{"id":2243,"date":"2023-07-23T02:52:08","date_gmt":"2023-07-23T02:52:08","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e9%80%bb%e8%be%91%e5%9b%9e%e5%bd%92%e7%9a%84%e5%8e%9f%e5%81%87%e8%ae%be\/"},"modified":"2023-07-23T02:52:08","modified_gmt":"2023-07-23T02:52:08","slug":"%e9%80%bb%e8%be%91%e5%9b%9e%e5%bd%92%e7%9a%84%e5%8e%9f%e5%81%87%e8%ae%be","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e9%80%bb%e8%be%91%e5%9b%9e%e5%bd%92%e7%9a%84%e5%8e%9f%e5%81%87%e8%ae%be\/","title":{"rendered":"\u4e86\u89e3\u903b\u8f91\u56de\u5f52\u7684\u539f\u5047\u8bbe"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/cn\/\u903b\u8f91\u56de\u5f521\/\" target=\"_blank\" rel=\"noopener\">\u903b\u8f91\u56de\u5f52<\/a>\u662f\u4e00\u79cd\u56de\u5f52\u6a21\u578b\uff0c\u5f53\u54cd\u5e94\u53d8\u91cf\u662f\u4e8c\u5143\u65f6\uff0c\u6211\u4eec\u53ef\u4ee5\u7528\u5b83\u6765\u7406\u89e3\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\u7684\u5173\u7cfb\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u5982\u679c\u6211\u4eec\u53ea\u6709\u4e00\u4e2a\u9884\u6d4b\u53d8\u91cf\u548c\u4e00\u4e2a\u54cd\u5e94\u53d8\u91cf\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528<strong>\u7b80\u5355\u903b\u8f91\u56de\u5f52<\/strong>\uff0c\u5b83\u4f7f\u7528\u4ee5\u4e0b\u516c\u5f0f\u6765\u4f30\u8ba1\u53d8\u91cf\u4e4b\u95f4\u7684\u5173\u7cfb\uff1a<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>log[p(X) \/ (1-p(X))] = \u03b2 <sub>0<\/sub> + \u03b2 <sub>1<\/sub><\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u65b9\u7a0b\u53f3\u4fa7\u7684\u516c\u5f0f\u9884\u6d4b\u54cd\u5e94\u53d8\u91cf\u53d6\u503c\u4e3a 1 \u7684\u51e0\u7387\u7684\u5bf9\u6570\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u7b80\u5355\u903b\u8f91\u56de\u5f52\u4f7f\u7528\u4ee5\u4e0b\u539f\u5047\u8bbe\u548c\u5907\u62e9\u5047\u8bbe\uff1a<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>H <sub>0<\/sub> :<\/strong> \u03b2 <sub>1<\/sub> = 0<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>H <sub>A<\/sub> :<\/strong> \u03b2 <sub>1<\/sub> \u2260 0<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u539f\u5047\u8bbe\u6307\u51fa\u7cfb\u6570 \u03b2 <sub>1<\/sub>\u7b49\u4e8e\u96f6\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u9884\u6d4b\u53d8\u91cf x \u548c\u54cd\u5e94\u53d8\u91cf y \u4e4b\u95f4\u4e0d\u5b58\u5728\u7edf\u8ba1\u4e0a\u663e\u7740\u7684\u5173\u7cfb\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u53e6\u7c7b\u5047\u8bbe\u6307\u51fa \u03b2 <sub>1<\/sub><em>\u4e0d<\/em>\u7b49\u4e8e\u96f6\u3002\u6362\u53e5\u8bdd\u8bf4\uff0cx \u548c y \u4e4b\u95f4<em>\u5b58\u5728<\/em>\u7edf\u8ba1\u4e0a\u663e\u7740\u7684\u5173\u7cfb\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u5982\u679c\u6211\u4eec\u6709\u591a\u4e2a\u9884\u6d4b\u53d8\u91cf\u548c\u4e00\u4e2a\u54cd\u5e94\u53d8\u91cf\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528<strong>\u591a\u91cd\u903b\u8f91\u56de\u5f52<\/strong>\uff0c\u5b83\u4f7f\u7528\u4ee5\u4e0b\u516c\u5f0f\u6765\u4f30\u8ba1\u53d8\u91cf\u4e4b\u95f4\u7684\u5173\u7cfb\uff1a<\/span><\/p>\n<p> <strong><span style=\"color: #000000;\">log[p(X) \/ (1-p(X))] = \u03b2 <sub>0<\/sub> + \u03b2 <sub>1<\/sub> x <sub>1<\/sub> + \u03b2 <sub>2<\/sub> x <sub>2<\/sub> + \u2026 + \u03b2 <sub>k<\/sub> x <sub>k<\/sub><\/span><\/strong><\/p>\n<p><span style=\"color: #000000;\">\u591a\u5143\u903b\u8f91\u56de\u5f52\u4f7f\u7528\u4ee5\u4e0b\u539f\u5047\u8bbe\u548c\u5907\u62e9\u5047\u8bbe\uff1a<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>H <sub>0<\/sub> :<\/strong> \u03b2 <sub>1<\/sub> = \u03b2 <sub>2<\/sub> = \u2026 = \u03b2 <sub>k<\/sub> = 0<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>H <sub>A<\/sub> :<\/strong> \u03b2 <sub>1<\/sub> = \u03b2 <sub>2<\/sub> = \u2026 = \u03b2 <sub>k<\/sub> \u2260 0<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u539f\u5047\u8bbe\u6307\u51fa\u6a21\u578b\u4e2d\u7684\u6240\u6709\u7cfb\u6570\u90fd\u4e3a\u96f6\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u6ca1\u6709\u4e00\u4e2a\u9884\u6d4b\u53d8\u91cf\u4e0e\u54cd\u5e94\u53d8\u91cf y \u5177\u6709\u7edf\u8ba1\u663e\u7740\u5173\u7cfb\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u53e6\u4e00\u79cd\u5047\u8bbe\u6307\u51fa\u5e76\u975e\u6240\u6709\u7cfb\u6570\u540c\u65f6\u4e3a\u96f6\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4ee5\u4e0b\u793a\u4f8b\u8bf4\u660e\u5982\u4f55\u51b3\u5b9a\u662f\u5426\u62d2\u7edd\u7b80\u5355\u903b\u8f91\u56de\u5f52\u548c\u591a\u5143\u903b\u8f91\u56de\u5f52\u6a21\u578b\u4e2d\u7684\u539f\u5047\u8bbe\u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u793a\u4f8b 1\uff1a\u7b80\u5355\u903b\u8f91\u56de\u5f52<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">\u5047\u8bbe\u4e00\u4f4d\u6559\u6388\u60f3\u8981\u4f7f\u7528\u5b66\u4e60\u5c0f\u65f6\u6570\u6765\u9884\u6d4b\u4ed6\u73ed\u4e0a\u7684\u5b66\u751f\u5c06\u8fbe\u5230\u7684\u8003\u8bd5\u6210\u7ee9\u3002\u5b83\u6536\u96c6 20 \u540d\u5b66\u751f\u7684\u6570\u636e\u5e76\u62df\u5408\u4e00\u4e2a\u7b80\u5355\u7684\u903b\u8f91\u56de\u5f52\u6a21\u578b\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u6211\u4eec\u53ef\u4ee5\u5728 R \u4e2d\u4f7f\u7528\u4ee5\u4e0b\u4ee3\u7801\u6765\u62df\u5408\u7b80\u5355\u7684\u903b\u8f91\u56de\u5f52\u6a21\u578b\uff1a<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#createdata\n<\/span>df &lt;- data. <span style=\"color: #3366ff;\">frame<\/span> (result=c(0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1),\n                 hours=c(1, 5, 5, 1, 2, 1, 3, 2, 2, 1, 2, 1, 3, 4, 4, 2, 1, 1, 4, 3))\n\n<span style=\"color: #008080;\">#fit simple logistic regression model\n<\/span>model &lt;- glm(result~hours, family=' <span style=\"color: #ff0000;\">binomial<\/span> ', data=df)\n\n<span style=\"color: #008080;\">#view summary of model fit\n<\/span>summary(model)\n\nCall:\nglm(formula = result ~ hours, family = \"binomial\", data = df)\n\nDeviance Residuals: \n    Min 1Q Median 3Q Max  \n-1.8244 -1.1738 0.7701 0.9460 1.2236  \n\nCoefficients:\n            Estimate Std. Error z value Pr(&gt;|z|)\n(Intercept) -0.4987 0.9490 -0.526 0.599\nhours 0.3906 0.3714 1.052 0.293\n\n(Dispersion parameter for binomial family taken to be 1)\n\n    Null deviance: 26,920 on 19 degrees of freedom\nResidual deviance: 25,712 on 18 degrees of freedom\nAIC: 29,712\n\nNumber of Fisher Scoring iterations: 4\n\n<span style=\"color: #008080;\">#calculate p-value of overall Chi-Square statistic\n<\/span>1-pchisq(26.920-25.712, 19-18)\n\n[1] 0.2717286\n<\/strong><\/pre>\n<p><span style=\"color: #000000;\">\u4e3a\u4e86\u786e\u5b9a\u5b66\u4e60\u65f6\u95f4\u548c\u8003\u8bd5\u6210\u7ee9\u4e4b\u95f4\u662f\u5426\u5b58\u5728\u7edf\u8ba1\u663e\u7740\u5173\u7cfb\uff0c\u6211\u4eec\u9700\u8981\u5206\u6790\u6a21\u578b\u7684\u6574\u4f53\u5361\u65b9\u503c\u548c\u76f8\u5e94\u7684 p \u503c\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u4ee5\u4e0b\u516c\u5f0f\u6765\u8ba1\u7b97\u6a21\u578b\u7684\u6574\u4f53\u5361\u65b9\u503c\uff1a<\/span><\/p>\n<p> <span style=\"color: #000000;\">X <sup>2<\/sup> =\uff08\u96f6\u504f\u5dee \u2013 \u6b8b\u4f59\u504f\u5dee\uff09\/\uff08\u96f6 Df \u2013 \u6b8b\u4f59 Df\uff09<\/span><\/p>\n<p> <span style=\"color: #000000;\">p \u503c\u4e3a<strong>0.2717286<\/strong> \u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u7531\u4e8e\u8be5 p \u503c\u4e0d\u5c0f\u4e8e 0.05\uff0c\u56e0\u6b64\u6211\u4eec\u65e0\u6cd5\u62d2\u7edd\u539f\u5047\u8bbe\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u5b66\u4e60\u65f6\u95f4\u548c\u8003\u8bd5\u6210\u7ee9\u4e4b\u95f4\u4e0d\u5b58\u5728\u7edf\u8ba1\u4e0a\u7684\u663e\u7740\u5173\u7cfb\u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u793a\u4f8b 2\uff1a\u591a\u5143\u903b\u8f91\u56de\u5f52<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">\u5047\u8bbe\u4e00\u4f4d\u6559\u6388\u60f3\u8981\u4f7f\u7528\u5b66\u4e60\u7684\u5c0f\u65f6\u6570\u548c\u51c6\u5907\u8003\u8bd5\u7684\u6b21\u6570\u6765\u9884\u6d4b\u5b66\u751f\u5728\u4ed6\u7684\u73ed\u7ea7\u4e2d\u83b7\u5f97\u7684\u6210\u7ee9\u3002\u5b83\u6536\u96c6 20 \u540d\u5b66\u751f\u7684\u6570\u636e\u5e76\u62df\u5408\u591a\u5143\u903b\u8f91\u56de\u5f52\u6a21\u578b\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u6211\u4eec\u53ef\u4ee5\u5728 R \u4e2d\u4f7f\u7528\u4ee5\u4e0b\u4ee3\u7801\u6765\u62df\u5408\u591a\u5143\u903b\u8f91\u56de\u5f52\u6a21\u578b\uff1a<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#create data\n<\/span>df &lt;- data. <span style=\"color: #3366ff;\">frame<\/span> (result=c(0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1),\n                 hours=c(1, 5, 5, 1, 2, 1, 3, 2, 2, 1, 2, 1, 3, 4, 4, 2, 1, 1, 4, 3),\n                 exams=c(1, 2, 2, 1, 2, 1, 1, 3, 2, 4, 3, 2, 2, 4, 4, 5, 4, 4, 3, 5))\n\n<span style=\"color: #008080;\">#fit simple logistic regression model\n<\/span>model &lt;- glm(result~hours+exams, family=' <span style=\"color: #ff0000;\">binomial<\/span> ', data=df)\n\n<span style=\"color: #008080;\">#view summary of model fit\n<\/span>summary(model)\n\nCall:\nglm(formula = result ~ hours + exams, family = \"binomial\", data = df)\n\nDeviance Residuals: \n    Min 1Q Median 3Q Max  \n-1.5061 -0.6395 0.3347 0.6300 1.7014  \n\nCoefficients:\n            Estimate Std. Error z value Pr(&gt;|z|)  \n(Intercept) -3.4873 1.8557 -1.879 0.0602 .\nhours 0.3844 0.4145 0.927 0.3538  \nexams 1.1549 0.5493 2.103 0.0355 *\n---\nSignificant. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n\n(Dispersion parameter for binomial family taken to be 1)\n\n    Null deviance: 26,920 on 19 degrees of freedom\nResidual deviance: 19,067 on 17 degrees of freedom\nAIC: 25,067\n\nNumber of Fisher Scoring iterations: 5\n\n<span style=\"color: #008080;\">#calculate p-value of overall Chi-Square statistic\n<\/span>1-pchisq(26.920-19.067, 19-17)\n\n[1] 0.01971255\n<\/strong><\/pre>\n<p><span style=\"color: #000000;\">\u6a21\u578b\u6574\u4f53\u5361\u65b9\u7edf\u8ba1\u91cf\u7684 p \u503c\u4e3a<strong>0.01971255<\/strong> \u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u7531\u4e8e\u8be5 p \u503c\u5c0f\u4e8e 0.05\uff0c\u56e0\u6b64\u6211\u4eec\u62d2\u7edd\u539f\u5047\u8bbe\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u5b66\u4e60\u65f6\u95f4\u548c\u51c6\u5907\u8003\u8bd5\u7684\u7ec4\u5408\u4e0e\u8003\u8bd5\u7684\u6700\u7ec8\u6210\u7ee9\u4e4b\u95f4\u5b58\u5728\u7edf\u8ba1\u4e0a\u7684\u663e\u7740\u5173\u7cfb\u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u5176\u4ed6\u8d44\u6e90<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">\u4ee5\u4e0b\u6559\u7a0b\u63d0\u4f9b\u4e86\u6709\u5173\u903b\u8f91\u56de\u5f52\u7684\u66f4\u591a\u4fe1\u606f\uff1a<\/span><\/p>\n<p><a href=\"https:\/\/statorials.org\/cn\/\u903b\u8f91\u56de\u5f521\/\" target=\"_blank\" rel=\"noopener\">\u903b\u8f91\u56de\u5f52\u7b80\u4ecb<\/a><br \/> <a href=\"https:\/\/statorials.org\/cn\/\u5982\u4f55\u62a5\u544a\u903b\u8f91\u56de\u5f52\u7ed3\u679c\/\" target=\"_blank\" rel=\"noopener\">\u5982\u4f55\u62a5\u544a\u903b\u8f91\u56de\u5f52\u7ed3\u679c<\/a><br \/><a href=\"https:\/\/statorials.org\/cn\/\u903b\u8f91\u56de\u5f52\u4e0e\u7ebf\u6027\u56de\u5f52\/\" target=\"_blank\" rel=\"noopener\">\u903b\u8f91\u56de\u5f52\u4e0e\u7ebf\u6027\u56de\u5f52\uff1a\u4e3b\u8981\u533a\u522b<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u903b\u8f91\u56de\u5f52\u662f\u4e00\u79cd\u56de\u5f52\u6a21\u578b\uff0c\u5f53\u54cd\u5e94\u53d8\u91cf\u662f\u4e8c\u5143\u65f6\uff0c\u6211\u4eec\u53ef\u4ee5\u7528\u5b83\u6765\u7406\u89e3\u4e00\u4e2a\u6216\u591a\u4e2a\u9884\u6d4b\u53d8\u91cf\u4e0e\u54cd\u5e94\u53d8\u91cf\u4e4b\u95f4\u7684\u5173\u7cfb\u3002 \u5982\u679c\u6211 [&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-2243","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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