{"id":433,"date":"2023-07-29T23:15:25","date_gmt":"2023-07-29T23:15:25","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e7%9a%ae%e5%b0%94%e9%80%8a%e7%9b%b8%e5%85%b3%e7%b3%bb%e6%95%b0\/"},"modified":"2023-07-29T23:15:25","modified_gmt":"2023-07-29T23:15:25","slug":"%e7%9a%ae%e5%b0%94%e9%80%8a%e7%9b%b8%e5%85%b3%e7%b3%bb%e6%95%b0","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e7%9a%ae%e5%b0%94%e9%80%8a%e7%9b%b8%e5%85%b3%e7%b3%bb%e6%95%b0\/","title":{"rendered":"\u76ae\u5c14\u900a\u76f8\u5173\u7cfb\u6570"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>Pearson \u76f8\u5173\u7cfb\u6570<\/strong>\uff08\u4e5f\u79f0\u4e3a\u201c\u4e58\u79ef\u77e9\u76f8\u5173\u7cfb\u6570\u201d\uff09\u662f\u4e24\u4e2a\u53d8\u91cf<em>X<\/em>\u548c<em>Y<\/em>\u4e4b\u95f4\u7ebf\u6027\u5173\u8054\u7684\u5ea6\u91cf\u3002\u5b83\u7684\u503c\u4ecb\u4e8e -1 \u548c 1 \u4e4b\u95f4\uff0c\u5176\u4e2d\uff1a<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">-1 \u8868\u793a\u4e24\u4e2a\u53d8\u91cf\u4e4b\u95f4\u5b8c\u5168\u8d1f\u7ebf\u6027\u76f8\u5173<\/span><\/li>\n<li><span style=\"color: #000000;\">0 \u8868\u793a\u4e24\u4e2a\u53d8\u91cf\u4e4b\u95f4\u4e0d\u5b58\u5728\u7ebf\u6027\u76f8\u5173<\/span><\/li>\n<li><span style=\"color: #000000;\">1 \u8868\u793a\u4e24\u4e2a\u53d8\u91cf\u4e4b\u95f4\u5b58\u5728\u5b8c\u5168\u6b63\u7ebf\u6027\u76f8\u5173<\/span><\/li>\n<\/ul>\n<h2><strong><span style=\"color: #000000;\">\u6c42\u76ae\u5c14\u900a\u76f8\u5173\u7cfb\u6570\u7684\u516c\u5f0f<\/span><\/strong><\/h2>\n<p><span style=\"color: #000000;\">\u7528\u4e8e\u67e5\u627e\u6570\u636e\u6837\u672c\u7684\u76ae\u5c14\u900a\u76f8\u5173\u7cfb\u6570\uff08\u8868\u793a\u4e3a<em>r<\/em> \uff09\u7684\u516c\u5f0f\u4e3a\uff08 <a href=\"https:\/\/en.wikipedia.org\/wiki\/Pearson_correlation_coefficient\" target=\"_blank\" rel=\"noopener\">\u6765\u81ea\u7ef4\u57fa\u767e\u79d1<\/a>\uff09\uff1a<\/span><\/p>\n<p><span style=\"color: #000000;\">\u60a8\u53ef\u80fd\u6c38\u8fdc\u4e0d\u9700\u8981\u624b\u52a8\u8ba1\u7b97\u8fd9\u4e2a\u516c\u5f0f\uff0c\u56e0\u4e3a\u60a8\u53ef\u4ee5\u4f7f\u7528\u8f6f\u4ef6\u6765\u8ba1\u7b97\u8fd9\u4e2a\u516c\u5f0f\uff0c\u4f46\u662f\u901a\u8fc7\u793a\u4f8b\u6765\u4e86\u89e3\u8fd9\u4e2a\u516c\u5f0f\u7684\u786e\u5207\u4f5c\u7528\u662f\u6709\u5e2e\u52a9\u7684\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u5047\u8bbe\u6211\u4eec\u6709\u4ee5\u4e0b\u6570\u636e\u96c6\uff1a<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-4985 size-full\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/correlationexemple.jpg\" alt=\"\" width=\"135\" height=\"154\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p><span style=\"color: #000000;\">\u5982\u679c\u6211\u4eec\u5c06\u8fd9\u4e9b\u5bf9 (X, Y) \u7ed8\u5236\u5728\u6563\u70b9\u56fe\u4e0a\uff0c\u5b83\u5c06\u5982\u4e0b\u6240\u793a\uff1a<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-1532 size-full\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/correl1-1.jpg\" alt=\"\u6563\u70b9\u56fe\u4e0a\u7684 Pearson \u76f8\u5173\u6027\u793a\u4f8b\" width=\"455\" height=\"362\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p><span style=\"color: #000000;\">\u53ea\u9700\u67e5\u770b\u8be5\u6563\u70b9\u56fe\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u770b\u5230\u53d8\u91cf X \u548c Y \u4e4b\u95f4\u5b58\u5728\u6b63\u76f8\u5173\u5173\u7cfb\uff1a\u968f\u7740 X \u7684\u589e\u52a0\uff0cY \u4e5f\u8d8b\u4e8e\u589e\u52a0\u3002<\/span><span style=\"color: #000000;\">\u4f46\u4e3a\u4e86\u51c6\u786e\u91cf\u5316\u8fd9\u4e24\u4e2a\u53d8\u91cf\u7684\u6b63\u76f8\u5173\u7a0b\u5ea6\uff0c\u6211\u4eec\u9700\u8981\u627e\u5230\u76ae\u5c14\u900a\u76f8\u5173\u7cfb\u6570\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u6211\u4eec\u53ea\u5173\u6ce8\u516c\u5f0f\u7684\u5206\u5b50\uff1a<\/span><\/p>\n<p><span style=\"color: #000000;\">\u5bf9\u4e8e\u6570\u636e\u96c6\u4e2d\u7684\u6bcf\u4e00\u5bf9 (X, Y)\uff0c\u6211\u4eec\u9700\u8981\u627e\u5230 x \u503c\u4e0e\u5e73\u5747 x \u503c\u4e4b\u95f4\u7684\u5dee\u503c\u3001y \u503c\u4e0e\u5e73\u5747 y \u503c\u4e4b\u95f4\u7684\u5dee\u503c\uff0c\u7136\u540e\u5c06\u8fd9\u4e24\u4e2a\u6570\u5b57\u76f8\u4e58\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4f8b\u5982\uff0c\u6211\u4eec\u7684\u7b2c\u4e00\u5bf9 (X, Y) \u662f (2, 2)\u3002\u8be5\u6570\u636e\u96c6\u4e2d x \u7684\u5e73\u5747\u503c\u4e3a 5\uff0c\u8be5\u6570\u636e\u96c6\u4e2d y \u7684\u5e73\u5747\u503c\u4e3a 7\u3002\u56e0\u6b64\u8be5\u5bf9\u7684 x \u503c\u4e0e x \u7684\u5e73\u5747\u503c\u4e4b\u5dee\u4e3a 2 \u2013 5 = -3\u3002\u8be5\u5bf9\u7684 y \u503c\u4e0e\u5e73\u5747 y \u503c\u4e4b\u5dee\u4e3a 2 \u2013 7 = -5\u3002\u7136\u540e\uff0c\u5f53\u6211\u4eec\u5c06\u8fd9\u4e24\u4e2a\u6570\u5b57\u76f8\u4e58\u65f6\uff0c\u6211\u4eec\u5f97\u5230 -3 * -5 = 15\u3002<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-1528 size-full\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/correl3.jpg\" alt=\"\u624b\u52a8\u76ae\u5c14\u900a\u76f8\u5173\u7cfb\u6570\" width=\"409\" height=\"157\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p><span style=\"color: #000000;\">\u8fd9\u662f\u6211\u4eec\u521a\u521a\u6240\u505a\u7684\u76f4\u89c2\u6982\u8ff0\uff1a<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-1533 size-full\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/correl3-1.jpg\" alt=\"\u76ae\u5c14\u900a\u76f8\u5173\u793a\u4f8b\" width=\"457\" height=\"356\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p><span style=\"color: #000000;\">\u7136\u540e\u5bf9\u6bcf\u4e00\u5bf9\u6267\u884c\u4ee5\u4e0b\u64cd\u4f5c\uff1a<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-1534 size-full\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/correl5.jpg\" alt=\"\u76ae\u5c14\u900a\u76f8\u5173\u793a\u4f8b\" width=\"414\" height=\"156\" srcset=\"\" sizes=\"auto, \"><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-1535 size-full\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/correl6.jpg\" alt=\"\u6563\u70b9\u56fe\u4e0a\u7684 Pearson \u76f8\u5173\u6027\u793a\u4f8b\" width=\"447\" height=\"352\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p><span style=\"color: #000000;\">\u83b7\u53d6\u516c\u5f0f\u5206\u5b50\u7684\u6700\u540e\u4e00\u6b65\u662f\u5c06\u6240\u6709\u8fd9\u4e9b\u503c\u7b80\u5355\u5730\u6dfb\u52a0\u5728\u4e00\u8d77\uff1a<\/span><\/p>\n<p style=\"text-align: center;\"> <span style=\"color: #000000;\">15 + 3 +3 + 15 = <strong>36<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u7136\u540e\u516c\u5f0f\u7684\u5206\u6bcd\u544a\u8bc9\u6211\u4eec\u627e\u5230 x \u548c y \u7684\u6240\u6709\u5e73\u65b9\u5dee\u4e4b\u548c\uff0c\u7136\u540e\u5c06\u8fd9\u4e24\u4e2a\u6570\u5b57\u76f8\u4e58\uff0c\u7136\u540e\u53d6\u5e73\u65b9\u6839\uff1a<\/span><\/p>\n<p><span style=\"color: #000000;\">\u9996\u5148\u6211\u4eec\u8981\u6c42 x \u548c y \u4e4b\u5dee\u7684\u5e73\u65b9\u548c\uff1a<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-1537 size-full\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/correl7.jpg\" alt=\"\" width=\"529\" height=\"137\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p><span style=\"color: #000000;\">\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u5c06\u8fd9\u4e24\u4e2a\u6570\u5b57\u76f8\u4e58\uff1a20 * 68 = 1,360\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u6700\u540e\uff0c\u6211\u4eec\u6c42\u5e73\u65b9\u6839\uff1a\u221a <span style=\"text-decoration: overline;\">1,360<\/span> = <strong>36.88<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u6240\u4ee5\u6211\u4eec\u53d1\u73b0\u516c\u5f0f\u7684\u5206\u5b50\u662f36\uff0c\u5206\u6bcd\u662f36.88\u3002\u8fd9\u610f\u5473\u7740\u6211\u4eec\u7684\u76ae\u5c14\u900a\u76f8\u5173\u7cfb\u6570\u4e3a r = 36 \/ 36.88 = <strong>0.976<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u8fd9\u4e2a\u6570\u5b57\u63a5\u8fd1 1\uff0c\u8868\u660e\u6211\u4eec\u7684\u53d8\u91cf<em>X<\/em>\u548c<em>Y<\/em>\u4e4b\u95f4\u5b58\u5728\u5f88\u5f3a\u7684\u6b63\u7ebf\u6027\u5173\u7cfb\u3002\u8fd9\u8bc1\u5b9e\u4e86\u6211\u4eec\u5728\u6563\u70b9\u56fe\u4e2d\u89c2\u5bdf\u5230\u7684\u5173\u7cfb\u3002<\/span><\/p>\n<h2><strong><span style=\"color: #000000;\">\u67e5\u770b\u76f8\u5173\u6027<\/span><\/strong><\/h2>\n<p><span style=\"color: #000000;\">\u8bf7\u8bb0\u4f4f\uff0c\u76ae\u5c14\u900a\u76f8\u5173\u7cfb\u6570\u544a\u8bc9\u6211\u4eec\u4e24\u4e2a\u53d8\u91cf\u4e4b\u95f4\u7684\u7ebf\u6027\u5173\u7cfb<strong>\u7c7b\u578b<\/strong>\uff08\u6b63\u3001\u8d1f\u3001\u65e0\uff09\u4ee5\u53ca\u8fd9\u79cd\u5173\u7cfb\u7684<strong>\u5f3a\u5ea6<\/strong>\uff08\u5f31\u3001\u4e2d\u7b49\u3001\u5f3a\uff09\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u5f53\u6211\u4eec\u521b\u5efa\u4e24\u4e2a\u53d8\u91cf\u7684\u6563\u70b9\u56fe\u65f6\uff0c\u6211\u4eec\u53ef\u4ee5<em>\u770b\u5230<\/em>\u4e24\u4e2a\u53d8\u91cf\u4e4b\u95f4\u7684\u771f\u5b9e\u5173\u7cfb\u3002\u4ee5\u4e0b\u662f\u6211\u4eec\u53ef\u80fd\u89c2\u5bdf\u5230\u7684\u591a\u79cd\u7c7b\u578b\u7684\u7ebf\u6027\u5173\u7cfb\uff1a<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>\u5f3a\u6b63\u76f8\u5173\u5173\u7cfb\uff1a<\/strong>\u968f\u7740 x \u8f74\u4e0a\u7684\u53d8\u91cf\u589e\u52a0\uff0cy \u8f74\u4e0a\u7684\u53d8\u91cf\u4e5f\u4f1a\u589e\u52a0\u3002\u8fd9\u4e9b\u70b9\u7d27\u5bc6\u805a\u96c6\uff0c\u8868\u660e\u5b58\u5728\u5f88\u5f3a\u7684\u5173\u7cfb\u3002<\/span> <span style=\"color: #000000;\"><img decoding=\"async\" loading=\"lazy\" class=\"wp-image-616 size-full aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/pos_strong.jpg\" alt=\"\" width=\"323\" height=\"301\" srcset=\"\" sizes=\"auto, \"><\/span><\/p>\n<p style=\"text-align: center;\"><span style=\"color: #000000;\">\u76ae\u5c14\u900a\u76f8\u5173\u7cfb\u6570\uff1a <strong>0.94<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>\u5f31\u6b63\u5173\u7cfb\uff1a<\/strong>\u968f\u7740 x \u8f74\u4e0a\u7684\u53d8\u91cf\u589e\u52a0\uff0cy \u8f74\u4e0a\u7684\u53d8\u91cf\u4e5f\u4f1a\u589e\u52a0\u3002\u8fd9\u4e9b\u70b9\u76f8\u5f53\u5206\u6563\uff0c\u8868\u660e\u5173\u7cfb\u8f83\u5f31\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\"><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-618 size-full\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/pos_faible.jpg\" alt=\"\" width=\"323\" height=\"297\" srcset=\"\" sizes=\"auto, \"><\/span><\/p>\n<p style=\"text-align: center;\"><span style=\"color: #000000;\">\u76ae\u5c14\u900a\u76f8\u5173\u7cfb\u6570\uff1a <strong>0.44<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>\u65e0\u5173\u7cfb\uff1a<\/strong>\u53d8\u91cf\u4e4b\u95f4\u6ca1\u6709\u660e\u786e\u7684\u5173\u7cfb\uff08\u6b63\u6216\u8d1f\uff09\u3002<\/span> <\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" loading=\"lazy\" class=\"wp-image-621 size-full aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/aucun.jpg\" alt=\"\" width=\"324\" height=\"296\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p style=\"text-align: center;\"><span style=\"color: #000000;\">\u76ae\u5c14\u900a\u76f8\u5173\u7cfb\u6570\uff1a <strong>0.03<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>\u5f3a\u8d1f\u5173\u7cfb\uff1a<\/strong>\u968f\u7740 x \u8f74\u4e0a\u7684\u53d8\u91cf\u589e\u52a0\uff0cy \u8f74\u4e0a\u7684\u53d8\u91cf\u51cf\u5c11\u3002\u8fd9\u4e9b\u70b9\u7d27\u5bc6\u5730\u5806\u79ef\u5728\u4e00\u8d77\uff0c\u8868\u660e\u5b58\u5728\u5f88\u5f3a\u7684\u5173\u7cfb\u3002<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-622 size-full\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/neg_strong.jpg\" alt=\"\" width=\"321\" height=\"297\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p style=\"text-align: center;\"><span style=\"color: #000000;\">\u76ae\u5c14\u900a\u76f8\u5173\u7cfb\u6570\uff1a <strong>-0.87<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>\u5f31\u8d1f\u5173\u7cfb\uff1a<\/strong>\u968f\u7740 x \u8f74\u4e0a\u7684\u53d8\u91cf\u589e\u52a0\uff0cy \u8f74\u4e0a\u7684\u53d8\u91cf\u51cf\u5c11\u3002\u8fd9\u4e9b\u70b9\u76f8\u5f53\u5206\u6563\uff0c\u8868\u660e\u5173\u7cfb\u8f83\u5f31\u3002<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-625 size-full\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/negatif_faible.jpg\" alt=\"\" width=\"324\" height=\"296\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p style=\"text-align: center;\"><span style=\"color: #000000;\">\u76ae\u5c14\u900a\u76f8\u5173\u7cfb\u6570\uff1a \u2013 <strong>0.46<\/strong><\/span><\/p>\n<h2><strong>\u6d4b\u8bd5 Pearson \u76f8\u5173\u7cfb\u6570\u7684\u663e\u7740\u6027<\/strong><\/h2>\n<p><span style=\"color: #000000;\">\u5f53\u6211\u4eec\u627e\u5230\u4e00\u7ec4\u6570\u636e\u7684\u76ae\u5c14\u900a\u76f8\u5173\u7cfb\u6570\u65f6\uff0c\u6211\u4eec\u901a\u5e38\u4f1a\u4f7f\u7528\u6765\u81ea\u8f83\u5927<em>\u603b\u4f53<\/em>\u7684\u6570\u636e<em>\u6837\u672c<\/em>\u3002\u8fd9\u610f\u5473\u7740\u5373\u4f7f\u4e24\u4e2a\u53d8\u91cf\u5728\u603b\u4f53\u4e2d\u5b9e\u9645\u4e0a\u4e0d\u76f8\u5173\uff0c\u4e5f\u53ef\u4ee5\u627e\u5230\u4e24\u4e2a\u53d8\u91cf\u7684\u975e\u96f6\u76f8\u5173\u6027\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4f8b\u5982\uff0c\u5047\u8bbe\u6211\u4eec\u4e3a\u6574\u4e2a\u603b\u4f53\u4e2d\u6bcf\u4e2a\u6570\u636e\u70b9\u7684\u53d8\u91cf<em>X<\/em>\u548c<em>Y<\/em>\u521b\u5efa\u4e00\u4e2a\u6563\u70b9\u56fe\uff0c\u5982\u4e0b\u6240\u793a\uff1a<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-1543 size-full\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/correl12.jpg\" alt=\"\u96f6\u76f8\u5173\u793a\u4f8b\" width=\"466\" height=\"251\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p><span style=\"color: #000000;\">\u5f88\u660e\u663e\uff0c\u8fd9\u4e24\u4e2a\u53d8\u91cf\u4e0d\u76f8\u5173\u3002\u7136\u800c\uff0c\u5f53\u6211\u4eec\u4ece\u603b\u4f53\u4e2d\u62bd\u53d6 10 \u4e2a\u70b9\u7684\u6837\u672c\u65f6\uff0c\u6211\u4eec\u53ef\u80fd\u4f1a\u9009\u62e9\u4ee5\u4e0b\u70b9\uff1a<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-1544 size-full\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/correl13.jpg\" alt=\"\u76f8\u5173\u6027\u793a\u4f8b\" width=\"460\" height=\"244\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p><span style=\"color: #000000;\">\u6211\u4eec\u53ef\u4ee5\u770b\u5230\uff0c\u8be5\u70b9\u6837\u672c\u7684 Pearson \u76f8\u5173\u7cfb\u6570\u4e3a 0.93\uff0c\u8868\u660e\u5c3d\u7ba1\u603b\u4f53\u76f8\u5173\u6027\u4e3a\u96f6\uff0c\u4f46\u4ecd\u5b58\u5728\u5f88\u5f3a\u7684\u6b63\u76f8\u5173\u6027\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4e3a\u4e86\u68c0\u9a8c\u4e24\u4e2a\u53d8\u91cf\u4e4b\u95f4\u7684\u76f8\u5173\u6027\u662f\u5426\u5177\u6709\u7edf\u8ba1\u663e\u7740\u6027\uff0c\u6211\u4eec\u53ef\u4ee5\u627e\u5230\u4ee5\u4e0b\u68c0\u9a8c\u7edf\u8ba1\u91cf\uff1a<\/span><\/p>\n<p><span style=\"color: #000000;\">\u68c0\u9a8c\u7edf\u8ba1\u91cf T = r * \u221a <span style=\"text-decoration: overline;\">(n-2) \/ (1-r <sup>2<\/sup> )<\/span><\/span><\/p>\n<p><span style=\"color: #000000;\">\u5176\u4e2d<em>n<\/em>\u662f\u6837\u672c\u4e2d\u7684\u5bf9\u6570\uff0c <em>r<\/em>\u662f Pearson \u76f8\u5173\u7cfb\u6570\uff0cT \u68c0\u9a8c\u7edf\u8ba1\u91cf\u9075\u5faa n-2 \u81ea\u7531\u5ea6\u7684\u5206\u5e03\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u8ba9\u6211\u4eec\u56de\u987e\u4e00\u4e0b\u5982\u4f55\u6d4b\u8bd5 Pearson \u76f8\u5173\u7cfb\u6570\u7684\u663e\u7740\u6027\u7684\u793a\u4f8b\u3002<\/span><\/p>\n<h3><strong><span style=\"color: #000000;\">\u4f8b\u5b50<\/span><\/strong><\/h3>\n<p><span style=\"color: #000000;\">\u4ee5\u4e0b\u6570\u636e\u96c6\u663e\u793a\u4e86 12 \u4e2a\u4eba\u7684\u8eab\u9ad8\u548c\u4f53\u91cd\uff1a<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-4986 size-full\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/correlationexemple2.jpg\" alt=\"\" width=\"193\" height=\"266\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p><span style=\"color: #000000;\">\u4e0b\u9762\u7684\u6563\u70b9\u56fe\u663e\u793a\u4e86\u8fd9\u4e24\u4e2a\u53d8\u91cf\u7684\u503c\uff1a<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-1547 size-full\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/correl15.jpg\" alt=\"\u76f8\u5173\u6563\u70b9\u56fe\" width=\"461\" height=\"335\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p><span style=\"color: #000000;\">\u8fd9\u4e24\u4e2a\u53d8\u91cf\u7684 Pearson \u76f8\u5173\u7cfb\u6570\u4e3a r = 0.836\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u68c0\u9a8c\u7edf\u8ba1\u91cf T = 0.836 * \u221a <span style=\"text-decoration: overline;\"><span style=\"color: #000000; text-decoration: overline;\">(12<\/span> -2) \/ (1-0.836 <sup>2<\/sup> )<\/span> = 4.804\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u6839\u636e\u6211\u4eec\u7684<a href=\"https:\/\/statorials.org\/cn\/\u7edf\u8ba1\u5b66\u4ee5\u7b80\u5355\u76f4\u63a5\u7684\u65b9\u5f0f\u89e3\u91ca\u6982\u5ff5\uff0c\u6211\u4eec\u4f7f\u5b66\u4e60\u7edf\u8ba1\u53d8\u5f97\u66f4\u5bb9\u6613\/\" target=\"_blank\" rel=\"noopener\">t \u5206\u5e03\u8ba1\u7b97\u5668<\/a>\uff0c\u81ea\u7531\u5ea6\u4e3a 10 \u7684\u5206\u6570 4.804 \u7684 p \u503c\u4e3a 0.0007\u3002\u7531\u4e8e 0.0007 &lt; 0.05\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u51fa\u7ed3\u8bba\uff0c\u672c\u4f8b\u4e2d\u4f53\u91cd\u548c\u8eab\u9ad8\u4e4b\u95f4\u7684\u76f8\u5173\u6027\u5728 alpha = 0.05 \u65f6\u5177\u6709\u7edf\u8ba1\u663e\u7740\u6027\u3002<\/span><\/p>\n<h2><strong><span style=\"color: #000000;\">\u9632\u8303\u63aa\u65bd<\/span><\/strong><\/h2>\n<p><span style=\"color: #000000;\">\u5c3d\u7ba1\u76ae\u5c14\u900a\u76f8\u5173\u7cfb\u6570\u53ef\u7528\u4e8e\u544a\u8bc9\u6211\u4eec\u4e24\u4e2a\u53d8\u91cf\u662f\u5426\u5177\u6709\u7ebf\u6027\u5173\u8054\uff0c\u4f46\u5728\u89e3\u91ca\u76ae\u5c14\u900a\u76f8\u5173\u7cfb\u6570\u65f6\uff0c\u6211\u4eec\u9700\u8981\u8bb0\u4f4f\u4e09\u4ef6\u4e8b\uff1a<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1.\u76f8\u5173\u6027\u5e76\u4e0d\u610f\u5473\u7740\u56e0\u679c\u5173\u7cfb\u3002<\/strong>\u5e76\u4e0d\u662f\u56e0\u4e3a\u4e24\u4e2a\u53d8\u91cf\u76f8\u5173\uff0c\u5176\u4e2d\u4e00\u4e2a\u53d8\u91cf\u5fc5\u7136\u4f1a<em>\u5bfc\u81f4<\/em>\u53e6\u4e00\u4e2a\u53d8\u91cf\u51fa\u73b0\u7684\u9891\u7387\u589e\u52a0\u6216\u51cf\u5c11\u3002\u4e00\u4e2a\u5178\u578b\u7684\u4f8b\u5b50\u662f\u51b0\u6dc7\u6dcb\u9500\u552e\u4e0e\u9ca8\u9c7c\u88ad\u51fb\u4e4b\u95f4\u7684\u6b63\u76f8\u5173\u5173\u7cfb\u3002\u5f53\u51b0\u6dc7\u6dcb\u9500\u91cf\u5728\u4e00\u5e74\u4e2d\u7684\u67d0\u4e9b\u65f6\u5019\u589e\u52a0\u65f6\uff0c\u9ca8\u9c7c\u88ad\u51fb\u4e8b\u4ef6\u4e5f\u5f80\u5f80\u4f1a\u589e\u52a0\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u8fd9\u662f\u5426\u610f\u5473\u7740\u5403\u51b0\u6dc7\u6dcb<em>\u4f1a\u5bfc\u81f4<\/em>\u9ca8\u9c7c\u88ad\u51fb\uff1f\u5f53\u7136\u4e0d\u662f\uff01\u8fd9\u4ec5\u4ec5\u610f\u5473\u7740\u5728\u590f\u5929\uff0c\u51b0\u7684\u6d88\u8017\u548c\u9ca8\u9c7c\u88ad\u51fb\u5f80\u5f80\u4f1a\u589e\u52a0\uff0c\u56e0\u4e3a\u51b0\u5728\u590f\u5929\u66f4\u53d7\u6b22\u8fce\uff0c\u66f4\u591a\u7684\u4eba\u5728\u590f\u5929\u8fdb\u5165\u6d77\u6d0b\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>2. \u76f8\u5173\u6027\u5bf9\u5f02\u5e38\u503c\u5f88\u654f\u611f\u3002<\/strong>\u6781\u7aef\u5f02\u5e38\u503c\u53ef\u4ee5\u663e\u7740\u6539\u53d8\u76ae\u5c14\u900a\u76f8\u5173\u7cfb\u6570\u3002\u8003\u8651\u4e0b\u9762\u7684\u4f8b\u5b50\uff1a<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-1539 size-full\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/correl9.jpg\" alt=\"\u76f8\u5173\u5f02\u5e38\u503c\u793a\u4f8b\" width=\"454\" height=\"306\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p><span style=\"color: #000000;\">\u53d8\u91cf<em>X<\/em>\u548c<em>Y<\/em>\u7684 Pearson \u76f8\u5173\u7cfb\u6570\u4e3a<strong>0.00<\/strong> \u3002\u4f46\u60f3\u8c61\u4e00\u4e0b\u6570\u636e\u96c6\u4e2d\u6709\u4e00\u4e2a\u5f02\u5e38\u503c\uff1a<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-1540 size-full\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/correl10.jpg\" alt=\"\u76ae\u5c14\u900a\u76f8\u5173\u793a\u4f8b\" width=\"456\" height=\"305\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p><span style=\"color: #000000;\">\u7136\u800c\uff0c\u8fd9\u4e24\u4e2a\u53d8\u91cf\u7684 Pearson \u76f8\u5173\u7cfb\u6570\u4e3a<strong>0.878<\/strong> \u3002\u8fd9\u4e2a\u5f02\u5e38\u503c\u6539\u53d8\u4e86\u4e00\u5207\u3002\u8fd9\u5c31\u662f\u4e3a\u4ec0\u4e48\u5728\u8ba1\u7b97\u4e24\u4e2a\u53d8\u91cf\u7684\u76f8\u5173\u6027\u65f6\uff0c\u6700\u597d\u4f7f\u7528\u6563\u70b9\u56fe\u53ef\u89c6\u5316\u53d8\u91cf\u6765\u68c0\u67e5\u5f02\u5e38\u503c\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>3. Pearson \u76f8\u5173\u7cfb\u6570\u4e0d\u80fd\u6355\u6349\u4e24\u4e2a\u53d8\u91cf\u4e4b\u95f4\u7684\u975e\u7ebf\u6027\u5173\u7cfb\u3002<\/strong>\u5047\u8bbe\u6211\u4eec\u6709\u4e24\u4e2a\u5177\u6709\u4ee5\u4e0b\u5173\u7cfb\u7684\u53d8\u91cf\uff1a<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-1541 size-full\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/correl11.jpg\" alt=\"\u975e\u7ebf\u6027\u5173\u7cfb\u7684\u76f8\u5173\u6027\" width=\"448\" height=\"307\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p><span style=\"color: #000000;\">\u8fd9\u4e24\u4e2a\u53d8\u91cf\u7684 Pearson \u76f8\u5173\u7cfb\u6570\u4e3a 0.00\uff0c\u56e0\u4e3a\u5b83\u4eec\u4e0d\u5177\u6709\u7ebf\u6027\u5173\u7cfb\u3002\u7136\u800c\uff0c\u8fd9\u4e24\u4e2a\u53d8\u91cf\u5177\u6709\u975e\u7ebf\u6027\u5173\u7cfb\uff1ay \u503c\u53ea\u662f x \u503c\u7684\u5e73\u65b9\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4f7f\u7528\u76ae\u5c14\u900a\u76f8\u5173\u7cfb\u6570\u65f6\uff0c\u8bf7\u8bb0\u4f4f\u60a8\u53ea\u662f\u6d4b\u8bd5\u4e24\u4e2a\u53d8\u91cf\u662f\u5426<em>\u7ebf\u6027<\/em>\u76f8\u5173\u3002\u5373\u4f7f\u76ae\u5c14\u900a\u76f8\u5173\u7cfb\u6570\u544a\u8bc9\u6211\u4eec\u4e24\u4e2a\u53d8\u91cf\u4e0d\u76f8\u5173\uff0c\u5b83\u4eec\u4ecd\u7136\u53ef\u80fd\u5177\u6709\u67d0\u79cd\u7c7b\u578b\u7684\u975e\u7ebf\u6027\u5173\u7cfb\u3002\u8fd9\u662f\u5728\u5206\u6790\u4e24\u4e2a\u53d8\u91cf\u4e4b\u95f4\u7684\u5173\u7cfb\u65f6\u521b\u5efa\u6563\u70b9\u56fe\u5f88\u6709\u7528\u7684\u53e6\u4e00\u4e2a\u539f\u56e0\uff1a\u5b83\u53ef\u4ee5\u5e2e\u52a9\u60a8\u68c0\u6d4b\u975e\u7ebf\u6027\u5173\u7cfb\u3002<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Pearson \u76f8\u5173\u7cfb\u6570\uff08\u4e5f\u79f0\u4e3a\u201c\u4e58\u79ef\u77e9\u76f8\u5173\u7cfb\u6570\u201d\uff09\u662f\u4e24\u4e2a\u53d8\u91cfX\u548cY\u4e4b\u95f4\u7ebf\u6027\u5173\u8054\u7684\u5ea6\u91cf\u3002\u5b83\u7684\u503c\u4ecb\u4e8e -1 \u548c  [&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-433","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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