u54cd\u70b9\uff0c\u6211\u4eec\u53ef\u4ee5\u8ba1\u7b97\u6570\u636e\u96c6\u4e2d\u6bcf\u4e2a\u89c2\u6d4b\u503c\u7684<strong>\u5e93\u514b\u8ddd\u79bb<\/strong>\uff0c\u7136\u540e\u7ed8\u5236\u8fd9\u4e9b\u8ddd\u79bb\u4ee5\u67e5\u770b\u54ea\u4e9b\u89c2\u6d4b\u503c\u9ad8\u4e8e\u4f20\u7edf\u9608\u503c 4\/n\uff1a<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#fit the linear regression model to the dataset with outliers<\/span>\nmodel &lt;- lm(y ~ x, data = outliers)\n\n<span style=\"color: #008080;\">#find Cook's distance for each observation in the dataset\n<\/span>cooksD &lt;- cooks.distance(model)\n\n<span style=\"color: #008080;\"># Plot Cook's Distance with a horizontal line at 4\/n to see which observations<\/span>\n<span style=\"color: #008080;\">#exceed this threshold<\/span>\nn &lt;- nrow(outliers)\nplot(cooksD, main = \"Cooks Distance for Influential Obs\")\nabline(h = 4\/n, lty = 2, col = \"steelblue\") <span style=\"color: #008080;\"># add cutoff line<\/span><\/strong><\/pre>\n<p><span style=\"color: #000000;\">\u6211\u4eec\u53ef\u4ee5\u6e05\u695a\u5730\u770b\u5230\u6570\u636e\u96c6\u4e2d\u7684\u7b2c\u4e00\u4e2a\u548c\u6700\u540e\u4e00\u4e2a\u89c2\u5bdf\u503c\u8d85\u8fc7\u4e86 4\/n \u9608\u503c\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5c06\u8fd9\u4e24\u4e2a\u89c2\u5bdf\u7ed3\u679c\u786e\u5b9a\u4e3a\u5bf9\u56de\u5f52\u6a21\u578b\u4ea7\u751f\u8d1f\u9762\u5f71\u54cd\u7684\u6709\u5f71\u54cd\u529b\u7684\u6570\u636e\u70b9\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u5982\u679c\u6211\u4eec\u60f3\u5220\u9664\u6240\u6709\u8d85\u8fc7 4\/n \u9608\u503c\u7684\u89c2\u6d4b\u503c\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u4ee5\u4e0b\u4ee3\u7801\u6765\u5b9e\u73b0\uff1a<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#identify influential points<\/span>\ninfluential_obs &lt;- as.numeric(names(cooksD)[(cooksD &gt; (4\/n))])\n\n<span style=\"color: #008080;\">#define new data frame with influential points removed\n<\/span>outliers_removed &lt;- outliers[-influential_obs, ]<\/strong><\/pre>\n<p><span style=\"color: #000000;\">\u7136\u540e\u6211\u4eec\u53ef\u4ee5\u6bd4\u8f83\u4e24\u4e2a\u6563\u70b9\u56fe\uff1a\u4e00\u4e2a\u663e\u793a\u5b58\u5728\u5f71\u54cd\u70b9\u7684\u56de\u5f52\u7ebf\uff0c\u53e6\u4e00\u4e2a\u663e\u793a\u5220\u9664\u5f71\u54cd\u70b9\u7684\u56de\u5f52\u7ebf\uff1a<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#create scatterplot with outliers present<\/span>\noutliers_present &lt;- ggplot(data = outliers, aes(x = x, y = y)) +\n  geom_point() +\n  geom_smooth(method = lm) +\n  ylim(0, 200) +\n  ggtitle(\"Outliers Present\")\n\n<span style=\"color: #008080;\">#create scatterplot with outliers removed<\/span>\noutliers_removed &lt;- ggplot(data = outliers_removed, aes(x = x, y = y)) +\n  geom_point() +\n  geom_smooth(method = lm) +\n  ylim(0, 200) +\n  ggtitle(\"Outliers Removed\")\n\n<span style=\"color: #008080;\">#plot both scatterplots side by side\n<\/span>gridExtra::grid.arrange(outliers_present, outliers_removed, ncol = 2)<\/strong><\/pre>\n<p><span style=\"color: #000000;\">\u4e00\u65e6\u79fb\u9664\u4e24\u4e2a\u6709\u5f71\u54cd\u7684\u6570\u636e\u70b9\uff0c\u6211\u4eec\u53ef\u4ee5\u6e05\u695a\u5730\u770b\u5230\u56de\u5f52\u7ebf\u5bf9\u6570\u636e\u7684\u62df\u5408\u6548\u679c\u5982\u4f55\u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u6280\u672f\u8bf4\u660e<\/strong><\/span><\/h3>\n<ul>\n<li><span style=\"color: #000000;\">\u5927\u591a\u6570\u7edf\u8ba1\u8f6f\u4ef6\u90fd\u80fd\u591f\u8f7b\u677e\u8ba1\u7b97\u6570\u636e\u96c6\u4e2d\u6bcf\u4e2a\u89c2\u6d4b\u503c\u7684\u5e93\u514b\u8ddd\u79bb\u3002<\/span><\/li>\n<li><span style=\"color: #000000;\">\u8bf7\u8bb0\u4f4f\uff0c\u5e93\u514b\u8ddd\u79bb\u53ea\u662f\u4e00\u79cd<em>\u8bc6\u522b<\/em>\u5f71\u54cd\u70b9\u7684\u65b9\u6cd5\u3002<\/span><\/li>\n<li><span style=\"color: #000000;\"><em>\u5904\u7406<\/em>\u6709\u5f71\u54cd\u7684\u70b9\u7684\u65b9\u6cd5\u6709\u5f88\u591a\uff0c\u5305\u62ec\uff1a\u5220\u9664\u8fd9\u4e9b\u70b9\uff0c\u7528\u5e73\u5747\u503c\u6216\u4e2d\u4f4d\u6570\u7b49\u503c\u66ff\u6362\u8fd9\u4e9b\u70b9\uff0c\u6216\u8005\u7b80\u5355\u5730\u5c06\u8fd9\u4e9b\u70b9\u4fdd\u7559\u5728\u6a21\u578b\u4e2d\uff0c\u4f46\u5728\u62a5\u544a\u7ed3\u679c\u56de\u5f52\u65f6\u4ed4\u7ec6\u8bb0\u4e0b\u5b83\u4eec\u3002<\/span><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>\u5e93\u514b\u8ddd\u79bb\uff08\u901a\u5e38\u8868\u793a\u4e3aDi\uff09\u5728\u56de\u5f52\u5206\u6790\u4e2d\u7528\u4e8e\u8bc6\u522b\u53ef\u80fd\u5bf9\u56de\u5f52\u6a21\u578b\u4ea7\u751f\u8d1f\u9762\u5f71\u54cd\u7684\u6709\u5f71\u54cd\u529b\u7684\u6570\u636e\u70b9\u3002 \u5e93\u514b\u8ddd\u79bb\u7684\u516c\u5f0f\u4e3a [&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-508","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>\u5982\u4f55\u4f7f\u7528\u5e93\u514b\u8ddd\u79bb\u8bc6\u522b\u6709\u5f71\u54cd\u529b\u7684\u6570\u636e\u70b9 - Statorials<\/title>\n<meta name=\"description\" content=\"\u672c\u6559\u7a0b\u4ecb\u7ecd\u5982\u4f55\u4f7f\u7528\u5e93\u514b\u8ddd\u79bb\u5728\u56de\u5f52\u5206\u6790\u4e2d\u8bc6\u522b\u6709\u5f71\u54cd\u7684\u6570\u636e\u70b9\u3002\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" 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