{"id":1063,"date":"2023-07-27T19:30:41","date_gmt":"2023-07-27T19:30:41","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e6%ae%8b%e5%b7%ae%e6%a0%87%e5%87%86%e8%af%af%e5%b7%aer\/"},"modified":"2023-07-27T19:30:41","modified_gmt":"2023-07-27T19:30:41","slug":"%e6%ae%8b%e5%b7%ae%e6%a0%87%e5%87%86%e8%af%af%e5%b7%aer","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e6%ae%8b%e5%b7%ae%e6%a0%87%e5%87%86%e8%af%af%e5%b7%aer\/","title":{"rendered":"\u5982\u4f55\u8ba1\u7b97 r \u4e2d\u7684\u6b8b\u5dee\u6807\u51c6\u8bef\u5dee"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">\u6bcf\u5f53\u6211\u4eec\u5728 R \u4e2d\u62df\u5408\u7ebf\u6027\u56de\u5f52\u6a21\u578b\u65f6\uff0c\u8be5\u6a21\u578b\u90fd\u91c7\u7528\u4ee5\u4e0b\u5f62\u5f0f\uff1a<\/span><\/p>\n<p> <span style=\"color: #000000;\">Y = \u03b2 <sub>0<\/sub> + \u03b2 <sub>1<\/sub> X + \u2026 + \u03b2 <sub>i<\/sub><\/span><\/p>\n<p><span style=\"color: #000000;\">\u5176\u4e2d \u03f5 \u662f\u72ec\u7acb\u4e8e X \u7684\u8bef\u5dee\u9879\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u65e0\u8bba\u5982\u4f55\u4f7f\u7528X\u6765\u9884\u6d4bY\u7684\u503c\uff0c\u6a21\u578b\u4e2d\u603b\u4f1a\u5b58\u5728\u968f\u673a\u8bef\u5dee\u3002\u6d4b\u91cf\u8be5\u968f\u673a\u8bef\u5dee\u7684\u5206\u6563\u6027\u7684\u4e00\u79cd\u65b9\u6cd5\u662f\u4f7f\u7528<strong>\u6b8b\u5dee\u6807\u51c6\u8bef\u5dee<\/strong>\uff0c\u8fd9\u662f\u6d4b\u91cf\u6b8b\u5dee \u03f5 \u6807\u51c6\u5dee\u7684\u4e00\u79cd\u65b9\u6cd5\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u56de\u5f52\u6a21\u578b\u7684\u6b8b\u5dee\u6807\u51c6\u8bef\u5dee\u8ba1\u7b97\u5982\u4e0b\uff1a<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>\u6b8b\u5dee\u6807\u51c6\u8bef = \u221a <span style=\"border-top: 1px solid black;\">SS<sub>\u6b8b\u5dee<\/sub>\/ df<sub>\u6b8b\u5dee<\/sub><\/span><\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u91d1\u5b50\uff1a<\/span><\/p>\n<ul>\n<li><span style=\"color: #000000;\"><strong><sub>\u6b8b\u5dee<\/sub>SS<\/strong> \uff1a\u6b8b\u5dee\u5e73\u65b9\u548c\u3002<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong><sub>\u6b8b\u5dee<\/sub>df<\/strong> \uff1a\u6b8b\u5dee\u81ea\u7531\u5ea6\uff0c\u8ba1\u7b97\u516c\u5f0f\u4e3a n \u2013 k \u2013 1\uff0c\u5176\u4e2d n = \u89c2\u6d4b\u503c\u603b\u6570\uff0ck = \u6a21\u578b\u53c2\u6570\u603b\u6570\u3002<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u4e09\u79cd\u65b9\u6cd5\u6765\u8ba1\u7b97 R \u4e2d\u56de\u5f52\u6a21\u578b\u7684\u6b8b\u5dee\u6807\u51c6\u8bef\u5dee\u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u65b9\u6cd5\u4e00\uff1a\u5206\u6790\u6a21\u578b\u6982\u8981<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">\u83b7\u53d6\u6b8b\u5dee\u6807\u51c6\u8bef\u5dee\u7684\u7b2c\u4e00\u79cd\u65b9\u6cd5\u662f\u7b80\u5355\u5730\u62df\u5408\u7ebf\u6027\u56de\u5f52\u6a21\u578b\uff0c\u7136\u540e\u4f7f\u7528<strong>summary()<\/strong>\u547d\u4ee4\u83b7\u53d6\u6a21\u578b\u7ed3\u679c\u3002\u7136\u540e\u53ea\u9700\u5728\u8f93\u51fa\u5e95\u90e8\u67e5\u627e\u201c\u5269\u4f59\u6807\u51c6\u8bef\u5dee\u201d\uff1a<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#load built-in <em>mtcars<\/em> dataset<\/span>\ndata(mtcars)\n\n<span style=\"color: #008080;\">#fit regression model\n<\/span>model &lt;- lm(mpg~disp+hp, data=mtcars)\n\n<span style=\"color: #008080;\">#view model summary\n<\/span>summary(model)\n\nCall:\nlm(formula = mpg ~ disp + hp, data = mtcars)\n\nResiduals:\n    Min 1Q Median 3Q Max \n-4.7945 -2.3036 -0.8246 1.8582 6.9363 \n\nCoefficients:\n             Estimate Std. Error t value Pr(&gt;|t|)    \n(Intercept) 30.735904 1.331566 23.083 &lt; 2nd-16 ***\navailable -0.030346 0.007405 -4.098 0.000306 ***\nhp -0.024840 0.013385 -1.856 0.073679 .  \n---\nSignificant. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n\nResidual standard error: <span style=\"color: #008000;\">3.127<\/span> on 29 degrees of freedom\nMultiple R-squared: 0.7482, Adjusted R-squared: 0.7309 \nF-statistic: 43.09 on 2 and 29 DF, p-value: 2.062e-09<\/strong><\/pre>\n<p><span style=\"color: #000000;\">\u6211\u4eec\u53ef\u4ee5\u770b\u5230\u6b8b\u5dee\u6807\u51c6\u8bef\u5dee\u4e3a<strong>3.127<\/strong> \u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u65b9\u6cd5 2\uff1a\u4f7f\u7528\u7b80\u5355\u7684\u516c\u5f0f<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">\u83b7\u5f97\u6b8b\u5dee\u6807\u51c6\u8bef\u5dee (RSE) \u7684\u53e6\u4e00\u79cd\u65b9\u6cd5\u662f\u62df\u5408\u7ebf\u6027\u56de\u5f52\u6a21\u578b\uff0c\u7136\u540e\u4f7f\u7528\u4ee5\u4e0b\u516c\u5f0f\u8ba1\u7b97 RSE\uff1a<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong>sqrt( <span style=\"color: #3366ff;\">deviance<\/span> (model)\/df. <span style=\"color: #3366ff;\">residual<\/span> (model))\n<\/strong><\/pre>\n<p><span style=\"color: #000000;\">\u4ee5\u4e0b\u662f\u5982\u4f55\u5728 R \u4e2d\u5b9e\u73b0\u8be5\u516c\u5f0f\uff1a<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#load built-in <em>mtcars<\/em> dataset<\/span>\ndata(mtcars)\n\n<span style=\"color: #008080;\">#fit regression model\n<\/span>model &lt;- lm(mpg~disp+hp, data=mtcars)\n\n<span style=\"color: #008080;\">#calculate residual standard error\n<\/span>sqrt( <span style=\"color: #3366ff;\">deviance<\/span> (model)\/df. <span style=\"color: #3366ff;\">residual<\/span> (model))\n\n[1] 3.126601\n<\/strong><\/pre>\n<p><span style=\"color: #000000;\">\u6211\u4eec\u53ef\u4ee5\u770b\u5230\u6b8b\u5dee\u6807\u51c6\u8bef\u5dee\u4e3a<strong>3.126601<\/strong> \u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u65b9\u6cd5 3\uff1a\u4f7f\u7528\u5206\u6b65\u516c\u5f0f<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">\u83b7\u5f97\u6b8b\u5dee\u6807\u51c6\u8bef\u5dee\u7684\u53e6\u4e00\u79cd\u65b9\u6cd5\u662f\u62df\u5408\u7ebf\u6027\u56de\u5f52\u6a21\u578b\uff0c\u7136\u540e\u4f7f\u7528\u9010\u6b65\u65b9\u6cd5\u8ba1\u7b97 RSE \u516c\u5f0f\u7684\u6bcf\u4e2a\u5355\u72ec\u7ec4\u4ef6\uff1a<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#load built-in <em>mtcars<\/em> dataset<\/span>\ndata(mtcars)\n\n<span style=\"color: #008080;\">#fit regression model\n<\/span>model &lt;- lm(mpg~disp+hp, data=mtcars)\n\n<span style=\"color: #008080;\">#calculate the number of model parameters - 1\n<\/span>k=length(model$ <span style=\"color: #3366ff;\">coefficients<\/span> )-1\n\n<span style=\"color: #008080;\">#calculate sum of squared residuals<\/span>\nSSE=sum(model$ <span style=\"color: #3366ff;\">residuals<\/span> **2)\n\n<span style=\"color: #008080;\">#calculate total observations in dataset<\/span>\nn=length(model$ <span style=\"color: #3366ff;\">residuals<\/span> )\n\n<span style=\"color: #008080;\">#calculate residual standard error<\/span>\nsqrt(SSE\/(n-(1+k)))\n\n[1] 3.126601\n<\/strong><\/pre>\n<p><span style=\"color: #000000;\">\u6211\u4eec\u53ef\u4ee5\u770b\u5230\u6b8b\u5dee\u6807\u51c6\u8bef\u5dee\u4e3a<strong>3.126601<\/strong> \u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u5982\u4f55\u89e3\u91ca\u6b8b\u5dee\u6807\u51c6\u8bef\u5dee<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">\u5982\u524d\u6240\u8ff0\uff0c\u6b8b\u5dee\u6807\u51c6\u8bef\u5dee (RSE) \u662f\u8861\u91cf\u56de\u5f52\u6a21\u578b\u4e2d\u6b8b\u5dee\u6807\u51c6\u5dee\u7684\u4e00\u79cd\u65b9\u6cd5\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\">CSR\u503c\u8d8a\u4f4e\uff0c\u6a21\u578b\u62df\u5408\u6570\u636e\u7684\u80fd\u529b\u5c31\u8d8a\u597d\uff08\u4f46\u8981\u5c0f\u5fc3<a href=\"https:\/\/statorials.org\/cn\/\u673a\u5668\u5b66\u4e60\u8fc7\u5ea6\u62df\u5408\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u8fc7\u5ea6\u62df\u5408<\/a>\uff09\u3002\u5728\u6bd4\u8f83\u4e24\u4e2a\u6216\u591a\u4e2a\u6a21\u578b\u4ee5\u786e\u5b9a\u54ea\u4e2a\u6a21\u578b\u6700\u9002\u5408\u6570\u636e\u65f6\uff0c\u8fd9\u53ef\u80fd\u662f\u4e00\u4e2a\u6709\u7528\u7684\u6307\u6807\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\/\u5982\u4f55\u89e3\u91ca\u6b8b\u5dee\u6807\u51c6\u8bef\u5dee\/\">\u5982\u4f55\u89e3\u91ca\u6b8b\u5dee\u6807\u51c6\u8bef\u5dee<\/a><br \/> <a href=\"https:\/\/statorials.org\/cn\/\u591a\u5143\u7ebf\u6027\u56de\u5f52\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u5982\u4f55\u5728 R \u4e2d\u6267\u884c\u591a\u5143\u7ebf\u6027\u56de\u5f52<\/a><br \/><a href=\"https:\/\/statorials.org\/cn\/\u5982\u4f55\u5728-r-\u4e2d\u5bf9\u6a21\u578b\u6027\u80fd\u8fdb\u884c\u4ea4\u53c9\u9a8c\u8bc1\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u5982\u4f55\u5728 R \u4e2d\u4ea4\u53c9\u9a8c\u8bc1\u6a21\u578b\u6027\u80fd<\/a><br \/><a href=\"https:\/\/statorials.org\/cn\/r-\u4e2d\u7684\u6807\u51c6\u5dee\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u5982\u4f55\u8ba1\u7b97 R \u4e2d\u7684\u6807\u51c6\u5dee<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u6bcf\u5f53\u6211\u4eec\u5728 R \u4e2d\u62df\u5408\u7ebf\u6027\u56de\u5f52\u6a21\u578b\u65f6\uff0c\u8be5\u6a21\u578b\u90fd\u91c7\u7528\u4ee5\u4e0b\u5f62\u5f0f\uff1a Y = \u03b2 0 + \u03b2 1 X + \u2026 + \u03b2  [&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-1063","post","type-post","status-publish","format-standard","hentry","category-11"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - 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