{"id":1335,"date":"2023-07-26T20:21:26","date_gmt":"2023-07-26T20:21:26","guid":{"rendered":"https:\/\/statorials.org\/cn\/r-%e4%b8%ad%e7%9a%84%e5%8a%a0%e6%9d%83%e6%9c%80%e5%b0%8f%e4%ba%8c%e4%b9%98%e6%b3%95\/"},"modified":"2023-07-26T20:21:26","modified_gmt":"2023-07-26T20:21:26","slug":"r-%e4%b8%ad%e7%9a%84%e5%8a%a0%e6%9d%83%e6%9c%80%e5%b0%8f%e4%ba%8c%e4%b9%98%e6%b3%95","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/r-%e4%b8%ad%e7%9a%84%e5%8a%a0%e6%9d%83%e6%9c%80%e5%b0%8f%e4%ba%8c%e4%b9%98%e6%b3%95\/","title":{"rendered":"\u5982\u4f55\u5728 r \u4e2d\u6267\u884c\u52a0\u6743\u6700\u5c0f\u4e8c\u4e58\u56de\u5f52"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/cn\/\u7ebf\u6027\u56de\u5f52\u5047\u8bbe\/\" target=\"_blank\" rel=\"noopener\">\u7ebf\u6027\u56de\u5f52\u7684\u5173\u952e\u5047\u8bbe<\/a>\u4e4b\u4e00\u662f<a href=\"https:\/\/statorials.org\/cn\/\u6b8b\u7559\u7269\/\" target=\"_blank\" rel=\"noopener\">\u6b8b\u5dee<\/a>\u5728\u9884\u6d4b\u53d8\u91cf\u7684\u6bcf\u4e2a\u6c34\u5e73\u4e0a\u4ee5\u76f8\u7b49\u65b9\u5dee\u5206\u5e03\u3002\u8fd9\u79cd\u5047\u8bbe\u79f0\u4e3a<strong>\u540c\u65b9\u5dee\u6027<\/strong>\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u5982\u679c\u4e0d\u9075\u5b88\u6b64\u5047\u8bbe\uff0c\u5219\u79f0\u6b8b\u5dee\u4e2d\u5b58\u5728<a href=\"https:\/\/statorials.org\/cn\/\u5f02\u65b9\u5dee\u56de\u5f52\/\" target=\"_blank\" rel=\"noopener\">\u5f02\u65b9\u5dee\u6027<\/a>\u3002\u5f53\u8fd9\u79cd\u60c5\u51b5\u53d1\u751f\u65f6\uff0c\u56de\u5f52\u7ed3\u679c\u53d8\u5f97\u4e0d\u53ef\u9760\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u89e3\u51b3\u6b64\u95ee\u9898\u7684\u4e00\u79cd\u65b9\u6cd5\u662f\u4f7f\u7528<strong>\u52a0\u6743\u6700\u5c0f\u4e8c\u4e58\u56de\u5f52<\/strong>\uff0c\u5b83\u4e3a<a href=\"https:\/\/statorials.org\/cn\/\u7edf\u8ba1\u89c2\u5bdf\/\" target=\"_blank\" rel=\"noopener\">\u89c2\u6d4b\u503c<\/a>\u5206\u914d\u6743\u91cd\uff0c\u4f7f\u5f97\u8bef\u5dee\u65b9\u5dee\u8f83\u5c0f\u7684\u89c2\u6d4b\u503c\u83b7\u5f97\u66f4\u591a\u6743\u91cd\uff0c\u56e0\u4e3a\u4e0e\u8bef\u5dee\u65b9\u5dee\u8f83\u5927\u7684\u89c2\u6d4b\u503c\u76f8\u6bd4\uff0c\u5b83\u4eec\u5305\u542b\u66f4\u591a\u4fe1\u606f\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u672c\u6559\u7a0b\u63d0\u4f9b\u4e86\u5982\u4f55\u5728 R \u4e2d\u6267\u884c\u52a0\u6743\u6700\u5c0f\u4e8c\u4e58\u56de\u5f52\u7684\u5206\u6b65\u793a\u4f8b\u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u7b2c 1 \u6b65\uff1a\u521b\u5efa\u6570\u636e<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">\u4ee5\u4e0b\u4ee3\u7801\u521b\u5efa\u4e00\u4e2a\u6570\u636e\u6846\uff0c\u5176\u4e2d\u5305\u542b 16 \u540d\u5b66\u751f\u7684\u5b66\u4e60\u5c0f\u65f6\u6570\u548c\u76f8\u5e94\u7684\u8003\u8bd5\u6210\u7ee9\uff1a<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong>df &lt;- data.frame(hours=c(1, 1, 2, 2, 2, 3, 4, 4, 4, 5, 5, 5, 6, 6, 7, 8),\n                 score=c(48, 78, 72, 70, 66, 92, 93, 75, 75, 80, 95, 97, 90, 96, 99, 99))\n<\/strong><\/pre>\n<h3><span style=\"color: #000000;\"><strong>\u7b2c 2 \u6b65\uff1a\u6267\u884c\u7ebf\u6027\u56de\u5f52<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u5c06\u4f7f\u7528<strong>lm()<\/strong>\u51fd\u6570\u6765\u62df\u5408\u4e00\u4e2a<a href=\"https:\/\/statorials.org\/cn\/\u7ebf\u6027\u56de\u5f521\/\" target=\"_blank\" rel=\"noopener\">\u7b80\u5355\u7684\u7ebf\u6027\u56de\u5f52\u6a21\u578b<\/a>\uff0c\u8be5\u6a21\u578b\u4f7f\u7528\u5c0f\u65f6\u4f5c\u4e3a\u9884\u6d4b\u53d8\u91cf\uff0c\u5f97\u5206\u4f5c\u4e3a<a href=\"https:\/\/statorials.org\/cn\/\u53d8\u91cf\u89e3\u91ca\u6027\u53cd\u5e94\/\" target=\"_blank\" rel=\"noopener\">\u54cd\u5e94\u53d8\u91cf<\/a>\uff1a<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#fit simple linear regression model\n<\/span>model &lt;- lm(score ~ hours, data = df)\n\n<span style=\"color: #008080;\">#view summary of model\n<\/span>summary(model)\n\nCall:\nlm(formula = score ~ hours, data = df)\n\nResiduals:\n    Min 1Q Median 3Q Max \n-17,967 -5,970 -0.719 7,531 15,032 \n\nCoefficients:\n            Estimate Std. Error t value Pr(&gt;|t|)    \n(Intercept) 60,467 5,128 11,791 1.17e-08 ***\nhours 5,500 1,127 4,879 0.000244 ***\n---\nSignificant. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n\nResidual standard error: 9.224 on 14 degrees of freedom\nMultiple R-squared: 0.6296, Adjusted R-squared: 0.6032 \nF-statistic: 23.8 on 1 and 14 DF, p-value: 0.0002438\n<\/strong><\/pre>\n<h3><span style=\"color: #000000;\"><strong>\u6b65\u9aa4 3\uff1a\u68c0\u9a8c\u5f02\u65b9\u5dee\u6027<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u5c06\u521b\u5efa\u6b8b\u5dee\u548c\u62df\u5408\u503c\u7684\u56fe\uff0c\u4ee5\u76f4\u89c2\u5730\u68c0\u67e5\u5f02\u65b9\u5dee\u6027\uff1a<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#create residual vs. fitted plot\n<\/span>plot( <span style=\"color: #3366ff;\">fitted<\/span> (model), <span style=\"color: #3366ff;\">resid<\/span> (model), xlab=' <span style=\"color: #008000;\">Fitted Values<\/span> ', ylab=' <span style=\"color: #008000;\">Residuals<\/span> ')\n\n<span style=\"color: #008080;\">#add a horizontal line at 0 \n<\/span>abline(0,0)<\/strong> <\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-13025 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/wls1.png\" alt=\"\" width=\"429\" height=\"391\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p><span style=\"color: #000000;\">\u4ece\u56fe\u4e2d\u6211\u4eec\u53ef\u4ee5\u770b\u51fa\uff0c\u6b8b\u5dee\u5448\u201c\u5706\u9525\u201d\u5f62\u72b6\uff1a\u5b83\u4eec\u5728\u6574\u4e2a\u56fe\u4e2d\u7684\u65b9\u5dee\u5206\u5e03\u5e76\u4e0d\u5747\u5300\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4e3a\u4e86\u6b63\u5f0f\u6d4b\u8bd5\u5f02\u65b9\u5dee\u6027\uff0c\u6211\u4eec\u53ef\u4ee5\u6267\u884c Breusch-Pagan \u6d4b\u8bd5\uff1a<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#load lmtest package\n<\/span><span style=\"color: #993300;\">library<\/span> (lmtest)\n\n<span style=\"color: #008080;\">#perform Breusch-Pagan test<\/span>\nbptest(model)\n\n\tstudentized Breusch-Pagan test\n\ndata: model\nBP = 3.9597, df = 1, p-value = 0.0466\n<\/strong><\/pre>\n<p> Breusch-Pagan \u68c0\u9a8c\u4f7f\u7528<span style=\"color: #000000;\">\u4ee5\u4e0b\u539f\u5047\u8bbe\u548c\u5907\u62e9<\/span><span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/cn\/\u5047\u8bbe\u68c0\u9a8c1\/\" target=\"_blank\" rel=\"noopener\">\u5047\u8bbe<\/a><\/span>\uff1a<\/p>\n<ul>\n<li><span style=\"color: #000000;\"><strong>\u96f6\u5047\u8bbe (H <sub>0<\/sub> )\uff1a<\/strong>\u5b58\u5728\u540c\u65b9\u5dee\u6027\uff08\u6b8b\u5dee\u4ee5\u7b49\u65b9\u5dee\u5206\u5e03\uff09<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong>\u5907\u62e9\u5047\u8bbe ( <sub>HA<\/sub> )\uff1a<\/strong>\u5b58\u5728\u5f02\u65b9\u5dee\u6027\uff08\u6b8b\u5dee\u4e0d\u4ee5\u7b49\u65b9\u5dee\u5206\u5e03\uff09<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u7531\u4e8e\u68c0\u9a8c\u7684 p \u503c\u4e3a<strong>0.0466<\/strong> \uff0c\u6211\u4eec\u5c06\u62d2\u7edd\u539f\u5047\u8bbe\u5e76\u5f97\u51fa\u5f02\u65b9\u5dee\u662f\u8be5\u6a21\u578b\u4e2d\u7684\u95ee\u9898\u7684\u7ed3\u8bba\u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u6b65\u9aa4 4\uff1a\u6267\u884c\u52a0\u6743\u6700\u5c0f\u4e8c\u4e58\u56de\u5f52<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">\u7531\u4e8e\u5b58\u5728\u5f02\u65b9\u5dee\u6027\uff0c\u6211\u4eec\u5c06\u901a\u8fc7\u8bbe\u7f6e\u6743\u91cd\u6765\u6267\u884c\u52a0\u6743\u6700\u5c0f\u4e8c\u4e58\u6cd5\uff0c\u4ee5\u4f7f\u65b9\u5dee\u8f83\u4f4e\u7684\u89c2\u6d4b\u503c\u83b7\u5f97\u66f4\u591a\u7684\u6743\u91cd\uff1a<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #008080;\">#define weights to use\n<\/span>wt &lt;- 1 \/ lm( <span style=\"color: #3366ff;\">abs<\/span> (model$residuals) ~ model$fitted. <span style=\"color: #3366ff;\">values<\/span> )$fitted. <span style=\"color: #3366ff;\">values<\/span> ^2\n\n<span style=\"color: #008080;\">#perform weighted least squares regression\n<\/span>wls_model &lt;- lm(score ~ hours, data = df, weights=wt)\n\n<span style=\"color: #008080;\">#view summary of model\n<\/span>summary(wls_model)\n\nCall:\nlm(formula = score ~ hours, data = df, weights = wt)\n\nWeighted Residuals:\n    Min 1Q Median 3Q Max \n-2.0167 -0.9263 -0.2589 0.9873 1.6977 \n\nCoefficients:\n            Estimate Std. Error t value Pr(&gt;|t|)    \n(Intercept) 63.9689 5.1587 12.400 6.13e-09 ***\nhours 4.7091 0.8709 5.407 9.24e-05 ***\n---\nSignificant. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n\nResidual standard error: 1.199 on 14 degrees of freedom\nMultiple R-squared: 0.6762, Adjusted R-squared: 0.6531 \nF-statistic: 29.24 on 1 and 14 DF, p-value: 9.236e-05\n<\/strong><\/span><\/pre>\n<p><span style=\"color: #000000;\">\u4ece\u7ed3\u679c\u4e2d\u6211\u4eec\u53ef\u4ee5\u770b\u5230\uff0c<em>\u5c0f\u65f6<\/em>\u9884\u6d4b\u53d8\u91cf\u7684\u7cfb\u6570\u4f30\u8ba1\u503c\u7565\u6709\u53d8\u5316\uff0c\u6574\u4f53\u6a21\u578b\u62df\u5408\u5ea6\u6709\u6240\u6539\u5584\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u52a0\u6743\u6700\u5c0f\u4e8c\u4e58\u6a21\u578b\u7684\u6b8b\u5dee\u6807\u51c6\u8bef\u5dee\u4e3a<strong>1.199<\/strong> \uff0c\u800c\u539f\u59cb\u7b80\u5355\u7ebf\u6027\u56de\u5f52\u6a21\u578b\u7684\u6b8b\u5dee\u6807\u51c6\u8bef\u5dee\u4e3a<strong>9.224<\/strong> \u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u8fd9\u8868\u660e\u4e0e\u7b80\u5355\u7ebf\u6027\u56de\u5f52\u6a21\u578b\u4ea7\u751f\u7684\u9884\u6d4b\u503c\u76f8\u6bd4\uff0c\u52a0\u6743\u6700\u5c0f\u4e8c\u4e58\u6a21\u578b\u4ea7\u751f\u7684\u9884\u6d4b\u503c\u66f4\u63a5\u8fd1\u5b9e\u9645\u89c2\u6d4b\u503c\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u52a0\u6743\u6700\u5c0f\u4e8c\u4e58\u6a21\u578b\u7684 R \u5e73\u65b9\u4e5f\u4e3a<strong>0.6762<\/strong> \uff0c\u800c\u539f\u59cb\u7b80\u5355\u7ebf\u6027\u56de\u5f52\u6a21\u578b\u4e2d\u7684 R \u5e73\u65b9\u4e3a<strong>0.6296<\/strong> \u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u8fd9\u8868\u660e\u52a0\u6743\u6700\u5c0f\u4e8c\u4e58\u6a21\u578b\u6bd4\u7b80\u5355\u7ebf\u6027\u56de\u5f52\u6a21\u578b\u80fd\u591f\u89e3\u91ca\u66f4\u591a\u7684\u8003\u8bd5\u6210\u7ee9\u65b9\u5dee\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u8fd9\u4e9b\u6d4b\u91cf\u7ed3\u679c\u8868\u660e\uff0c\u4e0e\u7b80\u5355\u7ebf\u6027\u56de\u5f52\u6a21\u578b\u76f8\u6bd4\uff0c\u52a0\u6743\u6700\u5c0f\u4e8c\u4e58\u6a21\u578b\u53ef\u4ee5\u66f4\u597d\u5730\u62df\u5408\u6570\u636e\u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u5176\u4ed6\u8d44\u6e90<\/strong><\/span><\/h3>\n<p><a href=\"https:\/\/statorials.org\/cn\/r-\u4e2d\u7684\u7b80\u5355\u7ebf\u6027\u56de\u5f52\/\" target=\"_blank\" rel=\"noopener\">\u5982\u4f55\u5728 R \u4e2d\u6267\u884c\u7b80\u5355\u7ebf\u6027\u56de\u5f52<\/a><br \/><a href=\"https:\/\/statorials.org\/cn\/\u591a\u5143\u7ebf\u6027\u56de\u5f52\/\" target=\"_blank\" rel=\"noopener\">\u5982\u4f55\u5728 R \u4e2d\u6267\u884c\u591a\u5143\u7ebf\u6027\u56de\u5f52<\/a><br \/><a href=\"https:\/\/statorials.org\/cn\/r\u4e2d\u7684\u5206\u4f4d\u6570\u56de\u5f52\/\" target=\"_blank\" rel=\"noopener\">\u5982\u4f55\u5728 R \u4e2d\u6267\u884c\u5206\u4f4d\u6570\u56de\u5f52<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u7ebf\u6027\u56de\u5f52\u7684\u5173\u952e\u5047\u8bbe\u4e4b\u4e00\u662f\u6b8b\u5dee\u5728\u9884\u6d4b\u53d8\u91cf\u7684\u6bcf\u4e2a\u6c34\u5e73\u4e0a\u4ee5\u76f8\u7b49\u65b9\u5dee\u5206\u5e03\u3002\u8fd9\u79cd\u5047\u8bbe\u79f0\u4e3a\u540c\u65b9\u5dee\u6027\u3002 \u5982\u679c\u4e0d\u9075\u5b88\u6b64\u5047\u8bbe\uff0c\u5219 [&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-1335","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\u5728 R \u4e2d\u6267\u884c\u52a0\u6743\u6700\u5c0f\u4e8c\u4e58\u56de\u5f52<\/title>\n<meta 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