{"id":305,"date":"2023-08-02T19:59:18","date_gmt":"2023-08-02T19:59:18","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e7%ae%80%e5%8d%95%e7%ba%bf%e6%80%a7%e5%9b%9e%e5%bd%92\/"},"modified":"2023-08-02T19:59:18","modified_gmt":"2023-08-02T19:59:18","slug":"%e7%ae%80%e5%8d%95%e7%ba%bf%e6%80%a7%e5%9b%9e%e5%bd%92","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e7%ae%80%e5%8d%95%e7%ba%bf%e6%80%a7%e5%9b%9e%e5%bd%92\/","title":{"rendered":"\u7b80\u5355\u7ebf\u6027\u56de\u5f52"},"content":{"rendered":"<p>\u672c\u6587\u89e3\u91ca\u4e86\u7edf\u8ba1\u5b66\u4e2d\u7684\u7b80\u5355\u7ebf\u6027\u56de\u5f52\u662f\u4ec0\u4e48\u4ee5\u53ca\u5b83\u662f\u5982\u4f55\u6267\u884c\u7684\u3002\u540c\u6837\uff0c\u60a8\u4f1a\u53d1\u73b0\u4e00\u4e2a\u7b80\u5355\u7684\u7ebf\u6027\u56de\u5f52\u7ec3\u4e60\u5df2\u89e3\u51b3\uff0c\u6b64\u5916\uff0c\u8fd8\u6709\u4e00\u4e2a\u7b80\u5355\u7684\u5728\u7ebf\u7ebf\u6027\u56de\u5f52\u8ba1\u7b97\u5668\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-regresion-lineal-simple\"><\/span>\u4ec0\u4e48\u662f\u7b80\u5355\u7ebf\u6027\u56de\u5f52\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u7b80\u5355\u7ebf\u6027\u56de\u5f52<\/strong>\u662f\u4e00\u79cd\u7528\u4e8e\u5173\u8054\u81ea\u53d8\u91cf\u7684\u7edf\u8ba1\u6a21\u578b\uff0c\u6211\u4eec\u5c1d\u8bd5\u8fd1\u4f3c\u4e24\u4e2a\u53d8\u91cf\u4e4b\u95f4\u7684\u5173\u7cfb\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u7b80\u5355\u7ebf\u6027\u56de\u5f52\u7528\u4e8e\u67e5\u627e\u5c06\u4e24\u4e2a\u53d8\u91cf\u7ebf\u6027\u76f8\u5173\u7684\u65b9\u7a0b\u3002\u4ece\u903b\u8f91\u4e0a\u8bb2\uff0c\u4e24\u4e2a\u53d8\u91cf\u4e4b\u95f4\u7684\u5173\u7cfb\u5fc5\u987b\u662f\u7ebf\u6027\u7684\uff0c\u5426\u5219\u5fc5\u987b\u4f7f\u7528\u53e6\u4e00\u79cd\u56de\u5f52\u6a21\u578b\u3002<\/p>\n<p>\u7b80\u5355\u7ebf\u6027\u56de\u5f52\u6a21\u578b\u7684\u65b9\u7a0b\u7531\u4e24\u4e2a\u7cfb\u6570\u7ec4\u6210\uff1a\u65b9\u7a0b\u5e38\u6570 (b <sub>0<\/sub> ) \u548c\u4e24\u4e2a\u53d8\u91cf\u4e4b\u95f4\u7684\u76f8\u5173\u7cfb\u6570 (b <sub>1<\/sub> )\u3002\u56e0\u6b64\uff0c\u7b80\u5355\u7ebf\u6027\u56de\u5f52\u6a21\u578b\u7684\u65b9\u7a0b\u4e3a y=b <sub>0<\/sub> +b <sub>1<\/sub> x\u3002<\/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-92da05e7be03363fecef8974393a84fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=b_0+b_1x\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"95\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p>\u7b80\u5355\u7ebf\u6027\u56de\u5f52\u65b9\u7a0b\u88ab\u7ed8\u5236\u4e3a\u4e00\u6761\u76f4\u7ebf\uff0c\u56e0\u6b64\u7cfb\u6570 b <sub>0<\/sub>\u662f\u622a\u8ddd\uff0c\u7cfb\u6570 b <sub>1<\/sub>\u662f\u76f4\u7ebf\u7684\u659c\u7387\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formulas-de-la-regresion-lineal-simple\"><\/span>\u7b80\u5355\u7ebf\u6027\u56de\u5f52\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p class=\"has-text-align-left\"><strong>\u7b80\u5355\u7ebf\u6027\u56de\u5f52\u7cfb\u6570\u7684\u8ba1\u7b97\u516c\u5f0f<\/strong>\u5982\u4e0b\uff1a <\/p>\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/formules-de-regression-lineaire-simple.png\" alt=\"\u7b80\u5355\u7ebf\u6027\u56de\u5f52\u516c\u5f0f\" class=\"wp-image-6494\" width=\"381\" height=\"380\" srcset=\"\" sizes=\"auto, \"><\/figure>\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\u7b80\u5355\u7ebf\u6027\u56de\u5f52\u7684\u7cfb\u6570\u3002<\/u><\/p>\n<p>\u663e\u7136\uff0c\u7b80\u5355\u7ebf\u6027\u56de\u5f52\u6a21\u578b\u5f97\u51fa\u7684\u65b9\u7a0b\u5c06\u65e0\u6cd5\u731c\u6d4b\u6240\u6709\u89c2\u6d4b\u503c\u7684\u51c6\u786e\u503c\uff0c\u56e0\u4e3a\u8be5\u6a21\u578b\u53ea\u662f\u8bd5\u56fe\u627e\u5230\u4e00\u4e2a\u8fd1\u4f3c\u4e24\u4e2a\u53d8\u91cf\u4e4b\u95f4\u5173\u7cfb\u7684\u65b9\u7a0b\u3002\u56e0\u6b64\uff0c\u6b8b\u5dee\u88ab\u5b9a\u4e49\u4e3a\u771f\u5b9e\u503c\u4e0e\u7ebf\u6027\u56de\u5f52\u6a21\u578b\u4f30\u8ba1\u503c\u4e4b\u95f4\u7684\u5dee\u5f02\u3002<\/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-2028e64ca2c0035860e93c4bf244e2f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"e_i=y_i-\\widehat{y}_i\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"87\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p>\u8bf7\u6ce8\u610f\uff0c\u7b80\u5355\u7ebf\u6027\u56de\u5f52\u6a21\u578b\u7684\u76ee\u6807\u662f\u6700\u5c0f\u5316\u6b8b\u5dee\u7684\u5e73\u65b9\uff0c\u5373\u7b80\u5355\u7ebf\u6027\u56de\u5f52\u57fa\u4e8e<a href=\"https:\/\/statorials.org\/cn\/\u6700\u5c0f\u4e8c\u4e58\u6cd5\/\">\u6700\u5c0f\u4e8c\u4e58<\/a>\u51c6\u5219\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-resuelto-de-una-regresion-lineal-simple\"><\/span>\u7b80\u5355\u7ebf\u6027\u56de\u5f52\u7684\u5177\u4f53\u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e3a\u4e86\u5b8c\u6210\u5bf9\u7b80\u5355\u7ebf\u6027\u56de\u5f52\u65b9\u6cd5\u7684\u7406\u89e3\uff0c\u8fd9\u91cc\u6709\u4e00\u4e2a\u5b9e\u9645\u7684\u5206\u6b65\u793a\u4f8b\uff0c\u5176\u4e2d\u7b80\u5355\u7ebf\u6027\u56de\u5f52\u6a21\u578b\u7684\u65b9\u7a0b\u662f\u6839\u636e\u4e00\u7ec4\u7edf\u8ba1\u6570\u636e\u8ba1\u7b97\u51fa\u6765\u7684\u3002<\/p>\n<ul>\n<li>\u53c2\u52a0\u7edf\u8ba1\u8003\u8bd5\u540e\uff0c\u4e94\u540d\u5b66\u751f\u88ab\u95ee\u53ca\u4ed6\u4eec\u4e3a\u8003\u8bd5\u6295\u5165\u4e86\u591a\u5c11\u65f6\u95f4\u3002\u6570\u636e\u5982\u4e0b\u8868\u6240\u793a\u3002\u5bf9\u6536\u96c6\u7684\u7edf\u8ba1\u6570\u636e\u6267\u884c\u7b80\u5355\u7684\u7ebf\u6027\u56de\u5f52\u6a21\u578b\uff0c\u5c06\u5b66\u4e60\u65f6\u95f4\u4e0e\u53d6\u5f97\u7684\u6210\u7ee9\u7ebf\u6027\u76f8\u5173\u3002 <\/li>\n<\/ul>\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/donnees-de-regression-lineaire-simple.png\" alt=\"\" class=\"wp-image-6503\" width=\"213\" height=\"220\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p>\u4e3a\u4e86\u5efa\u7acb\u7b80\u5355\u7684\u7ebf\u6027\u56de\u5f52\u6a21\u578b\uff0c\u6211\u4eec\u5fc5\u987b\u786e\u5b9a\u65b9\u7a0b\u7684\u7cfb\u6570 b <sub>0<\/sub>\u548c b <sub>1<\/sub> \uff0c\u4e3a\u6b64\uff0c\u6211\u4eec\u5fc5\u987b\u4f7f\u7528\u4e0a\u4e00\u8282\u4e2d\u770b\u5230\u7684\u516c\u5f0f\u3002<\/p>\n<p>\u7136\u800c\uff0c\u8981\u5e94\u7528\u7b80\u5355\u7ebf\u6027\u56de\u5f52\u516c\u5f0f\uff0c\u6211\u4eec\u5fc5\u987b\u9996\u5148\u8ba1\u7b97\u81ea\u53d8\u91cf\u7684\u5747\u503c\u548c\u56e0\u53d8\u91cf\u7684\u5747\u503c\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-7a7aa6f1f20fa4ff0d61a2ad0dd2ea1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}\\overline{x}=\\cfrac{11+5+10+12+7}{5}=9\\\\[4ex]\\overline{y}=\\cfrac{7+4+5+8+6}{5}=6\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"105\" width=\"226\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u73b0\u5728\u6211\u4eec\u77e5\u9053\u4e86\u53d8\u91cf\u7684\u5747\u503c\uff0c\u6211\u4eec\u4f7f\u7528\u76f8\u5e94\u7684\u516c\u5f0f\u8ba1\u7b97\u6a21\u578b\u7684\u7cfb\u6570 b <sub>1<\/sub> \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-c9d90c766487cd7b6924e6b23d2d9c78_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}b_1=\\cfrac{\\displaystyle \\sum_{i=1}^n (x_i-\\overline{x})(y_i-\\overline{y})}{\\displaystyle \\sum_{i=1}^n (x_i-\\overline{x})^2}\\\\[10ex] b_1=\\cfrac{\\begin{array}{c}(11-9)(7-6)+(5-9)(4-6)+(10-9)(5-6)+\\\\+(12-9)(8-6)+(7-9)(6-6)\\end{array}}{(11-9)^2+(5-9)^2+(10-9)^2+(12-9)^2+(7-9)^2}\\\\[6ex]b_1=0,4412\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"264\" width=\"459\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u6700\u540e\uff0c\u6211\u4eec\u4f7f\u7528\u76f8\u5e94\u7684\u516c\u5f0f\u8ba1\u7b97\u6a21\u578b\u7684\u7cfb\u6570b <sub>0<\/sub> \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-c72e6b89a75681a88cf751ca39079240_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}b_0=\\overline{y}-b_1\\overline{x}\\\\[3ex]b_0=6-0,4412\\cdot 9 \\\\[3ex]b_0=2,0294\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"106\" width=\"144\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u7b80\u800c\u8a00\u4e4b\uff0c\u8be5\u95ee\u9898\u7684\u7b80\u5355\u7ebf\u6027\u56de\u5f52\u6a21\u578b\u65b9\u7a0b\u4e3a\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-7097952b105295743a390d0332e7a2b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=2,0294+0,4412x\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"170\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p>\u4e0b\u9762\u60a8\u53ef\u4ee5\u770b\u5230\u6837\u672c\u6570\u636e\u7684\u56fe\u5f62\u8868\u793a\u4ee5\u53ca\u7b80\u5355\u7ebf\u6027\u56de\u5f52\u6a21\u578b\u7684\u76f4\u7ebf\uff1a <\/p>\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/exemple-de-regression-lineaire-simple.png\" alt=\"\u7b80\u5355\u7ebf\u6027\u56de\u5f52\u793a\u4f8b\" class=\"wp-image-6517\" width=\"454\" height=\"304\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p>\u6700\u540e\uff0c\u4e00\u65e6\u6211\u4eec\u8ba1\u7b97\u4e86\u7b80\u5355\u7ebf\u6027\u56de\u5f52\u6a21\u578b\u7684\u65b9\u7a0b\uff0c\u5269\u4e0b\u7684\u5c31\u662f\u89e3\u91ca\u6240\u83b7\u5f97\u7684\u7ed3\u679c\u3002\u4e3a\u6b64\uff0c\u5fc5\u987b\u8ba1\u7b97\u56de\u5f52\u6a21\u578b\u7684\u51b3\u5b9a\u7cfb\u6570\uff0c\u60a8\u53ef\u4ee5\u901a\u8fc7\u5728\u6211\u4eec\u7684\u7f51\u7ad9\u4e0a\u641c\u7d22\u76f8\u5e94\u7684\u6587\u7ae0\u6765\u4e86\u89e3\u8fd9\u662f\u5982\u4f55\u5b8c\u6210\u7684\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"supuestos-de-la-regresion-lineal-simple\"><\/span>\u7b80\u5355\u7ebf\u6027\u56de\u5f52\u5047\u8bbe<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e3a\u4e86\u6267\u884c\u7b80\u5355\u7ebf\u6027\u56de\u5f52\uff0c\u5fc5\u987b\u6ee1\u8db3\u4ee5\u4e0b\u5047\u8bbe\uff1a<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:16px\"><span style=\"color:#101010;font-weight: normal;\"><strong>\u72ec\u7acb\u6027<\/strong>\uff1a\u89c2\u5bdf\u5230\u7684\u6b8b\u57fa\u5fc5\u987b\u76f8\u4e92\u72ec\u7acb\u3002\u786e\u4fdd\u6a21\u578b\u72ec\u7acb\u6027\u7684\u5e38\u89c1\u65b9\u6cd5\u662f\u5728\u91c7\u6837\u8fc7\u7a0b\u4e2d\u6dfb\u52a0\u968f\u673a\u6027\u3002<\/span><\/li>\n<li style=\"margin-bottom:16px\"><span style=\"color:#101010;font-weight: normal;\"><strong>\u540c\u65b9\u5dee\u6027<\/strong>\uff1a\u6b8b\u5dee\u7684\u65b9\u5dee\u5fc5\u987b\u5177\u6709\u540c\u8d28\u6027\uff0c\u5373\u6b8b\u5dee\u7684\u53d8\u5f02\u6027\u5fc5\u987b\u6052\u5b9a\u3002<\/span><\/li>\n<li style=\"margin-bottom:16px\"><span style=\"color:#101010;font-weight: normal;\"><strong>\u6b63\u6001\u6027<\/strong>\uff1a\u6b8b\u5dee\u5fc5\u987b\u670d\u4ece\u6b63\u6001\u5206\u5e03\uff0c\u6362\u53e5\u8bdd\u8bf4\uff0c\u5b83\u4eec\u5fc5\u987b\u670d\u4ece\u5747\u503c\u4e3a 0 \u7684\u6b63\u6001\u5206\u5e03\u3002<\/span><\/li>\n<li style=\"margin-bottom:16px\"><span style=\"color:#101010;font-weight: normal;\"><strong>\u7ebf\u6027<\/strong>\u2014\u2014\u81ea\u53d8\u91cf\u548c\u56e0\u53d8\u91cf\u4e4b\u95f4\u7684\u5173\u7cfb\u5e94\u8be5\u662f\u7ebf\u6027\u7684\u3002<\/span> <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"calculadora-de-la-regresion-lineal-simple\"><\/span>\u7b80\u5355\u7ebf\u6027\u56de\u5f52\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\u4e2d\uff0c\u4ee5\u62df\u5408\u4e24\u4e2a\u53d8\u91cf\u4e4b\u95f4\u7684\u7b80\u5355\u7ebf\u6027\u56de\u5f52\u6a21\u578b\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')\" 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