{"id":2449,"date":"2023-07-22T05:51:57","date_gmt":"2023-07-22T05:51:57","guid":{"rendered":"https:\/\/statorials.org\/cn\/python-%e4%b8%ad%e7%9a%84-sst-ssr-sse\/"},"modified":"2023-07-22T05:51:57","modified_gmt":"2023-07-22T05:51:57","slug":"python-%e4%b8%ad%e7%9a%84-sst-ssr-sse","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/python-%e4%b8%ad%e7%9a%84-sst-ssr-sse\/","title":{"rendered":"\u5982\u4f55\u5728python\u4e2d\u8ba1\u7b97sst\u3001ssr\u548csse"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">\u6211\u4eec\u7ecf\u5e38\u4f7f\u7528\u4e09\u4e2a\u4e0d\u540c\u7684<a href=\"https:\/\/statorials.org\/cn\/sst-ssr-sse\/\" target=\"_blank\" rel=\"noopener\">\u5e73\u65b9\u548c<\/a>\u503c\u6765\u8861\u91cf<a href=\"https:\/\/statorials.org\/cn\/\u7ebf\u6027\u56de\u5f521\/\" target=\"_blank\" rel=\"noopener\">\u56de\u5f52\u7ebf<\/a>\u5bf9\u4e00\u7ec4\u6570\u636e\u7684\u62df\u5408\u7a0b\u5ea6\uff1a<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1. \u603b\u5e73\u65b9\u548c (SST) \u2013<\/strong>\u5404\u4e2a\u6570\u636e\u70b9 (y <sub>i<\/sub> ) \u4e0e\u54cd\u5e94\u53d8\u91cf\u5e73\u5747\u503c ( <span style=\"border-top: 1px solid black;\">y<\/span> ) \u4e4b\u5dee\u7684\u5e73\u65b9\u548c\u3002<\/span><\/p>\n<ul>\n<li><span style=\"color: #000000;\">\u6d77\u6e29 = \u03a3(y <sub>i<\/sub> \u2013 <span style=\"border-top: 1px solid black;\">y<\/span> ) <sup>2<\/sup><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>2. \u5e73\u65b9\u548c\u56de\u5f52 (SSR)<\/strong> \u2013 \u9884\u6d4b\u6570\u636e\u70b9 (\u0177 <sub>i<\/sub> ) \u4e0e\u54cd\u5e94\u53d8\u91cf\u5e73\u5747\u503c ( <span style=\"border-top: 1px solid black;\">y<\/span> ) \u4e4b\u95f4\u7684\u5dee\u503c\u7684\u5e73\u65b9\u548c\u3002<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">SSR = \u03a3(\u0177 <sub>i<\/sub> \u2013 <span style=\"border-top: 1px solid black;\">y<\/span> ) <sup>2<\/sup><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>3. \u8bef\u5dee\u5e73\u65b9\u548c (SSE)<\/strong> \u2013 \u9884\u6d4b\u6570\u636e\u70b9 (\u0177 <sub>i<\/sub> ) \u4e0e\u89c2\u6d4b\u6570\u636e\u70b9 (y <sub>i<\/sub> ) \u4e4b\u95f4\u5dee\u5f02\u7684\u5e73\u65b9\u548c\u3002<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">SSE = \u03a3(\u0177 <sub>i<\/sub> \u2013 y <sub>i<\/sub> ) <sup>2<\/sup><\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u4ee5\u4e0b\u5206\u6b65\u793a\u4f8b\u5c55\u793a\u4e86\u5982\u4f55\u5728 Python \u4e2d\u8ba1\u7b97\u7ed9\u5b9a\u56de\u5f52\u6a21\u578b\u7684\u6bcf\u4e2a\u6307\u6807\u3002<\/span><\/p>\n<h2><span style=\"color: #000000;\"><strong>\u7b2c 1 \u6b65\uff1a\u521b\u5efa\u6570\u636e<\/strong><\/span><\/h2>\n<p><span style=\"color: #000000;\">\u9996\u5148\uff0c\u6211\u4eec\u521b\u5efa\u4e00\u4e2a\u6570\u636e\u96c6\uff0c\u5176\u4e2d\u5305\u542b\u7ed9\u5b9a\u5927\u5b66 20 \u540d\u4e0d\u540c\u5b66\u751f\u7684\u5b66\u4e60\u5c0f\u65f6\u6570\u548c\u8003\u8bd5\u6210\u7ee9\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\n<span style=\"color: #008080;\">#create pandas DataFrame\n<\/span>df = pd. <span style=\"color: #3366ff;\">DataFrame<\/span> ({' <span style=\"color: #ff0000;\">hours<\/span> ': [1, 1, 1, 2, 2, 2, 2, 2, 3, 3,\n                             3, 4, 4, 4, 5, 5, 6, 7, 7, 8],\n                   ' <span style=\"color: #ff0000;\">score<\/span> ': [68, 76, 74, 80, 76, 78, 81, 84, 86, 83,\n                             88, 85, 89, 94, 93, 94, 96, 89, 92, 97]})\n\n<span style=\"color: #008080;\">#view first five rows of DataFrame\n<\/span>df. <span style=\"color: #3366ff;\">head<\/span> ()\n\n\thours score\n0 1 68\n1 1 76\n2 1 74\n3 2 80\n4 2 76\n<\/strong><\/pre>\n<h2><span style=\"color: #000000;\"><strong>\u7b2c 2 \u6b65\uff1a\u62df\u5408\u56de\u5f52\u6a21\u578b<\/strong><\/span><\/h2>\n<p><span style=\"color: #000000;\">\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u5c06\u4f7f\u7528<a href=\"https:\/\/www.statsmodels.org\/devel\/generated\/statsmodels.regression.linear_model.OLS.html\" target=\"_blank\" rel=\"noopener\">statsmodels<\/a>\u5e93\u4e2d\u7684<strong>OLS()<\/strong>\u51fd\u6570\u6765\u62df\u5408\u4e00\u4e2a\u7b80\u5355\u7684\u7ebf\u6027\u56de\u5f52\u6a21\u578b\uff0c\u4f7f\u7528\u5206\u6570\u4f5c\u4e3a\u54cd\u5e94\u53d8\u91cf\uff0c\u5c0f\u65f6\u6570\u4f5c\u4e3a\u9884\u6d4b\u53d8\u91cf\uff1a<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008000;\">import<\/span> statsmodels. <span style=\"color: #3366ff;\">api<\/span> <span style=\"color: #008000;\">as<\/span> sm\n\n<span style=\"color: #008080;\">#define response variable\n<\/span>y = df[' <span style=\"color: #ff0000;\">score<\/span> ']\n\n<span style=\"color: #008080;\">#define predictor variable\n<\/span>x = df[[' <span style=\"color: #ff0000;\">hours<\/span> ']]\n\n<span style=\"color: #008080;\">#add constant to predictor variables\n<\/span>x = sm. <span style=\"color: #3366ff;\">add_constant<\/span> (x)\n\n<span style=\"color: #008080;\">#fit linear regression model\n<\/span>model = sm. <span style=\"color: #3366ff;\">OLS<\/span> (y,x). <span style=\"color: #3366ff;\">fit<\/span> ()\n<\/strong><\/pre>\n<h2><span style=\"color: #000000;\"><strong>\u6b65\u9aa4 3\uff1a\u8ba1\u7b97 SST\u3001SSR \u548c SSE<\/strong><\/span><\/h2>\n<p><span style=\"color: #000000;\">\u6700\u540e\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u4ee5\u4e0b\u516c\u5f0f\u8ba1\u7b97\u6a21\u578b\u7684SST\u3001SSR\u548cSSE\u503c\uff1a<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008000;\">import<\/span> numpy <span style=\"color: #008000;\">as<\/span> np\n\n<span style=\"color: #008080;\">#calculate\n<\/span>sse = np. <span style=\"color: #3366ff;\">sum<\/span> ((model. <span style=\"color: #3366ff;\">fitted values<\/span> - df. <span style=\"color: #3366ff;\">score<\/span> ) <span style=\"color: #800080;\">**<\/span> 2)\n<span style=\"color: #008000;\">print<\/span> (sse)\n\n331.07488479262696\n\n<span style=\"color: #008080;\">#calculate ssr\n<\/span>ssr = np. <span style=\"color: #3366ff;\">sum<\/span> ((model. <span style=\"color: #3366ff;\">fitted values<\/span> - df. <span style=\"color: #3366ff;\">score<\/span> . <span style=\"color: #3366ff;\">mean<\/span> ()) <span style=\"color: #800080;\">**<\/span> 2)\n<span style=\"color: #008000;\">print<\/span> (ssr)\n\n917.4751152073725\n\n<span style=\"color: #008080;\">#calculate sst\n<\/span>sst = ssr + sse\n<span style=\"color: #008000;\">print<\/span> (sst)\n\n1248.5499999999995\n<\/strong><\/pre>\n<p><span style=\"color: #000000;\">\u6307\u6807\u7ed3\u679c\u662f\uff1a<\/span><\/p>\n<ul>\n<li><span style=\"color: #000000;\"><strong>\u603b\u5e73\u65b9\u548c (SST)\uff1a<\/strong> 1248.55<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong>\u5e73\u65b9\u548c\u56de\u5f52 (SSR)\uff1a<\/strong> 917.4751<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong>\u8bef\u5dee\u5e73\u65b9\u548c (SSE)\uff1a<\/strong> 331.0749<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u6211\u4eec\u53ef\u4ee5\u9a8c\u8bc1 SST = SSR + SSE\uff1a<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">SST = SSR + SSE<\/span><\/li>\n<li> <span style=\"color: #000000;\">1248.55 = 917.4751 + 331.0749<\/span><\/li>\n<\/ul>\n<h2><span style=\"color: #000000;\"><strong>\u5176\u4ed6\u8d44\u6e90<\/strong><\/span><\/h2>\n<p><span style=\"color: #000000;\">\u60a8\u53ef\u4ee5\u4f7f\u7528\u4ee5\u4e0b\u8ba1\u7b97\u5668\u81ea\u52a8\u8ba1\u7b97\u4efb\u4f55\u7b80\u5355\u7ebf\u6027\u56de\u5f52\u7ebf\u7684 SST\u3001SSR \u548c SSE\uff1a<\/span><\/p>\n<ul>\n<li>\u6d77\u6e29\u8ba1\u7b97\u5668<\/li>\n<li>RSS \u8ba1\u7b97\u5668<\/li>\n<li>ESS\u8ba1\u7b97\u5668<\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u4ee5\u4e0b\u6559\u7a0b\u4ecb\u7ecd\u4e86\u5982\u4f55\u5728\u5176\u4ed6\u7edf\u8ba1\u8f6f\u4ef6\u4e2d\u8ba1\u7b97SST\u3001SSR\u548cSSE\uff1a<\/span><\/p>\n<ul>\n<li><a href=\"https:\/\/statorials.org\/cn\/r-\u4e2d\u7684-sst-ssr-sse\/\" target=\"_blank\" rel=\"noopener\">\u5982\u4f55\u5728R\u4e2d\u8ba1\u7b97SST\u3001SSR\u548cSSE<\/a><\/li>\n<li><a href=\"https:\/\/statorials.org\/cn\/excel\u4e2d\u7684sst-ssr-sse\/\" target=\"_blank\" rel=\"noopener\">\u5982\u4f55\u5728Excel\u4e2d\u8ba1\u7b97SST\u3001SSR\u548cSSE<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>\u6211\u4eec\u7ecf\u5e38\u4f7f\u7528\u4e09\u4e2a\u4e0d\u540c\u7684\u5e73\u65b9\u548c\u503c\u6765\u8861\u91cf\u56de\u5f52\u7ebf\u5bf9\u4e00\u7ec4\u6570\u636e\u7684\u62df\u5408\u7a0b\u5ea6\uff1a 1. \u603b\u5e73\u65b9\u548c (SST) \u2013\u5404\u4e2a\u6570\u636e\u70b9 ( [&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-2449","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\u8ba1\u7b97 SST\u3001SSR \u548c SSE - Statorials<\/title>\n<meta name=\"description\" content=\"\u672c\u6559\u7a0b\u4ecb\u7ecd\u5982\u4f55\u4f7f\u7528 Python \u8ba1\u7b97\u56de\u5f52\u6a21\u578b\u7684\u5404\u79cd\u5e73\u65b9\u548c\uff0c\u5305\u62ec SST\u3001SSR \u548c SSE\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\/python-\u4e2d\u7684-sst-ssr-sse\/\" \/>\n<meta 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