{"id":306,"date":"2023-08-02T19:28:35","date_gmt":"2023-08-02T19:28:35","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e6%9c%80%e5%b0%8f%e4%ba%8c%e4%b9%98%e6%b3%95\/"},"modified":"2023-08-02T19:28:35","modified_gmt":"2023-08-02T19:28:35","slug":"%e6%9c%80%e5%b0%8f%e4%ba%8c%e4%b9%98%e6%b3%95","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e6%9c%80%e5%b0%8f%e4%ba%8c%e4%b9%98%e6%b3%95\/","title":{"rendered":"\u4e0b\u65b9\u5757"},"content":{"rendered":"<p>\u672c\u6587\u89e3\u91ca\u4e86\u4ec0\u4e48\u662f\u7edf\u8ba1\u5b66\u4e2d\u7684\u6700\u5c0f\u4e8c\u4e58\u6cd5\u3001\u4ec0\u4e48\u662f\u6700\u5c0f\u4e8c\u4e58\u6cd5\u4ee5\u53ca\u5982\u4f55\u901a\u8fc7\u6700\u5c0f\u4e8c\u4e58\u51c6\u5219\u62df\u5408\u56de\u5f52\u6a21\u578b\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-el-metodo-de-los-minimos-cuadrados\"><\/span>\u4ec0\u4e48\u662f\u6700\u5c0f\u4e8c\u4e58\u6cd5\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u6700\u5c0f\u4e8c\u4e58\u6cd5<\/strong>\u662f\u4e00\u79cd\u7528\u4e8e\u786e\u5b9a\u56de\u5f52\u65b9\u7a0b\u7684\u7edf\u8ba1\u65b9\u6cd5\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u6700\u5c0f\u4e8c\u4e58\u6cd5\u662f\u56de\u5f52\u6a21\u578b\u4e2d\u4f7f\u7528\u7684\u51c6\u5219\uff0c\u7528\u4e8e\u6700\u5c0f\u5316\u8ba1\u7b97\u56de\u5f52\u65b9\u7a0b\u65f6\u83b7\u5f97\u7684\u8bef\u5dee\u3002<\/p>\n<p>\u5177\u4f53\u6765\u8bf4\uff0c\u6700\u5c0f\u4e8c\u4e58\u6cd5\u5305\u62ec\u6700\u5c0f\u5316\u6b8b\u5dee\u5e73\u65b9\u548c\uff0c\u6216\u8005\u6362\u53e5\u8bdd\u8bf4\uff0c\u5b83\u57fa\u4e8e\u6700\u5c0f\u5316\u56de\u5f52\u6a21\u578b\u9884\u6d4b\u503c\u4e0e\u89c2\u6d4b\u503c\u4e4b\u95f4\u7684\u5dee\u503c\u5e73\u65b9\u548c\u3002 \u3002 \u3002\u4e0b\u9762\u6211\u4eec\u5c06\u8be6\u7ec6\u4e86\u89e3\u5982\u4f55\u901a\u8fc7\u6700\u5c0f\u4e8c\u4e58\u51c6\u5219\u62df\u5408\u56de\u5f52\u6a21\u578b\u3002<\/p>\n<p>\u6700\u5c0f\u4e8c\u4e58\u6cd5\u7684\u4e3b\u8981\u7279\u70b9\u662f\u89c2\u6d4b\u503c\u4e0e\u56de\u5f52\u51fd\u6570\u4e4b\u95f4\u7684\u6700\u957f\u8ddd\u79bb\u88ab\u6700\u5c0f\u5316\u3002\u4e0e\u5176\u4ed6\u56de\u5f52\u6807\u51c6\u4e0d\u540c\uff0c\u6700\u5c0f\u4e8c\u4e58\u6cd5\u8ba4\u4e3a\u6700\u5c0f\u5316\u5927\u6b8b\u5dee\u6bd4\u6700\u5c0f\u5316\u5c0f\u6b8b\u5dee\u66f4\u91cd\u8981\uff0c\u56e0\u4e3a\u5927\u6570\u7684\u5e73\u65b9\u6bd4\u5c0f\u6570\u7684\u5e73\u65b9\u5927\u5f97\u591a\u3002\u6570\u5b57\u3002<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"error-de-estimacion\"><\/span>\u4f30\u8ba1\u8bef\u5dee<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e3a\u4e86\u5145\u5206\u7406\u89e3\u6700\u5c0f\u4e8c\u4e58\u7684\u6982\u5ff5\uff0c\u6211\u4eec\u9996\u5148\u5fc5\u987b\u660e\u786e\u56de\u5f52\u6a21\u578b\u4e2d\u7684\u6b8b\u5dee\u662f\u4ec0\u4e48\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5c06\u5728\u4e0b\u9762\u770b\u5230\u4ec0\u4e48\u662f\u4f30\u8ba1\u8bef\u5dee\u4ee5\u53ca\u5b83\u662f\u5982\u4f55\u8ba1\u7b97\u7684\u3002<\/p>\n<p>\u5728\u7edf\u8ba1\u5b66\u4e2d\uff0c<strong>\u4f30\u8ba1\u8bef\u5dee<\/strong>\u4e5f\u79f0\u4e3a<strong>\u6b8b\u5dee<\/strong>\uff0c\u662f\u771f\u5b9e\u503c\u4e0e\u56de\u5f52\u6a21\u578b\u62df\u5408\u503c\u4e4b\u95f4\u7684\u5dee\u5f02\u3002\u56e0\u6b64\uff0c\u7edf\u8ba1\u6b8b\u5dee\u8ba1\u7b97\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-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 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-550848dfdd05b5c6464d4e22fbf52486_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"e_i\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"13\" style=\"vertical-align: -3px;\"><\/p>\n<p>\u662f\u6570\u636e i \u7684\u6b8b\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-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\u771f\u5b9e\u4ef7\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-a990a8fe969bd365cba7899d3d1c4406_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\u6570\u636e i \u7684\u56de\u5f52\u6a21\u578b\u63d0\u4f9b\u7684\u503c\u3002<\/li>\n<\/ul>\n<p>\u56e0\u6b64\uff0c\u4e00\u6761\u6570\u636e\u7684\u6b8b\u5dee\u8d8a\u5927\uff0c\u56de\u5f52\u6a21\u578b\u5bf9\u8fd9\u6761\u6570\u636e\u7684\u9002\u5e94\u80fd\u529b\u5c31\u8d8a\u5dee\u3002\u56e0\u6b64\uff0c\u6b8b\u5dee\u8d8a\u5c0f\uff0c\u5176\u5b9e\u9645\u503c\u4e0e\u9884\u6d4b\u503c\u4e4b\u95f4\u7684\u8ddd\u79bb\u8d8a\u5c0f\u3002<\/p>\n<p>\u540c\u6837\uff0c\u5982\u679c\u4e00\u6761\u6570\u636e\u7684\u6b8b\u5dee\u4e3a\u6b63\uff0c\u5219\u610f\u5473\u7740\u56de\u5f52\u6a21\u578b\u9884\u6d4b\u7684\u503c\u4f4e\u4e8e\u771f\u5b9e\u503c\u3002\u5982\u679c\u6b8b\u5dee\u4e3a\u8d1f\uff0c\u5219\u8868\u793a\u9884\u6d4b\u503c\u5927\u4e8e\u5b9e\u9645\u503c\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"minimizar-los-cuadrados-de-los-errores\"><\/span>\u6700\u5c0f\u5316\u8bef\u5dee\u5e73\u65b9<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u73b0\u5728\u6211\u4eec\u77e5\u9053\u4e86\u7edf\u8ba1\u5b66\u4e2d\u7684\u6b8b\u5dee\u662f\u4ec0\u4e48\uff0c\u5c31\u66f4\u5bb9\u6613\u7406\u89e3\u5982\u4f55\u6700\u5c0f\u5316\u8bef\u5dee\u5e73\u65b9\u4e86\u3002<\/p>\n<p><strong>\u8bef\u5dee\u7684\u5e73\u65b9<\/strong>\u662f\u6b8b\u5dee\u7684\u5e73\u65b9\uff0c\u56e0\u6b64\u8bef\u5dee\u7684\u5e73\u65b9\u7b49\u4e8e\u771f\u5b9e\u503c\u4e0e\u56de\u5f52\u6a21\u578b\u62df\u5408\u7684\u503c\u7684 2 \u6b21\u65b9\u4e4b\u5dee\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-f16302b9c06981bd49aad51ca8924592_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"e_i^2=(y_i-\\widehat{y}_i)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"111\" style=\"vertical-align: -5px;\"><\/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-56f396eccc309c513ef34dc82f6fcd9b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"e_i^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"15\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u662f\u6570\u636e i \u7684\u6b8b\u5dee\u7684\u5e73\u65b9\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\u771f\u5b9e\u4ef7\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-a990a8fe969bd365cba7899d3d1c4406_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\u6570\u636e i \u7684\u56de\u5f52\u6a21\u578b\u63d0\u4f9b\u7684\u503c\u3002<\/li>\n<\/ul>\n<p>\u56e0\u6b64\uff0c\u6700\u5c0f\u4e8c\u4e58\u6cd5\u5305\u62ec<strong>\u901a\u8fc7\u6700\u5c0f\u5316\u8bef\u5dee\u5e73\u65b9\u548c<\/strong>\u6765\u521b\u5efa\u56de\u5f52\u6a21\u578b\u3002\u56e0\u6b64\uff0c\u6700\u5c0f\u4e8c\u4e58\u51c6\u5219\u57fa\u4e8e\u4ee5\u4e0b\u8868\u8fbe\u5f0f\u7684\u6700\u5c0f\u5316\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-0a82d4d723b77093b4d584609f372cd7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" \\begin{array}{l} [MIN] \\ \\displaystyle \\sum_{i=1}^ne_i^2\\\\[4ex][MIN] \\ \\displaystyle \\sum_{i=1}^n(y_i-\\widehat{y}_i)^2\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"116\" width=\"158\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u8fd9\u5c31\u662f\u6700\u5c0f\u4e8c\u4e58\u51c6\u5219\u4e5f\u79f0\u4e3a\u6700\u5c0f\u4e8c\u4e58\u51c6\u5219\u7684\u539f\u56e0\u3002<\/p>\n<p>\u6b63\u5982\u60a8\u5728\u524d\u9762\u7684\u516c\u5f0f\u4e2d\u6240\u770b\u5230\u7684\uff0c\u6700\u5c0f\u4e8c\u4e58\u51c6\u5219\u5bf9\u4e8e\u6700\u5c0f\u5316\u5927\u6b8b\u5dee\u6bd4\u6700\u5c0f\u5316\u5c0f\u6b8b\u5dee\u66f4\u91cd\u8981\u3002\u4f8b\u5982\uff0c\u5982\u679c\u4e00\u4e2a\u6b8b\u6570\u4e3a 3\uff0c\u53e6\u4e00\u4e2a\u6b8b\u6570\u4e3a 5\uff0c\u5219\u5b83\u4eec\u7684\u5e73\u65b9\u5206\u522b\u4e3a 9 \u548c 25\uff0c\u56e0\u6b64\u6700\u5c0f\u4e8c\u4e58\u51c6\u5219\u5c06\u4f18\u5148\u6700\u5c0f\u5316\u7b2c\u4e8c\u4e2a\u6b8b\u6570\uff0c\u7136\u540e\u518d\u6700\u5c0f\u5316\u7b2c\u4e00\u4e2a\u6b8b\u6570\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ajuste-por-minimos-cuadrados\"><\/span>\u6700\u5c0f\u4e8c\u4e58\u8c03\u6574<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u4f7f\u7528\u6700\u5c0f\u4e8c\u4e58\u51c6\u5219\u62df\u5408\u56de\u5f52\u6a21\u578b<\/strong>\u5305\u62ec\u5bfb\u627e\u6700\u5c0f\u5316\u6b8b\u5dee\u5e73\u65b9\u7684\u56de\u5f52\u6a21\u578b\u3002\u56e0\u6b64\uff0c\u4ece\u56de\u5f52\u6a21\u578b\u83b7\u5f97\u7684\u65b9\u7a0b\u5c06\u662f\u89c2\u6d4b\u503c\u4e0e\u62df\u5408\u503c\u4e4b\u95f4\u7684\u5dee\u5f02\u5e73\u65b9\u6700\u5c0f\u7684\u65b9\u7a0b\u3002<\/p>\n<p>\u8bf7\u6ce8\u610f\uff0c\u5728\u4ee5\u4e0b\u793a\u4f8b\u4e2d\uff0c\u521b\u5efa\u56de\u5f52\u6a21\u578b\u6709\u66f4\u591a\u6807\u51c6\uff0c\u5e76\u4e14\u6839\u636e\u6240\u9009\u6807\u51c6\u7684\u4e0d\u540c\uff0c\u56de\u5f52\u65b9\u7a0b\u4e5f\u4e0d\u540c\u3002 <\/p>\n<figure class=\"wp-block-image aligncenter size-full\"><img decoding=\"async\" loading=\"lazy\" width=\"650\" height=\"355\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/ajustement-par-les-moindres-carres.png\" alt=\"\u6700\u5c0f\u4e8c\u4e58\u6cd5\u3001\u6700\u5c0f\u4e8c\u4e58\u5e73\u5dee\" class=\"wp-image-6548\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p>\u6b63\u5982\u60a8\u5728\u524d\u9762\u7684\u793a\u4f8b\u4e2d\u6240\u770b\u5230\u7684\uff0c\u4ece\u540c\u4e00\u6570\u636e\u96c6\u7684\u7ebf\u6027\u56de\u5f52\u6a21\u578b\u83b7\u5f97\u7684\u7ebf\u53d6\u51b3\u4e8e\u6240\u9009\u7684\u6807\u51c6\u3002\u901a\u5e38\uff0c\u6700\u5c0f\u4e8c\u4e58\u51c6\u5219\u7528\u4e8e\u56de\u5f52\u6a21\u578b\u3002<\/p>\n<p>\u5728\u7edf\u8ba1\u5b66\u4e2d\uff0c\u6700\u5e7f\u6cdb\u4f7f\u7528\u7684\u56de\u5f52\u6a21\u578b\u662f\u7b80\u5355\u7ebf\u6027\u56de\u5f52\u6a21\u578b\uff0c\u5b83\u4f7f\u7528\u76f4\u7ebf\u6765\u8fd1\u4f3c\u81ea\u53d8\u91cf X \u548c\u56e0\u53d8\u91cf Y \u4e4b\u95f4\u7684\u5173\u7cfb\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>\u56e0\u6b64\uff0c\u5c06\u6570\u636e\u96c6\u62df\u5408\u5230\u7b80\u5355\u7ebf\u6027\u56de\u5f52\u6a21\u578b\u7684\u516c\u5f0f\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-f4582a02500f36499fc60647a4dd5869_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"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}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"190\" style=\"vertical-align: -49px;\"><\/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-369b22bafb2489dc46579d38f5ac6917_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b_0=\\overline{y}-b_1\\overline{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"96\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p>\u60a8\u53ef\u4ee5\u901a\u8fc7\u5355\u51fb\u4ee5\u4e0b\u94fe\u63a5\u67e5\u770b\u5982\u4f55\u4f7f\u7528\u6700\u5c0f\u4e8c\u4e58\u51c6\u5219\u8ba1\u7b97\u7b80\u5355\u7ebf\u6027\u56de\u5f52\u6a21\u578b\u7684\u793a\u4f8b\uff1a <\/p>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 20px; padding-left: 30px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span><strong>\u8bf7\u53c2\u9605\uff1a<\/strong><a 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