{"id":1471,"date":"2023-07-26T06:28:59","date_gmt":"2023-07-26T06:28:59","guid":{"rendered":"https:\/\/statorials.org\/cn\/r-%e4%b8%ad%e7%9a%84-sst-ssr-sse\/"},"modified":"2023-07-26T06:28:59","modified_gmt":"2023-07-26T06:28:59","slug":"r-%e4%b8%ad%e7%9a%84-sst-ssr-sse","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/r-%e4%b8%ad%e7%9a%84-sst-ssr-sse\/","title":{"rendered":"\u5982\u4f55\u5728r\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>\u5b9e\u9645\u62df\u5408\u6570\u636e\u96c6\u7684\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\u8ba1\u7b97 R \u4e2d\u7ed9\u5b9a\u56de\u5f52\u6a21\u578b\u7684\u6bcf\u4e2a\u6307\u6807\u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u7b2c 1 \u6b65\uff1a\u521b\u5efa\u6570\u636e<\/strong><\/span><\/h3>\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: #008080;\">#create data frame<\/span>\ndf &lt;- data. <span style=\"color: #3366ff;\">frame<\/span> (hours=c(1, 1, 1, 2, 2, 2, 2, 2, 3, 3,\n                         3, 4, 4, 4, 5, 5, 6, 7, 7, 8),\n                 score=c(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 six rows of data frame\n<\/span>head(df)\n\n  hours score\n1 1 68\n2 1 76\n3 1 74\n4 2 80\n5 2 76\n6 2 78<\/strong><\/pre>\n<h3><span style=\"color: #000000;\"><strong>\u7b2c 2 \u6b65\uff1a\u62df\u5408\u56de\u5f52\u6a21\u578b<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\"><span style=\"color: #000000;\">\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u5c06\u4f7f\u7528<strong>lm()<\/strong>\u51fd\u6570\u6765\u62df\u5408\u4e00\u4e2a\u7b80\u5355\u7684\u7ebf\u6027\u56de\u5f52\u6a21\u578b\uff0c\u4f7f\u7528\u5206\u6570\u4f5c\u4e3a<a href=\"https:\/\/statorials.org\/cn\/\u53d8\u91cf\u89e3\u91ca\u6027\u53cd\u5e94\/\" target=\"_blank\" rel=\"noopener\">\u54cd\u5e94\u53d8\u91cf<\/a>\uff0c\u5c0f\u65f6\u6570\u4f5c\u4e3a\u9884\u6d4b\u53d8\u91cf\uff1a<\/span><\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#fit regression model<\/span>\nmodel &lt;- lm(score ~ hours, data = df)\n\n<span style=\"color: #008080;\">#view model summary\n<\/span>summary(model)\n\nCall:\nlm(formula = score ~ hours, data = df)\n\nResiduals:\n    Min 1Q Median 3Q Max \n-8.6970 -2.5156 -0.0737 3.1100 7.5495 \n\nCoefficients:\n            Estimate Std. Error t value Pr(&gt;|t|)    \n(Intercept) 73.4459 1.9147 38.360 &lt; 2nd-16 ***\nhours 3.2512 0.4603 7.063 1.38e-06 ***\n---\nSignificant. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n\nResidual standard error: 4.289 on 18 degrees of freedom\nMultiple R-squared: 0.7348, Adjusted R-squared: 0.7201 \nF-statistic: 49.88 on 1 and 18 DF, p-value: 1.378e-06\n<\/strong><\/pre>\n<h3><span style=\"color: #000000;\"><strong>\u6b65\u9aa4 3\uff1a\u8ba1\u7b97 SST\u3001SSR \u548c SSE<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u4ee5\u4e0b\u8bed\u6cd5\u6765\u8ba1\u7b97SST\u3001SSR\u548cSSE\uff1a<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#find sse<\/span>\nsse &lt;- <span style=\"color: #3366ff;\">sum<\/span> (( <span style=\"color: #3366ff;\">fitted<\/span> (model) - df$score)^2)\nsse\n\n[1] 331.0749\n\n<span style=\"color: #008080;\">#find ssr\n<\/span>ssr &lt;- <span style=\"color: #3366ff;\">sum<\/span> (( <span style=\"color: #3366ff;\">fitted<\/span> (model) - <span style=\"color: #3366ff;\">mean<\/span> (df$score))^2)\nssr\n\n[1] 917.4751\n\n<span style=\"color: #008080;\">#find sst\n<\/span>sst &lt;- ssr + sse\nsst\n\n[1] 1248.55\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<p><span style=\"color: #000000;\">\u6211\u4eec\u8fd8\u53ef\u4ee5\u624b\u52a8\u8ba1\u7b97\u56de\u5f52\u6a21\u578b\u7684<a href=\"https:\/\/statorials.org\/cn\/\u826f\u597d\u7684-r-\u5e73\u65b9\u503c\/\" target=\"_blank\" rel=\"noopener\">R\u5e73\u65b9<\/a>\uff1a<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">R \u5e73\u65b9 = SSR \/ SST<\/span><\/li>\n<li> <span style=\"color: #000000;\">R \u5e73\u65b9 = 917.4751 \/ 1248.55<\/span><\/li>\n<li> <span style=\"color: #000000;\">R \u5e73\u65b9 = 0.7348<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u8fd9\u544a\u8bc9\u6211\u4eec\uff0c <strong>73.48%<\/strong>\u7684\u8003\u8bd5\u6210\u7ee9\u5dee\u5f02\u53ef\u4ee5\u901a\u8fc7\u5b66\u4e60\u65f6\u6570\u6765\u89e3\u91ca\u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u5176\u4ed6\u8d44\u6e90<\/strong><\/span><\/h3>\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<p>\u6d77\u6e29\u8ba1\u7b97\u5668<br \/>RSS \u8ba1\u7b97\u5668<br \/>ESS\u8ba1\u7b97\u5668<\/p>\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\u5b9e\u9645\u62df\u5408\u6570\u636e\u96c6\u7684\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-1471","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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