{"id":3561,"date":"2023-07-16T20:16:40","date_gmt":"2023-07-16T20:16:40","guid":{"rendered":"https:\/\/statorials.org\/cn\/ols%e5%9b%9e%e5%bd%92-python\/"},"modified":"2023-07-16T20:16:40","modified_gmt":"2023-07-16T20:16:40","slug":"ols%e5%9b%9e%e5%bd%92-python","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/ols%e5%9b%9e%e5%bd%92-python\/","title":{"rendered":"\u5982\u4f55\u5728 python \u4e2d\u6267\u884c ols \u56de\u5f52\uff08\u9644\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 Python \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 pandas \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: #008000;\">import<\/span> pandas <span style=\"color: #008000;\">as<\/span> pd\n<span style=\"color: #008080;\">\n#createDataFrame<\/span>\ndf = pd. <span style=\"color: #3366ff;\">DataFrame<\/span> ({' <span style=\"color: #ff0000;\">hours<\/span> ': [1, 2, 4, 5, 5, 6, 6, 7, 8, 10, 11, 11, 12, 12, 14],\n                   ' <span style=\"color: #ff0000;\">score<\/span> ': [64, 66, 76, 73, 74, 81, 83, 82, 80, 88, 84, 82, 91, 93, 89]})\n\n<span style=\"color: #008080;\">#view DataFrame\n<\/span><span style=\"color: #008000;\">print<\/span> (df)\n\n    hours score\n0 1 64\n1 2 66\n2 4 76\n3 5 73\n4 5 74\n5 6 81\n6 6 83\n7 7 82\n8 8 80\n9 10 88\n10 11 84\n11 11 82\n12 12 91\n13 12 93\n14 14 89<\/strong><\/pre>\n<h2><span style=\"color: #000000;\"><b>\u6b65\u9aa4 2\uff1a\u6267\u884c OLS \u56de\u5f52<\/b><\/span><\/h2>\n<p><span style=\"color: #000000;\">\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528<a href=\"https:\/\/www.statsmodels.org\/stable\/index.html\" target=\"_blank\" rel=\"noopener\">statsmodels<\/a>\u6a21\u5757\u4e2d\u7684\u51fd\u6570\u6765\u6267\u884c OLS \u56de\u5f52\uff0c\u4f7f\u7528<strong>\u5c0f\u65f6<\/strong>\u4f5c\u4e3a\u9884\u6d4b\u53d8\u91cf\uff0c\u5f97\u5206\u4f5c\u4e3a<strong>\u54cd\u5e94<\/strong>\u53d8\u91cf\uff1a<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\"><span style=\"color: #000000;\"><span style=\"color: #008000;\">import<\/span> statsmodels.api <span style=\"color: #008000;\">as<\/span> sm\n<\/span>\n#define predictor and response variables\n<span style=\"color: #000000;\">y = df[' <span style=\"color: #ff0000;\">score<\/span> ']\nx = df[' <span style=\"color: #ff0000;\">hours<\/span> ']<\/span>\n\n#add constant to predictor variables\n<span style=\"color: #000000;\">x = sm. <span style=\"color: #3366ff;\">add_constant<\/span> (x)\n<\/span>\n#fit linear regression model\n<span style=\"color: #000000;\">model = sm. <span style=\"color: #3366ff;\">OLS<\/span> (y,x). <span style=\"color: #3366ff;\">fit<\/span> ()\n<\/span>\n#view model summary\n<span style=\"color: #000000;\"><span style=\"color: #008000;\">print<\/span> ( <span style=\"color: #3366ff;\">model.summary<\/span> ())\n\n                            OLS Regression Results                            \n==================================================== ============================\nDept. Variable: R-squared score: 0.831\nModel: OLS Adj. R-squared: 0.818\nMethod: Least Squares F-statistic: 63.91\nDate: Fri, 26 Aug 2022 Prob (F-statistic): 2.25e-06\nTime: 10:42:24 Log-Likelihood: -39,594\nNo. Observations: 15 AIC: 83.19\nDf Residuals: 13 BIC: 84.60\nModel: 1                                         \nCovariance Type: non-robust                                         \n==================================================== ============================\n                 coef std err t P&gt;|t| [0.025 0.975]\n-------------------------------------------------- ----------------------------\nconst 65.3340 2.106 31.023 0.000 60.784 69.884\nhours 1.9824 0.248 7.995 0.000 1.447 2.518\n==================================================== ============================\nOmnibus: 4,351 Durbin-Watson: 1,677\nProb(Omnibus): 0.114 Jarque-Bera (JB): 1.329\nSkew: 0.092 Prob(JB): 0.515\nKurtosis: 1.554 Cond. No. 19.2\n==================================================== ============================<\/span><\/span><\/strong><\/pre>\n<p><span style=\"color: #000000;\">\u4ece<strong>coef<\/strong>\u5217\u4e2d\uff0c\u6211\u4eec\u53ef\u4ee5\u770b\u5230\u56de\u5f52\u7cfb\u6570\u5e76\u5199\u51fa\u4ee5\u4e0b\u62df\u5408\u56de\u5f52\u65b9\u7a0b\uff1a<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>\u5206\u6570 = 65.334 + 1.9824*\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>1.9824<\/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>85.158<\/strong>\u7684\u8003\u8bd5\u6210\u7ee9\uff1a<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>\u5206\u6570 = 65.334 + 1.9824*(10) = 85.158<\/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>P(&gt;|t|)\uff1a<\/strong>\u8fd9\u662f\u4e0e\u6a21\u578b\u7cfb\u6570\u76f8\u5173\u7684 p \u503c\u3002\u7531\u4e8e<em>\u5c0f\u65f6\u6570<\/em>(0.000) \u7684 p \u503c\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>R \u5e73\u65b9\uff1a<\/strong>\u8fd9\u544a\u8bc9\u6211\u4eec\uff0c\u8003\u8bd5\u6210\u7ee9\u7684\u53d8\u5316\u767e\u5206\u6bd4\u53ef\u4ee5\u901a\u8fc7\u5b66\u4e60\u7684\u5c0f\u65f6\u6570\u6765\u89e3\u91ca\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>F \u7edf\u8ba1\u91cf\u548c p \u503c\uff1a<\/strong> F \u7edf\u8ba1\u91cf ( <strong>63.91<\/strong> ) \u548c\u76f8\u5e94\u7684 p \u503c ( <strong>2.25e-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 3 \u6b65\uff1a\u53ef\u89c6\u5316\u6700\u4f73\u62df\u5408\u7ebf<\/strong><\/span><\/h2>\n<p><span style=\"color: #000000;\">\u6700\u540e\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528<strong>matplotlib<\/strong>\u6570\u636e\u53ef\u89c6\u5316\u5305\u6765\u53ef\u89c6\u5316\u62df\u5408\u5230\u5b9e\u9645\u6570\u636e\u70b9\u7684\u56de\u5f52\u7ebf\uff1a<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\"><span style=\"color: #000000;\"><span style=\"color: #008000;\">import<\/span> matplotlib. <span style=\"color: #3366ff;\">pyplot<\/span> <span style=\"color: #008000;\">as<\/span> plt\n<\/span>\n#find line of best fit\n<span style=\"color: #000000;\">a, b = np. <span style=\"color: #3366ff;\">polyfit<\/span> (df[' <span style=\"color: #ff0000;\">hours<\/span> '], df[' <span style=\"color: #ff0000;\">score<\/span> '], <span style=\"color: #008000;\">1<\/span> )\n<\/span>\n#add points to plot\n<span style=\"color: #000000;\">plt. <span style=\"color: #3366ff;\">scatter<\/span> (df[' <span style=\"color: #ff0000;\">hours<\/span> '], df[' <span style=\"color: #ff0000;\">score<\/span> '], color=' <span style=\"color: #ff0000;\">purple<\/span> ')\n<\/span>\n#add line of best fit to plot\n<span style=\"color: #000000;\">plt. <span style=\"color: #3366ff;\">plot<\/span> (df[' <span style=\"color: #ff0000;\">hours<\/span> '], a*df[' <span style=\"color: #ff0000;\">hours<\/span> ']+b)\n<\/span>\n#add fitted regression equation to plot\n<span style=\"color: #000000;\">plt. <span style=\"color: #3366ff;\">text<\/span> ( <span style=\"color: #008000;\">1<\/span> , <span style=\"color: #008000;\">90<\/span> , 'y = ' + '{:.3f}'.format(b) + ' + {:.3f}'.format(a) + 'x', size= <span style=\"color: #008000;\">12<\/span> )\n\n<span style=\"color: #008080;\">#add axis labels\n<\/span>plt. <span style=\"color: #3366ff;\">xlabel<\/span> (' <span style=\"color: #ff0000;\">Hours Studied<\/span> ')\nplt. <span style=\"color: #3366ff;\">ylabel<\/span> (' <span style=\"color: #ff0000;\">Exam Score<\/span> ')\n<\/span><\/span><\/strong><\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-29456 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/ligne11.jpg\" alt=\"\" width=\"502\" height=\"385\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p><span style=\"color: #000000;\">\u7d2b\u8272\u70b9\u4ee3\u8868\u5b9e\u9645\u6570\u636e\u70b9\uff0c\u84dd\u8272\u7ebf\u4ee3\u8868\u62df\u5408\u56de\u5f52\u7ebf\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u6211\u4eec\u8fd8\u4f7f\u7528<strong>plt.text()<\/strong>\u51fd\u6570\u5c06\u62df\u5408\u7684\u56de\u5f52\u65b9\u7a0b\u6dfb\u52a0\u5230\u56fe\u7684\u5de6\u4e0a\u89d2\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4ece\u56fe\u8868\u4e2d\u53ef\u4ee5\u770b\u51fa\uff0c\u62df\u5408\u7684\u56de\u5f52\u7ebf\u5f88\u597d\u5730\u6355\u6349\u4e86<strong>\u5c0f\u65f6<\/strong>\u53d8\u91cf\u548c<strong>\u5206\u6570<\/strong>\u53d8\u91cf\u4e4b\u95f4\u7684\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 Python \u4e2d\u6267\u884c\u5176\u4ed6\u5e38\u89c1\u4efb\u52a1\uff1a<\/span><\/p>\n<p><a href=\"https:\/\/statorials.org\/cn\/\u903b\u8f91\u56de\u5f52-python\/\" target=\"_blank\" rel=\"noopener\">\u5982\u4f55\u5728 Python \u4e2d\u6267\u884c\u903b\u8f91\u56de\u5f52<\/a><br \/><a href=\"https:\/\/statorials.org\/cn\/\u6307\u6570\u56de\u5f52-python\/\" target=\"_blank\" rel=\"noopener\">\u5982\u4f55\u5728 Python \u4e2d\u6267\u884c\u6307\u6570\u56de\u5f52<\/a><br \/><a href=\"https:\/\/statorials.org\/cn\/\u87d2\u86c7\u4e2d\u7684aic\/\" target=\"_blank\" rel=\"noopener\">\u5982\u4f55\u7528Python\u8ba1\u7b97\u56de\u5f52\u6a21\u578b\u7684AIC<\/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-3561","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 Python \u4e2d\u6267\u884c OLS \u56de\u5f52\uff08\u5e26\u793a\u4f8b\uff09 - Statorials<\/title>\n<meta name=\"description\" content=\"\u672c\u6559\u7a0b\u63d0\u4f9b\u4e86\u5982\u4f55\u5728 Python \u4e2d\u6267\u884c\u666e\u901a\u6700\u5c0f\u4e8c\u4e58 (OLS) \u56de\u5f52\u7684\u5206\u6b65\u793a\u4f8b\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\/ols\u56de\u5f52-python\/\" \/>\n<meta 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