{"id":308,"date":"2023-08-02T18:39:40","date_gmt":"2023-08-02T18:39:40","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e5%86%b3%e5%ae%9a%e7%b3%bb%e6%95%b0-r-%e5%b9%b3%e6%96%b9\/"},"modified":"2023-08-02T18:39:40","modified_gmt":"2023-08-02T18:39:40","slug":"%e5%86%b3%e5%ae%9a%e7%b3%bb%e6%95%b0-r-%e5%b9%b3%e6%96%b9","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e5%86%b3%e5%ae%9a%e7%b3%bb%e6%95%b0-r-%e5%b9%b3%e6%96%b9\/","title":{"rendered":"\u51b3\u5b9a\u7cfb\u6570\uff08r \u5e73\u65b9\uff09"},"content":{"rendered":"<p>\u672c\u6587\u89e3\u91ca\u4e86\u7edf\u8ba1\u5b66\u4e2d\u7684\u51b3\u5b9a\u7cfb\u6570\uff08\u6216 R \u65b9\uff09\u3002\u56e0\u6b64\uff0c\u60a8\u5c06\u4e86\u89e3\u5982\u4f55\u8ba1\u7b97\u51b3\u5b9a\u7cfb\u6570\u3001\u5982\u4f55\u89e3\u91ca\u5b83\uff0c\u4ee5\u53ca\u7528\u4e8e\u8ba1\u7b97\u6570\u636e\u6837\u672c\u51b3\u5b9a\u7cfb\u6570\u7684\u5728\u7ebf\u8ba1\u7b97\u5668\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-el-coeficiente-de-determinacion-r-cuadrado\"><\/span>\u51b3\u5b9a\u7cfb\u6570\uff08R \u5e73\u65b9\uff09\u662f\u591a\u5c11\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u51b3\u5b9a\u7cfb\u6570<\/strong>\uff0c\u5176\u7b26\u53f7\u4e3a<strong>R <sup>2<\/sup><\/strong> ( <strong>R \u5e73\u65b9<\/strong>)\uff0c\u662f\u8861\u91cf\u56de\u5f52\u6a21\u578b\u62df\u5408\u4f18\u5ea6\u7684\u7edf\u8ba1\u91cf\u3002\u51b3\u5b9a\u7cfb\u6570\u8868\u793a\u56de\u5f52\u6a21\u578b\u5bf9\u6570\u636e\u96c6\u7684\u62df\u5408\u7a0b\u5ea6\uff0c\u5373\u8868\u793a\u56de\u5f52\u6a21\u578b\u89e3\u91ca\u7684\u767e\u5206\u6bd4\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u51b3\u5b9a\u7cfb\u6570\u8d8a\u9ad8\uff0c\u56de\u5f52\u6a21\u578b\u8d8a\u597d\u3002\u5c3d\u7ba1\u8fd9\u4e2a\u6761\u4ef6\u5e76\u4e0d\u603b\u662f\u6ee1\u8db3\uff0c\u4f46\u6211\u4eec\u539f\u5219\u4e0a\u5bf9\u5c3d\u53ef\u80fd\u5927\u7684\u51b3\u5b9a\u7cfb\u6570\u611f\u5174\u8da3\u3002\u6211\u4eec\u5c06\u5728\u4e0b\u9762\u770b\u5230\u5982\u4f55\u89e3\u91ca\u51b3\u5b9a\u7cfb\u6570\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-del-coeficiente-de-determinacion\"><\/span>\u786e\u5b9a\u7cfb\u6570\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u51b3\u5b9a\u7cfb\u6570\u7b49\u4e8e\u4e00\u51cf\u53bb\u6b8b\u5dee\u65b9\u5dee\u4e0e\u56e0\u53d8\u91cf\u65b9\u5dee\u4e4b\u6bd4\u3002\u786e\u5b9a\u7cfb\u6570\u4e5f\u53ef\u4ee5\u901a\u8fc7\u4ece\u603b\u5e73\u65b9\u548c\u7684\u6b8b\u5dee\u4e2d\u51cf\u53bb\u4e00\u51cf\u53bb\u5e73\u65b9\u548c\u6765\u8ba1\u7b97\u3002<\/p>\n<p>\u56e0\u6b64\uff0c<strong>\u51b3\u5b9a\u7cfb\u6570\u7684\u8ba1\u7b97\u516c\u5f0f<\/strong>\u5982\u4e0b\uff1a <\/p>\n<figure class=\"wp-block-image aligncenter size-full\"><img decoding=\"async\" loading=\"lazy\" width=\"390\" height=\"298\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/coefficient-de-determination-r-carre-formule.png\" alt=\"\u51b3\u5b9a\u7cfb\u6570\u516c\u5f0f\u3001r \u5e73\u65b9\u516c\u5f0f\" class=\"wp-image-6598\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p style=\"margin-bottom:5px\">\u91d1\u5b50\uff1a<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-c7d6931063ed333ca39b952ccfd482b8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"R^2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"21\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u662f\u51b3\u5b9a\u7cfb\u6570\u3002<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-25aba4ace37fe21924a7e7013a12f820_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sigma_r^2\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"18\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u662f\u6b8b\u5dee\u65b9\u5dee\u3002<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-c6d52162ef1ec2e8130fb00687aca707_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sigma^2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"18\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u662f\u56e0\u53d8\u91cf Y \u7684\u65b9\u5dee\u3002<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-5d2426a81957d42ba1d03e90ab09e303_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y_{i}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u662f\u89c2\u6d4b\u56e0\u53d8\u91cf i \u7684\u503c\u3002<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-d695c8bd6fa2155d85c8699b167f3999_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\widehat{y}_{i}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"14\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u662f\u89c2\u6d4b\u503c i \u7684\u56de\u5f52\u6a21\u578b\u7684\u8fd1\u4f3c\u503c\u3002<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ed5becac4ccb36fec040f449ba9fa52d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{y}\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"10\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u662f\u6240\u6709\u89c2\u6d4b\u503c\u4e2d\u56e0\u53d8\u91cf\u7684\u5e73\u5747\u503c\u3002<\/li>\n<\/ul>\n<p> \ud83d\udc49<u style=\"text-decoration-color:#FF8A05;\">\u60a8\u53ef\u4ee5\u4f7f\u7528\u4e0b\u9762\u7684\u8ba1\u7b97\u5668\u6765\u8ba1\u7b97\u4efb\u4f55\u6570\u636e\u96c6\u7684\u51b3\u5b9a\u7cfb\u6570\u3002<\/u><\/p>\n<p>\u5bf9\u4e8e\u7ebf\u6027\u56de\u5f52\u6a21\u578b\u7684\u60c5\u51b5\uff0c\u51b3\u5b9a\u7cfb\u6570\u7b49\u4e8e<a href=\"https:\/\/statorials.org\/cn\/\u76ae\u5c14\u900a\u76f8\u5173\u7cfb\u6570-1\/\">\u76f8\u5173\u7cfb\u6570<\/a>\u7684\u5e73\u65b9\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-f6812088c3fb9d2efc5807244046e3d7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"R^2=\\cfrac{\\sigma_{XY}^2}{\\sigma_X^2\\sigma_Y^2}=\\rho^2\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"132\" style=\"vertical-align: -18px;\"><\/p>\n<\/p>\n<p>\u91d1\u5b50<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-79f46756b768c4ccda071fed1bcc144a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sigma_{XY}^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"33\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u662f\u53d8\u91cf X \u548c Y \u7684<a href=\"https:\/\/statorials.org\/cn\/\u534f\u65b9\u5dee\/\">\u534f\u65b9\u5dee<\/a>\uff0c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-a3c8551c63e9116f7df70371c127741a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sigma_X^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"22\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u548c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-03e4ace849d460fee5d2f7879630b3b9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sigma_Y^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"21\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u5206\u522b\u662f\u81ea\u53d8\u91cf X \u548c\u56e0\u53d8\u91cf Y \u7684<a href=\"https:\/\/statorials.org\/cn\/\u65b9\u5dee\/\">\u65b9\u5dee<\/a>\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"calculadora-del-coeficiente-de-determinacion\"><\/span>\u51b3\u5b9a\u7cfb\u6570\u8ba1\u7b97\u5668<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5c06\u6837\u672c\u6570\u636e\u63d2\u5165\u4e0b\u9762\u7684\u8ba1\u7b97\u5668\u4ee5\u62df\u5408\u7b80\u5355\u7684\u7ebf\u6027\u56de\u5f52\u6a21\u578b\u5e76\u8ba1\u7b97\u5176\u51b3\u5b9a\u7cfb\u6570\u3002\u60a8\u9700\u8981\u5206\u79bb\u6570\u636e\u5bf9\uff0c\u4ee5\u4fbf\u7b2c\u4e00\u4e2a\u6846\u4e2d\u53ea\u6709\u81ea\u53d8\u91cf X \u7684\u503c\uff0c\u7b2c\u4e8c\u4e2a\u6846\u4e2d\u53ea\u6709\u56e0\u53d8\u91cf Y \u7684\u503c\u3002<\/p>\n<p>\u6570\u636e\u5fc5\u987b\u7528\u7a7a\u683c\u5206\u9694\uff0c\u5e76\u4f7f\u7528\u53e5\u70b9\u4f5c\u4e3a\u5c0f\u6570\u70b9\u5206\u9694\u7b26\u8f93\u5165\u3002<\/p>\n<form action=\"\" method=\"post\">\n<ul>\n<li>\u81ea\u53d8\u91cf<\/li>\n<\/ul>\n<p><textarea name=\"datosX\" style=\"border:1.5px solid #4FC3F7; border-radius:15px;\" placeholder=\"1 4 8 5 7.2 9 ...\" required=\"\" oninvalid=\"this.setCustomValidity('Introduce los datos de la variable explicativa aqu\u00ed')\" oninput=\"this.setCustomValidity('')\"><\/textarea><\/p>\n<ul style=\"margin-top:25px\">\n<li>\u56e0\u53d8\u91cf Y\uff1a <\/li>\n<\/ul>\n<p><textarea name=\"datosY\" style=\"border:1.5px solid #4FC3F7; border-radius:15px;\" placeholder=\"2 5 7 3 2 1 ...\" required=\"\" oninvalid=\"this.setCustomValidity('Introduce los datos de la variable respuesta aqu\u00ed')\" oninput=\"this.setCustomValidity('')\"><\/textarea><\/p>\n<div style=\"text-align:center\"><input align=\"center\" style=\"border-radius:30px; margin: 20px\" type=\"submit\" name=\"submit\" value=\"\u8ba1\u7b97\"><\/div>\n<\/form>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"interpretacion-del-coeficiente-de-determinacion\"><\/span>\u51b3\u5b9a\u7cfb\u6570\u7684\u89e3\u91ca<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5728\u672c\u8282\u4e2d\uff0c\u6211\u4eec\u5c06\u4e86\u89e3\u5982\u4f55\u89e3\u91ca\u51b3\u5b9a\u7cfb\u6570\uff0c\u56e0\u4e3a\u5982\u679c\u60a8\u7a0d\u540e\u4e0d\u77e5\u9053\u51b3\u5b9a\u7cfb\u6570\u7684\u542b\u4e49\uff0c\u90a3\u4e48\u77e5\u9053\u51b3\u5b9a\u7cfb\u6570\u7684\u503c\u662f\u6ca1\u6709\u610f\u4e49\u7684\u3002<\/p>\n<p>\u51b3\u5b9a\u7cfb\u6570\u7684\u503c\u53ef\u4ee5\u4ece 0 \u5230 1\uff0c\u4f46\u901a\u5e38\u4ee5\u767e\u5206\u6bd4\u8868\u793a\uff0c\u56e0\u6b64\u6700\u5c0f\u503c\u4e3a 0%\uff0c\u6700\u5927\u503c\u4e3a 100%\u3002<\/p>\n<p>\u5173\u4e8e<strong>\u51b3\u5b9a\u7cfb\u6570\u7684\u89e3\u91ca<\/strong>\uff0c\u5176\u503c\u8d8a\u9ad8\u610f\u5473\u7740\u56de\u5f52\u6a21\u578b\u5bf9\u6570\u636e\u6837\u672c\u7684\u89e3\u91ca\u8d8a\u597d\u3002\u56e0\u6b64\uff0c\u51b3\u5b9a\u7cfb\u6570\u8d8a\u63a5\u8fd11\uff0c\u6a21\u578b\u8c03\u6574\u7684\u5e45\u5ea6\u5c31\u8d8a\u5927\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u5b83\u8d8a\u63a5\u8fd1 0\uff0c\u751f\u6210\u7684\u56de\u5f52\u6a21\u578b\u7684\u53ef\u9760\u6027\u5c31\u8d8a\u4f4e\u3002<\/p>\n<p>\u7136\u800c\uff0c\u5f53\u6bd4\u8f83\u4e24\u4e2a\u56de\u5f52\u6a21\u578b\u65f6\uff0c\u56de\u5f52\u7cfb\u6570\u8f83\u9ad8\u7684\u6a21\u578b\u5e76\u4e0d\u603b\u662f\u66f4\u597d\u3002\u4f8b\u5982\uff0c\u56de\u5f52\u6a21\u578b\u53ef\u80fd\u5177\u6709\u56de\u5f52\u7cfb\u6570R <sup>2<\/sup> = 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href=\"https:\/\/statorials.org\/cn\/\u7edf\u8ba1\u56fe\/\">\u7edf\u8ba1\u56fe\u8868<\/a>\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"coeficiente-de-determinacion-ajustado\"><\/span>\u8c03\u6574\u51b3\u5b9a\u7cfb\u6570<span 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