{"id":3470,"date":"2023-07-17T07:59:02","date_gmt":"2023-07-17T07:59:02","guid":{"rendered":"https:\/\/statorials.org\/cn\/r%e4%b8%ad%e7%9a%84ols%e5%9b%9e%e5%bd%92\/"},"modified":"2023-07-17T07:59:02","modified_gmt":"2023-07-17T07:59:02","slug":"r%e4%b8%ad%e7%9a%84ols%e5%9b%9e%e5%bd%92","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/r%e4%b8%ad%e7%9a%84ols%e5%9b%9e%e5%bd%92\/","title":{"rendered":"\u5982\u4f55\u5728 r \u4e2d\u6267\u884c ols \u56de\u5f52\uff08\u5e26\u6709\u793a\u4f8b\uff09"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">\u666e\u901a\u6700\u5c0f\u4e8c\u4e58 (OLS) \u56de\u5f52\u662f\u4e00\u79cd\u65b9\u6cd5\uff0c\u53ef\u8ba9\u6211\u4eec\u627e\u5230\u6700\u80fd\u63cf\u8ff0\u4e00\u4e2a\u6216\u591a\u4e2a\u9884\u6d4b\u53d8\u91cf\u4e0e<a href=\"https:\/\/statorials.org\/cn\/\u53d8\u91cf\u89e3\u91ca\u6027\u53cd\u5e94\/\" target=\"_blank\" rel=\"noopener\">\u54cd\u5e94\u53d8\u91cf<\/a>\u4e4b\u95f4\u5173\u7cfb\u7684\u76f4\u7ebf\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u8be5\u65b9\u6cd5\u4f7f\u6211\u4eec\u80fd\u591f\u627e\u5230\u4ee5\u4e0b\u65b9\u7a0b\uff1a<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u0177 = b <sub>0<\/sub> + b <sub>1<\/sub> x<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u91d1\u5b50\uff1a<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>\u0177<\/strong> : \u4f30\u8ba1\u54cd\u5e94\u503c<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong>b <sub>0<\/sub><\/strong> \uff1a\u56de\u5f52\u7ebf\u7684\u539f\u70b9<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong>b <sub>1<\/sub><\/strong> \uff1a\u56de\u5f52\u7ebf\u7684\u659c\u7387<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u8be5\u65b9\u7a0b\u53ef\u4ee5\u5e2e\u52a9\u6211\u4eec\u7406\u89e3\u9884\u6d4b\u53d8\u91cf\u548c\u54cd\u5e94\u53d8\u91cf\u4e4b\u95f4\u7684\u5173\u7cfb\uff0c\u5e76\u4e14\u53ef\u4ee5\u7528\u4e8e\u5728\u7ed9\u5b9a\u9884\u6d4b\u53d8\u91cf\u503c\u7684\u60c5\u51b5\u4e0b\u9884\u6d4b\u54cd\u5e94\u53d8\u91cf\u7684\u503c\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4ee5\u4e0b\u5206\u6b65\u793a\u4f8b\u5c55\u793a\u4e86\u5982\u4f55\u5728 R \u4e2d\u6267\u884c OLS \u56de\u5f52\u3002<\/span><\/p>\n<h2><span style=\"color: #000000;\"><b>\u7b2c 1 \u6b65\uff1a\u521b\u5efa\u6570\u636e<\/b><\/span><\/h2>\n<p><span style=\"color: #000000;\">\u5728\u6b64\u793a\u4f8b\u4e2d\uff0c\u6211\u4eec\u5c06\u4e3a 15 \u540d\u5b66\u751f\u521b\u5efa\u4e00\u4e2a\u5305\u542b\u4ee5\u4e0b\u4e24\u4e2a\u53d8\u91cf\u7684\u6570\u636e\u96c6\uff1a<\/span><\/p>\n<ul>\n<li><span style=\"color: #000000;\">\u5b66\u4e60\u603b\u65f6\u6570<\/span><\/li>\n<li><span style=\"color: #000000;\">\u8003\u8bd5\u6210\u7ee9<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u6211\u4eec\u5c06\u6267\u884c OLS \u56de\u5f52\uff0c\u4f7f\u7528\u5c0f\u65f6\u4f5c\u4e3a\u9884\u6d4b\u53d8\u91cf\uff0c\u4f7f\u7528\u8003\u8bd5\u6210\u7ee9\u4f5c\u4e3a\u54cd\u5e94\u53d8\u91cf\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4ee5\u4e0b\u4ee3\u7801\u5c55\u793a\u4e86\u5982\u4f55\u5728 R \u4e2d\u521b\u5efa\u8fd9\u4e2a\u5047\u6570\u636e\u96c6\uff1a<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#create dataset<\/span>\ndf &lt;- data. <span style=\"color: #3366ff;\">frame<\/span> (hours=c(1, 2, 4, 5, 5, 6, 6, 7, 8, 10, 11, 11, 12, 12, 14),\n                 score=c(64, 66, 76, 73, 74, 81, 83, 82, 80, 88, 84, 82, 91, 93, 89))\n\n<span style=\"color: #008080;\">#view first six rows of dataset\n<\/span>head(df)\n\n  hours score\n1 1 64\n2 2 66\n3 4 76\n4 5 73\n5 5 74\n6 6 81\n<\/strong><\/pre>\n<h2><span style=\"color: #000000;\"><b>\u7b2c 2 \u6b65\uff1a\u53ef\u89c6\u5316\u6570\u636e<\/b><\/span><\/h2>\n<p><span style=\"color: #000000;\">\u5728\u6267\u884c OLS \u56de\u5f52\u4e4b\u524d\uff0c\u8ba9\u6211\u4eec\u521b\u5efa\u4e00\u4e2a\u6563\u70b9\u56fe\u6765\u53ef\u89c6\u5316\u5c0f\u65f6\u6570\u548c\u8003\u8bd5\u6210\u7ee9\u4e4b\u95f4\u7684\u5173\u7cfb\uff1a<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008000;\">library<\/span> (ggplot2)\n\n<span style=\"color: #008080;\">#create scatterplot\n<\/span>ggplot(df, aes(x=hours, y=score)) +\n  geom_point(size= <span style=\"color: #008000;\">2<\/span> )\n<\/strong><\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-28969 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/vieux1.jpg\" alt=\"\" width=\"486\" height=\"410\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p><span style=\"color: #000000;\">\u7ebf\u6027\u56de\u5f52\u7684<a href=\"https:\/\/statorials.org\/cn\/\u7ebf\u6027\u56de\u5f52\u5047\u8bbe\/\" target=\"_blank\" rel=\"noopener\">\u56db\u4e2a\u5047\u8bbe<\/a>\u4e4b\u4e00\u662f\u9884\u6d4b\u53d8\u91cf\u548c\u54cd\u5e94\u53d8\u91cf\u4e4b\u95f4\u5b58\u5728\u7ebf\u6027\u5173\u7cfb\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4ece\u56fe\u4e2d\u6211\u4eec\u53ef\u4ee5\u770b\u51fa\uff0c\u8fd9\u79cd\u5173\u7cfb\u4f3c\u4e4e\u662f\u7ebf\u6027\u7684\u3002\u968f\u7740\u5c0f\u65f6\u6570\u7684\u589e\u52a0\uff0c\u5206\u6570\u4e5f\u8d8b\u4e8e\u7ebf\u6027\u589e\u52a0\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u7136\u540e\u6211\u4eec\u53ef\u4ee5\u521b\u5efa\u4e00\u4e2a\u7bb1\u7ebf\u56fe\u6765\u53ef\u89c6\u5316\u8003\u8bd5\u7ed3\u679c\u7684\u5206\u5e03\u5e76\u68c0\u67e5\u5f02\u5e38\u503c\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>\u6ce8<\/strong>\uff1a\u5982\u679c\u89c2\u6d4b\u503c\u662f\u7b2c\u4e09\u4e2a\u56db\u5206\u4f4d\u6570\u4ee5\u4e0a\u56db\u5206\u4f4d\u8ddd\u7684 1.5 \u500d\u6216\u7b2c\u4e00\u56db\u5206\u4f4d\u6570\u4ee5\u4e0b\u56db\u5206\u4f4d\u8ddd\u7684 1.5 \u500d\uff0c\u5219 R \u5c06\u89c2\u6d4b\u503c\u5b9a\u4e49\u4e3a\u79bb\u7fa4\u503c\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u5982\u679c\u89c2\u5bdf\u503c\u5f02\u5e38\uff0c\u7bb1\u7ebf\u56fe\u4e2d\u4f1a\u51fa\u73b0\u4e00\u4e2a\u5c0f\u5706\u5708\uff1a<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008000;\">library<\/span> (ggplot2)\n\n<span style=\"color: #008080;\">#create scatterplot\n<\/span>ggplot(df, aes(y=score)) +\n  geom_boxplot()<\/strong> <\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-28970 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/vieux2.jpg\" alt=\"\" width=\"333\" height=\"384\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p><span style=\"color: #000000;\">\u7bb1\u7ebf\u56fe\u4e2d\u6ca1\u6709\u5c0f\u5706\u5708\uff0c\u8fd9\u610f\u5473\u7740\u6211\u4eec\u7684\u6570\u636e\u96c6\u4e2d\u6ca1\u6709\u5f02\u5e38\u503c\u3002<\/span><\/p>\n<h2><span style=\"color: #000000;\"><b>\u6b65\u9aa4 3\uff1a\u6267\u884c OLS \u56de\u5f52<\/b><\/span><\/h2>\n<p><span style=\"color: #000000;\"><span style=\"color: #000000;\">\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528 R \u4e2d\u7684<strong>lm()<\/strong>\u51fd\u6570\u6267\u884c OLS \u56de\u5f52\uff0c\u4f7f\u7528\u5c0f\u65f6\u4f5c\u4e3a\u9884\u6d4b\u53d8\u91cf\uff0c\u5f97\u5206\u4f5c\u4e3a\u54cd\u5e94\u53d8\u91cf\uff1a<\/span><\/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 model summary<\/span>\nsummary(model)\n\nCall:\nlm(formula = score ~ hours)\n\nResiduals:\n   Min 1Q Median 3Q Max \n-5,140 -3,219 -1,193 2,816 5,772 \n\nCoefficients:\n            Estimate Std. Error t value Pr(&gt;|t|)    \n(Intercept) 65,334 2,106 31,023 1.41e-13 ***\nhours 1.982 0.248 7.995 2.25e-06 ***\n---\nSignificant. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n\nResidual standard error: 3.641 on 13 degrees of freedom\nMultiple R-squared: 0.831, Adjusted R-squared: 0.818 \nF-statistic: 63.91 on 1 and 13 DF, p-value: 2.253e-06\n<\/strong><\/pre>\n<p><span style=\"color: #000000;\">\u4ece\u6a21\u578b\u603b\u7ed3\u4e2d\u6211\u4eec\u53ef\u4ee5\u770b\u51fa\uff0c\u62df\u5408\u7684\u56de\u5f52\u65b9\u7a0b\u4e3a\uff1a<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>\u5206\u6570 = 65.334 + 1.982*\uff08\u5c0f\u65f6\uff09<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u8fd9\u610f\u5473\u7740\u6bcf\u591a\u5b66\u4e60\u4e00\u5c0f\u65f6\uff0c\u5e73\u5747\u8003\u8bd5\u6210\u7ee9\u5c31\u4f1a\u589e\u52a0<strong>1,982<\/strong>\u5206\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u539f\u59cb\u503c<strong>65,334<\/strong>\u544a\u8bc9\u6211\u4eec\u96f6\u5b66\u4e60\u65f6\u95f4\u7684\u5b66\u751f\u7684\u5e73\u5747\u9884\u671f\u8003\u8bd5\u6210\u7ee9\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u6211\u4eec\u8fd8\u53ef\u4ee5\u4f7f\u7528\u8fd9\u4e2a\u65b9\u7a0b\u6839\u636e\u5b66\u751f\u5b66\u4e60\u7684\u5c0f\u65f6\u6570\u627e\u5230\u9884\u671f\u7684\u8003\u8bd5\u6210\u7ee9\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4f8b\u5982\uff0c\u5b66\u4e60 10 \u5c0f\u65f6\u7684\u5b66\u751f\u5e94\u83b7\u5f97<strong>85.15<\/strong>\u7684\u8003\u8bd5\u6210\u7ee9\uff1a<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>\u5206\u6570 = 65.334 + 1.982*(10) = 85.15<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u4ee5\u4e0b\u662f\u5982\u4f55\u89e3\u91ca\u6a21\u578b\u6458\u8981\u7684\u5176\u4f59\u90e8\u5206\uff1a<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>Pr(&gt;|t|)\uff1a<\/strong>\u8fd9\u662f\u4e0e\u6a21\u578b\u7cfb\u6570\u76f8\u5173\u7684 p \u503c\u3002\u7531\u4e8e<em>\u5c0f\u65f6\u6570<\/em>(2.25e-06) \u7684 p \u503c\u663e\u7740\u5c0f\u4e8e 0.05\uff0c\u56e0\u6b64\u6211\u4eec\u53ef\u4ee5\u8bf4<em>\u5c0f\u65f6\u6570<\/em>\u548c<em>\u5206\u6570<\/em>\u4e4b\u95f4\u5b58\u5728\u7edf\u8ba1\u4e0a\u663e\u7740\u7684\u5173\u8054\u3002<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong>\u591a\u91cd R \u5e73\u65b9\uff1a<\/strong>\u8fd9\u4e2a\u6570\u5b57\u544a\u8bc9\u6211\u4eec\uff0c\u8003\u8bd5\u6210\u7ee9\u7684\u53d8\u5316\u767e\u5206\u6bd4\u53ef\u4ee5\u7528\u5b66\u4e60\u7684\u5c0f\u65f6\u6570\u6765\u89e3\u91ca\u3002\u4e00\u822c\u6765\u8bf4\uff0c\u56de\u5f52\u6a21\u578b\u7684 R \u5e73\u65b9\u503c\u8d8a\u5927\uff0c\u9884\u6d4b\u53d8\u91cf\u5bf9\u54cd\u5e94\u53d8\u91cf\u503c\u7684\u9884\u6d4b\u6548\u679c\u5c31\u8d8a\u597d\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c <strong>83.1%<\/strong>\u7684\u5206\u6570\u5dee\u5f02\u53ef\u4ee5\u7528\u5b66\u4e60\u65f6\u95f4\u6765\u89e3\u91ca\u3002<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong>\u6b8b\u5dee\u6807\u51c6\u8bef\u5dee\uff1a<\/strong>\u8fd9\u662f\u89c2\u6d4b\u503c\u4e0e\u56de\u5f52\u7ebf\u4e4b\u95f4\u7684\u5e73\u5747\u8ddd\u79bb\u3002\u8be5\u503c\u8d8a\u4f4e\uff0c\u56de\u5f52\u7ebf\u8d8a\u80fd\u4e0e\u89c2\u5bdf\u5230\u7684\u6570\u636e\u76f8\u5bf9\u5e94\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u8003\u8bd5\u4e2d\u89c2\u5bdf\u5230\u7684\u5e73\u5747\u5206\u6570\u4e0e\u56de\u5f52\u7ebf\u9884\u6d4b\u7684\u5206\u6570\u76f8\u5dee<strong>3,641<\/strong>\u5206\u3002<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>F \u7edf\u8ba1\u91cf\u548c p \u503c\uff1a<\/strong> F \u7edf\u8ba1\u91cf ( <strong>63.91<\/strong> ) \u548c\u76f8\u5e94\u7684 p \u503c ( <strong>2.253e-06<\/strong> ) \u544a\u8bc9\u6211\u4eec\u56de\u5f52\u6a21\u578b\u7684\u6574\u4f53\u663e\u7740\u6027\uff0c\u5373\u6a21\u578b\u4e2d\u7684\u9884\u6d4b\u53d8\u91cf\u662f\u5426\u6709\u52a9\u4e8e\u89e3\u91ca\u53d8\u5f02\u3002\u5728\u54cd\u5e94\u53d8\u91cf\u4e2d\u3002\u7531\u4e8e\u6b64\u793a\u4f8b\u4e2d\u7684 p \u503c\u5c0f\u4e8e 0.05\uff0c\u56e0\u6b64\u6211\u4eec\u7684\u6a21\u578b\u5177\u6709\u7edf\u8ba1\u663e\u7740\u6027\uff0c\u5e76\u4e14<em>\u5c0f\u65f6\u6570<\/em>\u88ab\u8ba4\u4e3a\u6709\u52a9\u4e8e\u89e3\u91ca<em>\u5206\u6570<\/em>\u53d8\u5316\u3002<\/span><\/li>\n<\/ul>\n<h2><span style=\"color: #000000;\"><strong>\u7b2c 4 \u6b65\uff1a\u521b\u5efa\u6b8b\u5dee\u56fe<\/strong><\/span><\/h2>\n<p><span style=\"color: #000000;\">\u6700\u540e\uff0c\u6211\u4eec\u9700\u8981\u521b\u5efa\u6b8b\u5dee\u56fe\u6765\u68c0\u67e5<a href=\"https:\/\/statorials.org\/cn\/\u5f02\u65b9\u5dee\u56de\u5f52\/\" target=\"_blank\" rel=\"noopener\">\u540c\u65b9\u5dee\u6027<\/a>\u548c<a href=\"https:\/\/statorials.org\/cn\/\u6b63\u6001\u5047\u8bbe\/\" target=\"_blank\" rel=\"noopener\">\u6b63\u6001\u6027<\/a>\u7684\u5047\u8bbe\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>\u540c\u65b9\u5dee\u6027<\/strong>\u5047\u8bbe\u662f\u56de\u5f52\u6a21\u578b\u7684<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\u5177\u6709\u8fd1\u4f3c\u76f8\u7b49\u7684\u65b9\u5dee\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4e3a\u4e86\u9a8c\u8bc1\u8fd9\u4e2a\u5047\u8bbe\u662f\u5426\u5f97\u5230\u6ee1\u8db3\uff0c\u6211\u4eec\u53ef\u4ee5\u521b\u5efa<strong>\u6b8b\u5dee\u4e0e\u62df\u5408\u7684\u56fe<\/strong>\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\">x \u8f74\u663e\u793a\u62df\u5408\u503c\uff0cy \u8f74\u663e\u793a\u6b8b\u5dee\u3002\u53ea\u8981\u6b8b\u5dee\u770b\u8d77\u6765\u5728\u96f6\u503c\u5468\u56f4\u968f\u673a\u4e14\u5747\u5300\u5730\u5206\u5e03\u5728\u6574\u4e2a\u56fe\u4e2d\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u5047\u8bbe\u4e0d\u8fdd\u53cd\u540c\u65b9\u5dee\u6027\uff1a<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#define residuals\n<\/span>res &lt;- resid(model)\n\n<span style=\"color: #008080;\">#produce residual vs. fitted plot\n<\/span>plot(fitted(model), res)\n\n<span style=\"color: #008080;\">#add a horizontal line at 0 \n<\/span>abline(0,0)\n<\/strong><\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-28971 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/ols3.jpg\" alt=\"\" width=\"501\" height=\"364\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p><span style=\"color: #000000;\">\u6b8b\u5dee\u4f3c\u4e4e\u968f\u673a\u5206\u6563\u5728\u96f6\u9644\u8fd1\uff0c\u5e76\u4e14\u6ca1\u6709\u663e\u793a\u51fa\u660e\u663e\u7684\u6a21\u5f0f\uff0c\u56e0\u6b64\u6ee1\u8db3\u6b64\u5047\u8bbe\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\"><b>\u6b63\u6001\u6027<\/b>\u5047\u8bbe\u8868\u660e\u56de\u5f52\u6a21\u578b\u7684<a href=\"https:\/\/statorials.org\/cn\/\u6b8b\u7559\u7269\/\" target=\"_blank\" rel=\"noopener\">\u6b8b\u5dee<\/a>\u8fd1\u4f3c\u5448\u6b63\u6001\u5206\u5e03\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4e3a\u4e86\u68c0\u67e5\u8fd9\u4e2a\u5047\u8bbe\u662f\u5426\u6ee1\u8db3\uff0c\u6211\u4eec\u53ef\u4ee5\u521b\u5efa\u4e00\u4e2a<strong>QQ \u56fe<\/strong>\u3002\u5982\u679c\u7ed8\u56fe\u70b9\u4f4d\u4e8e\u5f62\u6210 45 \u5ea6\u89d2\u7684\u5927\u81f4\u76f4\u7ebf\u4e0a\uff0c\u5219\u6570\u636e\u5448\u6b63\u6001\u5206\u5e03\uff1a<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#create QQ plot for residuals\n<\/span>qqnorm(res)\n\n<span style=\"color: #008080;\">#add a straight diagonal line to the plot\n<\/span>qqline(res) \n<\/strong><\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-28972 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/ols4.jpg\" alt=\"\" width=\"416\" height=\"394\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p><span style=\"color: #000000;\">\u6b8b\u5dee\u7a0d\u5fae\u504f\u79bb 45 \u5ea6\u7ebf\uff0c\u4f46\u4e0d\u8db3\u4ee5\u5f15\u8d77\u4e25\u91cd\u5173\u6ce8\u3002\u6211\u4eec\u53ef\u4ee5\u5047\u8bbe\u6ee1\u8db3\u6b63\u6001\u6027\u5047\u8bbe\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u7531\u4e8e\u6b8b\u5dee\u5448\u6b63\u6001\u5206\u5e03\u4e14\u540c\u65b9\u5dee\uff0c\u6211\u4eec\u9a8c\u8bc1\u4e86 OLS \u56de\u5f52\u6a21\u578b\u7684\u5047\u8bbe\u5f97\u5230\u6ee1\u8db3\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u56e0\u6b64\uff0c\u6211\u4eec\u6a21\u578b\u7684\u8f93\u51fa\u662f\u53ef\u9760\u7684\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>\u6ce8\u610f<\/strong>\uff1a\u5982\u679c\u4e00\u4e2a\u6216\u591a\u4e2a\u5047\u8bbe\u4e0d\u6ee1\u8db3\uff0c\u6211\u4eec\u53ef\u4ee5\u5c1d\u8bd5<a href=\"https:\/\/statorials.org\/cn\/\u5c06\u6570\u636e\u8f6c\u6362\u4e3ar\/\" target=\"_blank\" rel=\"noopener\">\u8f6c\u6362<\/a>\u6211\u4eec\u7684\u6570\u636e\u3002<\/span><\/p>\n<h2><span style=\"color: #000000;\"><strong>\u5176\u4ed6\u8d44\u6e90<\/strong><\/span><\/h2>\n<p><span style=\"color: #000000;\">\u4ee5\u4e0b\u6559\u7a0b\u89e3\u91ca\u4e86\u5982\u4f55\u5728 R \u4e2d\u6267\u884c\u5176\u4ed6\u5e38\u89c1\u4efb\u52a1\uff1a<\/span><\/p>\n<p><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\u6307\u6570\u56de\u5f52\/\" target=\"_blank\" rel=\"noopener\">\u5982\u4f55\u5728 R \u4e2d\u6267\u884c\u6307\u6570\u56de\u5f52<\/a><br \/> <a href=\"https:\/\/statorials.org\/cn\/r-\u4e2d\u7684\u52a0\u6743\u6700\u5c0f\u4e8c\u4e58\u6cd5\/\" target=\"_blank\" rel=\"noopener\">\u5982\u4f55\u5728 R \u4e2d\u6267\u884c\u52a0\u6743\u6700\u5c0f\u4e8c\u4e58\u56de\u5f52<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u666e\u901a\u6700\u5c0f\u4e8c\u4e58 (OLS) \u56de\u5f52\u662f\u4e00\u79cd\u65b9\u6cd5\uff0c\u53ef\u8ba9\u6211\u4eec\u627e\u5230\u6700\u80fd\u63cf\u8ff0\u4e00\u4e2a\u6216\u591a\u4e2a\u9884\u6d4b\u53d8\u91cf\u4e0e\u54cd\u5e94\u53d8\u91cf\u4e4b\u95f4\u5173\u7cfb\u7684\u76f4\u7ebf\u3002 \u8be5 [&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-3470","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 OLS \u56de\u5f52\uff08\u5e26\u6709\u793a\u4f8b\uff09-Statorials<\/title>\n<meta name=\"description\" content=\"\u672c\u6559\u7a0b\u901a\u8fc7\u4e00\u4e2a\u5b8c\u6574\u7684\u793a\u4f8b\u89e3\u91ca\u4e86\u5982\u4f55\u5728 R \u4e2d\u6267\u884c OLS \u56de\u5f52\u3002\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/statorials.org\/cn\/r\u4e2d\u7684ols\u56de\u5f52\/\" \/>\n<meta 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