{"id":311,"date":"2023-08-02T17:33:25","date_gmt":"2023-08-02T17:33:25","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e5%9b%9e%e5%bd%92%e7%ba%bf\/"},"modified":"2023-08-02T17:33:25","modified_gmt":"2023-08-02T17:33:25","slug":"%e5%9b%9e%e5%bd%92%e7%ba%bf","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e5%9b%9e%e5%bd%92%e7%ba%bf\/","title":{"rendered":"\u56de\u5f52\u7ebf"},"content":{"rendered":"<p>\u672c\u6587\u89e3\u91ca\u4e86\u7edf\u8ba1\u5b66\u4e2d\u7684\u56de\u5f52\u7ebf\u3002\u56e0\u6b64\uff0c\u60a8\u5c06\u4e86\u89e3\u5982\u4f55\u8ba1\u7b97\u4e24\u4e2a\u53d8\u91cf\u4e4b\u95f4\u7684\u56de\u5f52\u7ebf\u3001\u5df2\u89e3\u51b3\u7684\u7ec3\u4e60\u4ee5\u53ca\u7528\u4e8e\u8ba1\u7b97\u4efb\u4f55\u6570\u636e\u6837\u672c\u7684\u56de\u5f52\u7ebf\u7684\u5728\u7ebf\u8ba1\u7b97\u5668\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-recta-de-regresion\"><\/span>\u4ec0\u4e48\u662f\u56de\u5f52\u7ebf\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5728\u7edf\u8ba1\u5b66\u4e2d\uff0c<strong>\u56de\u5f52\u7ebf<\/strong>\u662f\u4ece<a href=\"https:\/\/statorials.org\/cn\/\u7b80\u5355\u7ebf\u6027\u56de\u5f52\/\">\u7b80\u5355\u7ebf\u6027\u56de\u5f52\u6a21\u578b<\/a>\u5f97\u5230\u7684\u7ebf\u3002\u66f4\u51c6\u786e\u5730\u8bf4\uff0c\u56de\u5f52\u7ebf\u662f\u6700\u9002\u5408\u6563\u70b9\u56fe\u7684\u7ebf\uff0c\u56e0\u6b64\u6700\u80fd\u63cf\u8ff0\u4e00\u7ec4\u7edf\u8ba1\u6570\u636e\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u56de\u5f52\u7ebf\u65b9\u7a0b\u5728\u6570\u5b66\u4e0a\u5c06\u4e00\u7ec4\u6570\u636e\u7684\u81ea\u53d8\u91cf X \u548c\u56e0\u53d8\u91cf Y \u8054\u7cfb\u8d77\u6765\u3002\u5c3d\u7ba1\u56de\u5f52\u7ebf\u901a\u5e38\u65e0\u6cd5\u7cbe\u786e\u786e\u5b9a\u6bcf\u4e2a\u89c2\u6d4b\u503c\uff0c\u4f46\u5b83\u53ef\u4ee5\u63d0\u4f9b\u5176\u503c\u7684\u8fd1\u4f3c\u503c\u3002 <\/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\/ligne-de-regression.png\" alt=\"\u56de\u5f52\u7ebf\" class=\"wp-image-6708\" width=\"235\" height=\"219\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p>\u6b63\u5982\u60a8\u5728\u4e0a\u56fe\u4e2d\u6240\u770b\u5230\u7684\uff0c\u56de\u5f52\u7ebf\u5e2e\u52a9\u6211\u4eec\u4e86\u89e3\u6570\u636e\u96c6\u7684\u8d8b\u52bf\u4ee5\u53ca\u81ea\u53d8\u91cf\u548c\u56e0\u53d8\u91cf\u4e4b\u95f4\u5b58\u5728\u4ec0\u4e48\u7c7b\u578b\u7684\u5173\u7cfb\u3002\u4e0b\u9762\u6211\u4eec\u6765\u770b\u770b\u56de\u5f52\u7ebf\u7684\u5e94\u7528\u3002<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-recta-de-regresion\"><\/span>\u56de\u5f52\u7ebf\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u73b0\u5728\u6211\u4eec\u77e5\u9053\u4e86\u56de\u5f52\u7ebf\u7684\u5b9a\u4e49\uff0c\u8ba9\u6211\u4eec\u770b\u770b\u5982\u4f55\u8ba1\u7b97\u7ebf\u6027\u56de\u5f52\u6a21\u578b\u7684\u76f4\u7ebf\u65b9\u7a0b\u3002<\/p>\n<p>\u4e0e\u4efb\u4f55\u76f4\u7ebf\u4e00\u6837\uff0c\u56de\u5f52\u7ebf\u7684\u65b9\u7a0b\u7531\u5e38\u6570 (b <sub>0<\/sub> ) \u548c\u659c\u7387 (b <sub>1<\/sub> ) \u7ec4\u6210\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-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>\u56e0\u6b64\uff0c<strong>\u7ebf\u6027\u56de\u5f52\u7ebf\u7cfb\u6570\u7684\u8ba1\u7b97\u516c\u5f0f<\/strong>\u5982\u4e0b\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-6dc6f56cacf0a233977c358d6a62fca8_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}\\\\[12ex]b_0=\\overline{y}-b_1\\overline{x}\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"176\" width=\"190\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\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-81208591cba625e2b376233eb1869a4c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b_0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"15\" style=\"vertical-align: -3px;\"><\/p>\n<p>\u662f\u56de\u5f52\u7ebf\u7684\u5e38\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-19b7b5affd373068ff85c800b567b901_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b_1\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"14\" style=\"vertical-align: -3px;\"><\/p>\n<p>\u662f\u56de\u5f52\u7ebf\u7684\u659c\u7387\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-dad27a9703483183e1afd245f5232b83_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x_i\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"15\" style=\"vertical-align: -3px;\"><\/p>\n<p>\u662f\u6570\u636e i \u7684\u81ea\u53d8\u91cf X \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-761333a1d61654bd1cb5c7224b0d1994_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\u6570\u636e i \u7684\u56e0\u53d8\u91cf Y \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-a39858a792fb4fe9a3173e004701f2a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u662f\u81ea\u53d8\u91cf\u503c\u7684\u5e73\u5747\u503c<\/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\u56e0\u53d8\u91cf Y \u503c\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\u56de\u5f52\u7ebf\u3002<\/u> <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-resuelto-de-la-recta-de-regresion\"><\/span>\u56de\u5f52\u7ebf\u7684\u5177\u4f53\u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e3a\u4e86\u8fdb\u4e00\u6b65\u63a2\u8ba8\u56de\u5f52\u7ebf\u7684\u6982\u5ff5\uff0c\u4e0b\u9762\u662f\u5982\u4f55\u521b\u5efa\u56de\u5f52\u7ebf\u7684\u5de5\u4f5c\u793a\u4f8b\u3002<\/p>\n<ul>\n<li>\u5728\u53c2\u52a0\u7edf\u8ba1\u8003\u8bd5\u540e\uff0c\u4e94\u540d\u5b66\u751f\u88ab\u95ee\u53ca\u4ed6\u4eec\u5728\u8003\u8bd5\u4e0a\u82b1\u8d39\u4e86\u591a\u5c11\u65f6\u95f4\uff0c\u6570\u636e\u5982\u4e0b\u8868\u6240\u793a\u3002\u6839\u636e\u6536\u96c6\u7684\u7edf\u8ba1\u6570\u636e\u8ba1\u7b97\u56de\u5f52\u7ebf\uff0c\u5c06\u5b66\u4e60\u65f6\u95f4\u4e0e\u83b7\u5f97\u7684\u6210\u7ee9\u7ebf\u6027\u76f8\u5173\u3002\u63a5\u4e0b\u6765\uff0c\u786e\u5b9a\u5b66\u4e60 8 \u5c0f\u65f6\u7684\u5b66\u751f\u5c06\u83b7\u5f97\u4ec0\u4e48\u6210\u7ee9\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\u627e\u5230\u6837\u672c\u6570\u636e\u7684\u56de\u5f52\u7ebf\uff0c\u6211\u4eec\u9700\u8981\u786e\u5b9a\u65b9\u7a0b\u7684\u7cfb\u6570 b <sub>0<\/sub>\u548c b <sub>1<\/sub> \uff0c\u4e3a\u6b64\uff0c\u6211\u4eec\u9700\u8981\u4f7f\u7528\u4e0a\u4e00\u8282\u4e2d\u770b\u5230\u7684\u516c\u5f0f\u3002<\/p>\n<p>\u7136\u800c\uff0c\u8981\u5e94\u7528\u7ebf\u6027\u56de\u5f52\u7ebf\u7684\u516c\u5f0f\uff0c\u6211\u4eec\u5fc5\u987b\u9996\u5148\u8ba1\u7b97\u81ea\u53d8\u91cf\u7684\u5e73\u5747\u503c\u548c\u56e0\u53d8\u91cf\u7684\u5e73\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\u95ee\u9898\u7684\u7ebf\u6027\u56de\u5f52\u7ebf\u65b9\u7a0b\u5982\u4e0b\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=\"\u7ebf\u6027\u56de\u5f52\u7ebf\u793a\u4f8b\" class=\"wp-image-6517\" width=\"454\" height=\"304\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p>\u4e00\u65e6\u6211\u4eec\u8ba1\u7b97\u51fa\u56de\u5f52\u7ebf\uff0c\u8981\u9884\u6d4b\u5b66\u4e60 8 \u5c0f\u65f6\u7684\u5b66\u751f\u5c06\u83b7\u5f97\u7684\u6210\u7ee9\uff0c\u53ea\u9700\u5c06\u8be5\u503c\u4ee3\u5165\u6240\u83b7\u5f97\u7684\u56de\u5f52\u7ebf\u65b9\u7a0b\u5373\u53ef\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-d1ef36c064448262d7c58b7f51b215c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=2,0294+0,4412\\cdot 8=5,56\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"239\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u6839\u636e\u6240\u8fdb\u884c\u7684\u7ebf\u6027\u56de\u5f52\u6a21\u578b\uff0c\u5982\u679c\u4e00\u4e2a\u5b66\u751f\u5b66\u4e60\u4e86\u516b\u4e2a\u5c0f\u65f6\uff0c\u4ed6\u7684\u8003\u8bd5\u6210\u7ee9\u5c06\u4e3a5.56\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfpara-que-sirve-una-recta-de-regresion\"><\/span>\u56de\u5f52\u7ebf\u6709\u4ec0\u4e48\u7528\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u56de\u5f52\u7ebf\u4e3b\u8981\u6709\u4e24\u4e2a\u7528\u9014\uff1a\u56de\u5f52\u7ebf\u7528\u4e8e\u786e\u5b9a\u4e24\u4e2a\u53d8\u91cf\u4e4b\u95f4\u5b58\u5728\u4ec0\u4e48\u7c7b\u578b\u7684\u5173\u7cfb\uff0c\u53e6\u4e00\u65b9\u9762\uff0c\u56de\u5f52\u7ebf\u8fd8\u5141\u8bb8\u60a8\u5bf9\u65b0\u89c2\u5bdf\u503c\u8fdb\u884c\u9884\u6d4b\u3002<\/p>\n<p>\u56de\u5f52\u7ebf\u7684\u659c\u7387\u544a\u8bc9\u6211\u4eec\u81ea\u53d8\u91cf\u548c\u56e0\u53d8\u91cf\u4e4b\u95f4\u7684<a 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