{"id":1722,"date":"2023-07-25T06:08:27","date_gmt":"2023-07-25T06:08:27","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e5%a6%82%e4%bd%95%e8%a7%a3%e9%87%8a%e6%ae%8b%e5%b7%ae%e6%a0%87%e5%87%86%e8%af%af%e5%b7%ae\/"},"modified":"2023-07-25T06:08:27","modified_gmt":"2023-07-25T06:08:27","slug":"%e5%a6%82%e4%bd%95%e8%a7%a3%e9%87%8a%e6%ae%8b%e5%b7%ae%e6%a0%87%e5%87%86%e8%af%af%e5%b7%ae","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e5%a6%82%e4%bd%95%e8%a7%a3%e9%87%8a%e6%ae%8b%e5%b7%ae%e6%a0%87%e5%87%86%e8%af%af%e5%b7%ae\/","title":{"rendered":"\u5982\u4f55\u89e3\u91ca\u6b8b\u5dee\u6807\u51c6\u8bef\u5dee"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>\u6b8b\u5dee\u6807\u51c6\u8bef\u5dee<\/strong>\u7528\u4e8e\u8861\u91cf<a href=\"https:\/\/statorials.org\/cn\/\u7ebf\u6027\u56de\u5f521\/\" target=\"_blank\" rel=\"noopener\">\u56de\u5f52\u6a21\u578b<\/a>\u5bf9\u6570\u636e\u96c6\u7684\u62df\u5408\u7a0b\u5ea6\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u7b80\u800c\u8a00\u4e4b\uff0c\u5b83\u6d4b\u91cf\u56de\u5f52\u6a21\u578b\u4e2d\u6b8b\u5dee\u7684\u6807\u51c6\u5dee\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\"><span style=\"color: #000000;\">\u8ba1\u7b97\u65b9\u6cd5\u5982\u4e0b\uff1a<\/span><\/span><\/p>\n<p><strong><span style=\"color: #000000;\">\u6b8b\u5dee\u6807\u51c6\u8bef\u5dee = \u221a <span style=\"border-top: 1px solid black;\">\u03a3(y \u2013 \u0177) <sup>2<\/sup> \/df<\/span><\/span><\/strong><\/p>\n<p><span style=\"color: #000000;\">\u91d1\u5b50\uff1a<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>y\uff1a<\/strong>\u89c2\u6d4b\u503c<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong>\u0177\uff1a<\/strong>\u9884\u6d4b\u503c<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong>df\uff1a<\/strong>\u81ea\u7531\u5ea6\uff0c\u8ba1\u7b97\u4e3a\u89c2\u5bdf\u603b\u6570 &#8211; \u6a21\u578b\u53c2\u6570\u603b\u6570\u3002<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u6b8b\u5dee\u6807\u51c6\u8bef\u5dee\u8d8a\u5c0f\uff0c\u56de\u5f52\u6a21\u578b\u5bf9\u6570\u636e\u96c6\u7684\u62df\u5408\u6548\u679c\u8d8a\u597d\u3002\u76f8\u53cd\uff0c\u6b8b\u5dee\u6807\u51c6\u8bef\u5dee\u8d8a\u9ad8\uff0c\u56de\u5f52\u6a21\u578b\u5bf9\u6570\u636e\u96c6\u7684\u62df\u5408\u7a0b\u5ea6\u5c31\u8d8a\u5dee\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u5177\u6709\u8f83\u5c0f\u6b8b\u5dee\u6807\u51c6\u8bef\u5dee\u7684\u56de\u5f52\u6a21\u578b\u7684\u6570\u636e\u70b9\u5c06\u7d27\u5bc6\u805a\u96c6\u5728\u62df\u5408\u56de\u5f52\u7ebf\u5468\u56f4\uff1a<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-15730 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/standarderrorestimate1.png\" alt=\"\" width=\"431\" height=\"322\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p><span style=\"color: #000000;\">\u8be5\u6a21\u578b\u7684<a href=\"https:\/\/statorials.org\/cn\/\u6b8b\u7559\u7269\/\" target=\"_blank\" rel=\"noopener\">\u6b8b\u5dee<\/a>\uff08\u89c2\u6d4b\u503c\u4e0e\u9884\u6d4b\u503c\u4e4b\u95f4\u7684\u5dee\u5f02\uff09\u4f1a\u5f88\u5c0f\uff0c\u610f\u5473\u7740\u6b8b\u5dee\u6807\u51c6\u8bef\u5dee\u4e5f\u4f1a\u5f88\u5c0f\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u76f8\u53cd\uff0c\u5177\u6709\u8f83\u5927\u6b8b\u5dee\u6807\u51c6\u8bef\u5dee\u7684\u56de\u5f52\u6a21\u578b\u7684\u6570\u636e\u70b9\u5c06\u66f4\u52a0\u677e\u6563\u5730\u5206\u6563\u5728\u62df\u5408\u56de\u5f52\u7ebf\u5468\u56f4\uff1a<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-15731 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/standarderrorestimate2.png\" alt=\"\" width=\"445\" height=\"325\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p><span style=\"color: #000000;\">\u8be5\u6a21\u578b\u7684<a href=\"https:\/\/statorials.org\/cn\/\u6b8b\u7559\u7269\/\" target=\"_blank\" rel=\"noopener\">\u6b8b\u5dee<\/a>\u4f1a\u66f4\u5927\uff0c\u8fd9\u610f\u5473\u7740\u6b8b\u5dee\u6807\u51c6\u8bef\u5dee\u4e5f\u4f1a\u66f4\u5927\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4ee5\u4e0b\u793a\u4f8b\u6f14\u793a\u5982\u4f55\u8ba1\u7b97\u548c\u89e3\u91ca R \u4e2d\u56de\u5f52\u6a21\u578b\u7684\u6b8b\u5dee\u6807\u51c6\u8bef\u5dee\u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u793a\u4f8b\uff1a\u89e3\u91ca\u6b8b\u5dee\u6807\u51c6\u8bef\u5dee<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">\u5047\u8bbe\u6211\u4eec\u8981\u62df\u5408\u4ee5\u4e0b\u591a\u5143\u7ebf\u6027\u56de\u5f52\u6a21\u578b\uff1a<\/span><\/p>\n<p> <span style=\"color: #000000;\">mpg = \u03b2 <sub>0<\/sub> + \u03b2 <sub>1<\/sub> (\u6392\u91cf) + \u03b2 <sub>2<\/sub> (\u529f\u7387)<\/span><\/p>\n<p><span style=\"color: #000000;\">\u8be5\u6a21\u578b\u4f7f\u7528\u9884\u6d4b\u53d8\u91cf\u201c\u6392\u91cf\u201d\u548c\u201c\u9a6c\u529b\u201d\u6765\u9884\u6d4b\u7ed9\u5b9a\u6c7d\u8f66\u6bcf\u52a0\u4ed1\u884c\u9a76\u7684\u82f1\u91cc\u6570\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4ee5\u4e0b\u4ee3\u7801\u663e\u793a\u4e86\u5982\u4f55\u5728 R \u4e2d\u62df\u5408\u6b64\u56de\u5f52\u6a21\u578b\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;\">\u5728\u7ed3\u679c\u7684\u5e95\u90e8\uff0c\u6211\u4eec\u53ef\u4ee5\u770b\u5230\u8be5\u6a21\u578b\u7684\u5269\u4f59\u6807\u51c6\u8bef\u5dee\u4e3a<strong>3.127<\/strong> \u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u8fd9\u544a\u8bc9\u6211\u4eec\uff0c\u56de\u5f52\u6a21\u578b\u9884\u6d4b\u6c7d\u8f66 mpg \u7684\u5e73\u5747\u8bef\u5dee\u7ea6\u4e3a 3,127\u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u4f7f\u7528\u6b8b\u5dee\u6807\u51c6\u8bef\u5dee\u6765\u6bd4\u8f83\u6a21\u578b<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">\u6b8b\u5dee\u6807\u51c6\u8bef\u5dee\u5bf9\u4e8e\u6bd4\u8f83\u4e0d\u540c\u56de\u5f52\u6a21\u578b\u7684\u62df\u5408\u7279\u522b\u6709\u7528\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4f8b\u5982\uff0c\u5047\u8bbe\u6211\u4eec\u62df\u5408\u4e24\u4e2a\u4e0d\u540c\u7684\u56de\u5f52\u6a21\u578b\u6765\u9884\u6d4b\u6c7d\u8f66\u6bcf\u52a0\u4ed1\u82f1\u91cc\u6570\u3002\u5404\u6a21\u578b\u7684\u6b8b\u5dee\u6807\u51c6\u8bef\u5982\u4e0b\uff1a<\/span><\/p>\n<ul>\n<li><span style=\"color: #000000;\">\u6a21\u578b1\u7684\u6b8b\u5dee\u6807\u51c6\u8bef\u5dee\uff1a <strong>3.127<\/strong><\/span><\/li>\n<li><span style=\"color: #000000;\">\u6a21\u578b2\u7684\u6b8b\u5dee\u6807\u51c6\u8bef\u5dee\uff1a <strong>5.657<\/strong><\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u7531\u4e8e\u6a21\u578b 1 \u7684\u6b8b\u5dee\u6807\u51c6\u8bef\u5dee\u8f83\u4f4e\uff0c\u56e0\u6b64\u5b83\u6bd4\u6a21\u578b 2 \u66f4\u9002\u5408\u6570\u636e\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u66f4\u613f\u610f\u4f7f\u7528\u6a21\u578b 1 \u6765\u9884\u6d4b\u6c7d\u8f66 mpg\uff0c\u56e0\u4e3a\u5b83\u6240\u505a\u7684\u9884\u6d4b\u66f4\u63a5\u8fd1\u89c2\u5bdf\u5230\u7684\u6c7d\u8f66 mpg \u503c\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\/\u6b8b\u7559\u75d5\u91cf\/\" target=\"_blank\" rel=\"noopener\">\u5982\u4f55\u5728 R \u4e2d\u521b\u5efa\u6b8b\u5dee\u56fe<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u6b8b\u5dee\u6807\u51c6\u8bef\u5dee\u7528\u4e8e\u8861\u91cf\u56de\u5f52\u6a21\u578b\u5bf9\u6570\u636e\u96c6\u7684\u62df\u5408\u7a0b\u5ea6\u3002 \u7b80\u800c\u8a00\u4e4b\uff0c\u5b83\u6d4b\u91cf\u56de\u5f52\u6a21\u578b\u4e2d\u6b8b\u5dee\u7684\u6807\u51c6\u5dee\u3002 \u8ba1\u7b97\u65b9\u6cd5\u5982\u4e0b\uff1a \u6b8b [&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-1722","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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