{"id":4152,"date":"2023-07-13T06:17:20","date_gmt":"2023-07-13T06:17:20","guid":{"rendered":"https:\/\/statorials.org\/cn\/r-%e4%b8%ad%e5%9b%9e%e5%bd%92%e7%ba%bf%e6%96%9c%e7%8e%87%e7%9a%84-t-%e6%a3%80%e9%aa%8c\/"},"modified":"2023-07-13T06:17:20","modified_gmt":"2023-07-13T06:17:20","slug":"r-%e4%b8%ad%e5%9b%9e%e5%bd%92%e7%ba%bf%e6%96%9c%e7%8e%87%e7%9a%84-t-%e6%a3%80%e9%aa%8c","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/r-%e4%b8%ad%e5%9b%9e%e5%bd%92%e7%ba%bf%e6%96%9c%e7%8e%87%e7%9a%84-t-%e6%a3%80%e9%aa%8c\/","title":{"rendered":"\u5982\u4f55\u5bf9 r \u4e2d\u56de\u5f52\u7ebf\u7684\u659c\u7387\u8fdb\u884c t \u68c0\u9a8c"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">\u6211\u4eec\u6267\u884c<a href=\"https:\/\/statorials.org\/cn\/\u7ebf\u6027\u56de\u5f521\/\" target=\"_blank\" rel=\"noopener\">\u7b80\u5355\u7684\u7ebf\u6027\u56de\u5f52<\/a>\uff0c\u6700\u7ec8\u5f97\u5230\u4ee5\u4e0b\u4f30\u8ba1\u56de\u5f52\u65b9\u7a0b\uff1a<\/span><\/p>\n<p> <strong><span style=\"color: #000000;\">\u0177 = b <sub>0<\/sub> + b <sub>1<\/sub> x<\/span><\/strong><\/p>\n<p><span style=\"color: #000000;\">\u6211\u4eec\u901a\u5e38\u60f3\u77e5\u9053\u659c\u7387\u7cfb\u6570 b <sub>1<\/sub>\u662f\u5426\u5177\u6709\u7edf\u8ba1\u663e\u7740\u6027\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4e3a\u4e86\u786e\u5b9a b <sub>1<\/sub>\u662f\u5426\u5177\u6709\u7edf\u8ba1\u663e\u7740\u6027\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u4ee5\u4e0b\u68c0\u9a8c\u7edf\u8ba1\u91cf\u8fdb\u884c t \u68c0\u9a8c\uff1a<\/span><\/p>\n<p> <strong><span style=\"color: #000000;\">t = b <sub>1<\/sub> \/ se(b <sub>1<\/sub> )<\/span><\/strong><\/p>\n<p><span style=\"color: #000000;\">\u91d1\u5b50\uff1a<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>se(b <sub>1<\/sub> )<\/strong>\u8868\u793a b <sub>1<\/sub>\u7684\u6807\u51c6\u8bef\u5dee\u3002<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u7136\u540e\u6211\u4eec\u53ef\u4ee5\u8ba1\u7b97\u4e0e n-2 \u81ea\u7531\u5ea6\u7684\u68c0\u9a8c\u7edf\u8ba1\u91cf\u76f8\u5bf9\u5e94\u7684<a href=\"https:\/\/statorials.org\/cn\/p\u503c\u7edf\u8ba1\u663e\u7740\u6027\/\" target=\"_blank\" rel=\"noopener\">p \u503c<\/a>\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u5982\u679c p \u503c\u5c0f\u4e8e\u67d0\u4e2a\u9608\u503c\uff08\u4f8b\u5982 \u03b1 = 0.05\uff09\uff0c\u5219\u6211\u4eec\u53ef\u4ee5\u5f97\u51fa\u659c\u7387\u7cfb\u6570\u975e\u96f6\u7684\u7ed3\u8bba\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u6362\u53e5\u8bdd\u8bf4\uff0c\u6a21\u578b\u4e2d\u7684\u9884\u6d4b\u53d8\u91cf\u548c<a href=\"https:\/\/statorials.org\/cn\/\u53d8\u91cf\u89e3\u91ca\u6027\u53cd\u5e94\/\" target=\"_blank\" rel=\"noopener\">\u54cd\u5e94\u53d8\u91cf<\/a>\u4e4b\u95f4\u5b58\u5728\u7edf\u8ba1\u4e0a\u663e\u7740\u7684\u5173\u7cfb\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4ee5\u4e0b\u793a\u4f8b\u6f14\u793a\u5982\u4f55\u5bf9 R \u4e2d\u7684\u56de\u5f52\u7ebf\u659c\u7387\u6267\u884c t \u68c0\u9a8c\u3002<\/span><\/p>\n<h2><span style=\"color: #000000;\"><strong>\u793a\u4f8b\uff1a\u5bf9 R \u4e2d\u56de\u5f52\u7ebf\u7684\u659c\u7387\u8fd0\u884c t \u68c0\u9a8c<\/strong><\/span><\/h2>\n<p><span style=\"color: #000000;\">\u5047\u8bbe\u6211\u4eec\u5728 R \u4e2d\u6709\u4ee5\u4e0b\u6570\u636e\u6846\uff0c\u5176\u4e2d\u5305\u542b\u6709\u5173\u73ed\u7ea7 12 \u540d\u5b66\u751f\u7684\u5b66\u4e60\u65f6\u95f4\u548c\u671f\u672b\u8003\u8bd5\u6210\u7ee9\u7684\u4fe1\u606f\uff1a<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#create data frame\n<\/span>df &lt;- data. <span style=\"color: #3366ff;\">frame<\/span> (hours=c(1, 1, 2, 2, 3, 4, 5, 5, 5, 6, 6, 8),\n                 score=c(65, 67, 78, 75, 73, 84, 80, 76, 89, 91, 83, 82))\n\n<span style=\"color: #008080;\">#view data frame\n<\/span>df\n\n   hours score\n1 1 65\n2 1 67\n3 2 78\n4 2 75\n5 3 73\n6 4 84\n7 5 80\n8 5 76\n9 5 89\n10 6 91\n11 6 83\n12 8 82<\/strong><\/pre>\n<p><span style=\"color: #000000;\">\u5047\u8bbe\u6211\u4eec\u60f3\u8981\u62df\u5408\u4e00\u4e2a\u7b80\u5355\u7684\u7ebf\u6027\u56de\u5f52\u6a21\u578b\u6765\u786e\u5b9a\u5b66\u4e60\u65f6\u95f4\u548c\u8003\u8bd5\u6210\u7ee9\u4e4b\u95f4\u662f\u5426\u5b58\u5728\u7edf\u8ba1\u4e0a\u663e\u7740\u7684\u5173\u7cfb\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528 R \u4e2d\u7684<a href=\"https:\/\/statorials.org\/cn\/r\u4e2d\u7684lm\u51fd\u6570\/\" target=\"_blank\" rel=\"noopener\">lm()<\/a>\u51fd\u6570\u6765\u62df\u5408\u8fd9\u4e2a\u56de\u5f52\u6a21\u578b\uff1a<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#fit simple linear regression model\n<\/span>fit &lt;- lm(score ~ hours, data=df)\n\n<span style=\"color: #008080;\">#view model summary\n<\/span>summary(fit)\n\nCall:\nlm(formula = score ~ hours, data = df)\n\nResiduals:\n   Min 1Q Median 3Q Max \n-7,398 -3,926 -1,139 4,972 7,713 \n\nCoefficients:\n            Estimate Std. Error t value Pr(&gt;|t|)    \n(Intercept) 67.7685 3.3757 20.075 2.07e-09 ***\nhours 2.7037 0.7456 3.626 0.00464 ** \n---\nSignificant. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n\nResidual standard error: 5.479 on 10 degrees of freedom\nMultiple R-squared: 0.568, Adjusted R-squared: 0.5248 \nF-statistic: 13.15 on 1 and 10 DF, p-value: 0.004641\n<\/strong><\/pre>\n<p><span style=\"color: #000000;\">\u4ece\u6a21\u578b\u7ed3\u679c\u53ef\u4ee5\u770b\u51fa\uff0c\u4f30\u8ba1\u7684\u56de\u5f52\u65b9\u7a0b\u4e3a\uff1a<\/span><\/p>\n<p><span style=\"color: #000000;\">\u8003\u8bd5\u6210\u7ee9 = 67.7685 + 2.7037\uff08\u5c0f\u65f6\uff09<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4e3a\u4e86\u68c0\u9a8c\u659c\u7387\u7cfb\u6570\u662f\u5426\u5177\u6709\u7edf\u8ba1\u663e\u7740\u6027\uff0c\u6211\u4eec\u53ef\u4ee5\u8ba1\u7b97t\u68c0\u9a8c\u7edf\u8ba1\u91cf\uff0c\u5982\u4e0b\uff1a<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">t = b <sub>1<\/sub> \/ se(b <sub>1<\/sub> )<\/span><\/li>\n<li> <span style=\"color: #000000;\">t = 2.7037 \/ 0.7456<\/span><\/li>\n<li> <span style=\"color: #000000;\">t = <strong>3.626<\/strong><\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u4e0e\u6b64 t \u68c0\u9a8c\u7edf\u8ba1\u91cf\u5bf9\u5e94\u7684 p \u503c\u663e\u793a\u5728\u8f93\u51fa\u4e2d\u540d\u4e3a<strong>Pr(&gt; |t|)<\/strong>\u7684\u5217\u4e2d\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\">p \u503c\u4e3a<strong>0.00464<\/strong> \u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u7531\u4e8e\u8be5 p \u503c\u5c0f\u4e8e 0.05\uff0c\u56e0\u6b64\u6211\u4eec\u5f97\u51fa\u7ed3\u8bba\uff0c\u659c\u7387\u7cfb\u6570\u5177\u6709\u7edf\u8ba1\u663e\u7740\u6027\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u6362\u53e5\u8bdd\u8bf4\uff0c\u5b66\u4e60\u65f6\u6570\u4e0e\u5b66\u751f\u8003\u8bd5\u7684\u6700\u7ec8\u6210\u7ee9\u4e4b\u95f4\u5b58\u5728\u7edf\u8ba1\u4e0a\u7684\u663e\u7740\u5173\u7cfb\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\/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\/\u89e3\u91ca-r-\u4e2d\u7684\u56de\u5f52\u8f93\u51fa\/\" target=\"_blank\" rel=\"noopener\">\u5982\u4f55\u89e3\u91ca R \u4e2d\u7684\u56de\u5f52\u8f93\u51fa<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u6211\u4eec\u6267\u884c\u7b80\u5355\u7684\u7ebf\u6027\u56de\u5f52\uff0c\u6700\u7ec8\u5f97\u5230\u4ee5\u4e0b\u4f30\u8ba1\u56de\u5f52\u65b9\u7a0b\uff1a \u0177 = b 0 + b 1 x \u6211\u4eec\u901a\u5e38\u60f3\u77e5\u9053\u659c\u7387\u7cfb\u6570 b [&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-4152","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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