{"id":6174,"date":"2024-06-26T16:14:54","date_gmt":"2024-06-26T08:14:54","guid":{"rendered":"https:\/\/t.n-years.com\/?p=6174"},"modified":"2024-06-26T16:15:06","modified_gmt":"2024-06-26T08:15:06","slug":"%e7%bb%9f%e8%ae%a1%e5%ad%a6%ef%bc%9a%e5%8d%8f%e6%96%b9%e5%b7%ae","status":"publish","type":"post","link":"https:\/\/t.n-years.com\/?p=6174","title":{"rendered":"\u7edf\u8ba1\u5b66\uff1a\u534f\u65b9\u5dee"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">\u534f\u65b9\u5dee\uff08Covariance\uff09\u662f\u7528\u4e8e\u5ea6\u91cf\u4e24\u4e2a\u968f\u673a\u53d8\u91cf\u4e4b\u95f4\u5171\u540c\u53d8\u5316\u7684\u7edf\u8ba1\u91cf\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u534f\u65b9\u5dee\u53ef\u4ee5\u8868\u793a\u4e00\u4e2a\u53d8\u91cf\u53d8\u52a8\u65f6\uff0c\u53e6\u4e00\u4e2a\u53d8\u91cf\u7684\u53d8\u52a8\u65b9\u5411\uff08\u6b63\u5411\u6216\u53cd\u5411\uff09\u3002\u534f\u65b9\u5dee\u7684\u7b26\u53f7\u8868\u793a\u53d8\u91cf\u4e4b\u95f4\u7684\u5173\u7cfb\u65b9\u5411\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u6b63\u534f\u65b9\u5dee<\/strong>\uff1a\u5f53\u4e00\u4e2a\u53d8\u91cf\u589e\u52a0\u65f6\uff0c\u53e6\u4e00\u4e2a\u53d8\u91cf\u4e5f\u503e\u5411\u4e8e\u589e\u52a0\uff0c\u8bf4\u660e\u4e24\u8005\u5448\u6b63\u76f8\u5173\u5173\u7cfb\u3002<\/li>\n\n\n\n<li><strong>\u8d1f\u534f\u65b9\u5dee<\/strong>\uff1a\u5f53\u4e00\u4e2a\u53d8\u91cf\u589e\u52a0\u65f6\uff0c\u53e6\u4e00\u4e2a\u53d8\u91cf\u503e\u5411\u4e8e\u51cf\u5c11\uff0c\u8bf4\u660e\u4e24\u8005\u5448\u8d1f\u76f8\u5173\u5173\u7cfb\u3002<\/li>\n\n\n\n<li><strong>\u96f6\u534f\u65b9\u5dee<\/strong>\uff1a\u4e24\u8005\u4e4b\u95f4\u6ca1\u6709\u7ebf\u6027\u5173\u7cfb\u3002<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\u534f\u65b9\u5dee\u7684\u8ba1\u7b97\u516c\u5f0f<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u5bf9\u4e8e\u4e24\u4e2a\u968f\u673a\u53d8\u91cf (X) \u548c (Y)\uff0c\u5176\u534f\u65b9\u5dee\u5b9a\u4e49\u5982\u4e0b\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u603b\u4f53\u534f\u65b9\u5dee<\/strong>\uff1a<br>[<br>\\sigma_{XY} = \\frac{1}{N} \\sum_{i=1}^{N} (X_i - \\mu_X)(Y_i - \\mu_Y)<br>]<br>\u5176\u4e2d\uff1a<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( N ) \u662f\u603b\u4f53\u7684\u6570\u91cf\u3002<\/li>\n\n\n\n<li>( X_i ) \u548c ( Y_i ) \u662f\u7b2c ( i ) \u4e2a\u89c2\u6d4b\u503c\u3002<\/li>\n\n\n\n<li>( \\mu_X ) \u548c ( \\mu_Y ) \u5206\u522b\u662f ( X ) \u548c ( Y ) \u7684\u5747\u503c\u3002<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u6837\u672c\u534f\u65b9\u5dee<\/strong>\uff1a<br>[<br>s_{XY} = \\frac{1}{n-1} \\sum_{i=1}^{n} (X_i - \\bar{X})(Y_i - \\bar{Y})<br>]<br>\u5176\u4e2d\uff1a<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( n ) \u662f\u6837\u672c\u7684\u6570\u91cf\u3002<\/li>\n\n\n\n<li>( \\bar{X} ) \u548c ( \\bar{Y} ) \u5206\u522b\u662f ( X ) \u548c ( Y ) \u7684\u6837\u672c\u5747\u503c\u3002<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\u534f\u65b9\u5dee\u7684\u6027\u8d28<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u5355\u4f4d<\/strong>\uff1a\u534f\u65b9\u5dee\u7684\u5355\u4f4d\u662f\u4e24\u4e2a\u53d8\u91cf\u5355\u4f4d\u7684\u4e58\u79ef\uff0c\u56e0\u6b64\u5728\u89e3\u91ca\u65f6\u4e0d\u5982\u76f8\u5173\u7cfb\u6570\u76f4\u89c2\u3002<\/li>\n\n\n\n<li><strong>\u8303\u56f4<\/strong>\uff1a\u534f\u65b9\u5dee\u7684\u8303\u56f4\u4e0d\u662f\u56fa\u5b9a\u7684\uff0c\u6570\u503c\u53ef\u4ee5\u5f88\u5927\u6216\u5f88\u5c0f\uff0c\u8fd9\u53d6\u51b3\u4e8e\u53d8\u91cf\u7684\u5c3a\u5ea6\u3002<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\u793a\u4f8b\u8ba1\u7b97<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u5047\u8bbe\u6709\u5982\u4e0b\u4e24\u4e2a\u53d8\u91cf\u7684\u6837\u672c\u6570\u636e\uff1a<br>[ X = [1, 2, 3, 4, 5] ]<br>[ Y = [2, 4, 6, 8, 10] ]<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u8ba1\u7b97\u5747\u503c\uff1a<br>[<br>\\bar{X} = \\frac{1+2+3+4+5}{5} = 3<br>]<br>[<br>\\bar{Y} = \\frac{2+4+6+8+10}{5} = 6<br>]<\/li>\n\n\n\n<li>\u8ba1\u7b97\u534f\u65b9\u5dee\uff08\u6837\u672c\uff09\uff1a<br>[<br>s_{XY} = \\frac{1}{5-1} \\sum_{i=1}^{5} (X_i - \\bar{X})(Y_i - \\bar{Y})<br>]<br>[<br>s_{XY} = \\frac{1}{4} [(1-3)(2-6) + (2-3)(4-6) + (3-3)(6-6) + (4-3)(8-6) + (5-3)(10-6)]<br>]<br>[<br>s_{XY} = \\frac{1}{4} [(1-3)(2-6) + (2-3)(4-6) + (3-3)(6-6) + (4-3)(8-6) + (5-3)(10-6)]<br>]<br>[<br>s_{XY} = \\frac{1}{4} [(-2)(-4) + (-1)(-2) + 0 + 1 \\cdot 2 + 2 \\cdot 4]<br>]<br>[<br>s_{XY} = \\frac{1}{4} [8 + 2 + 0 + 2 + 8] = \\frac{1}{4} \\cdot 20 = 5<br>]<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">\u56e0\u6b64\uff0c\u8fd9\u4e24\u4e2a\u53d8\u91cf\u7684\u6837\u672c\u534f\u65b9\u5dee\u4e3a 5\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u534f\u65b9\u5dee\u77e9\u9635<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u5bf9\u4e8e\u591a\u7ef4\u6570\u636e\uff0c\u53ef\u4ee5\u8ba1\u7b97\u534f\u65b9\u5dee\u77e9\u9635\uff0c\u6bcf\u4e2a\u5143\u7d20\u8868\u793a\u4e00\u5bf9\u53d8\u91cf\u4e4b\u95f4\u7684\u534f\u65b9\u5dee\u3002\u4f8b\u5982\uff0c\u5bf9\u4e8e\u4e09\u4e2a\u53d8\u91cf ( X ), ( Y ), \u548c ( Z )\uff0c\u534f\u65b9\u5dee\u77e9\u9635\u5982\u4e0b\uff1a<br>[<br>\\Sigma =<br>\\begin{pmatrix}<br>\\sigma_{XX} &amp; \\sigma_{XY} &amp; \\sigma_{XZ} \\<br>\\sigma_{YX} &amp; \\sigma_{YY} &amp; \\sigma_{YZ} \\<br>\\sigma_{ZX} &amp; \\sigma_{ZY} &amp; \\sigma_{ZZ}<br>\\end{pmatrix}<br>]<br>\u5176\u4e2d\uff0c(\\sigma_{XY}) \u8868\u793a (X) \u548c (Y) \u7684\u534f\u65b9\u5dee\uff0c(\\sigma_{XX}) \u8868\u793a (X) \u7684\u65b9\u5dee\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u603b\u7ed3<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u534f\u65b9\u5dee\u7528\u4e8e\u8861\u91cf\u4e24\u4e2a\u53d8\u91cf\u4e4b\u95f4\u7684\u7ebf\u6027\u5173\u7cfb\u3002\u867d\u7136\u5b83\u63d0\u4f9b\u4e86\u53d8\u91cf\u95f4\u5173\u7cfb\u7684\u65b9\u5411\uff08\u6b63\u6216\u8d1f\uff09\uff0c\u4f46\u6570\u503c\u672c\u8eab\u4e0d\u76f4\u89c2\u3002\u4e3a\u4e86\u66f4\u76f4\u89c2\u5730\u7406\u89e3\u53d8\u91cf\u4e4b\u95f4\u7684\u5173\u7cfb\uff0c\u901a\u5e38\u4f1a\u8ba1\u7b97\u76f8\u5173\u7cfb\u6570\uff0c\u5176\u4e3a\u534f\u65b9\u5dee\u6807\u51c6\u5316\u540e\u7684\u503c\uff0c\u8303\u56f4\u5728 -1 \u5230 1 \u4e4b\u95f4\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u534f\u65b9\u5dee\uff08Covariance\uff09\u662f\u7528\u4e8e\u5ea6\u91cf\u4e24\u4e2a\u968f\u673a\u53d8\u91cf\u4e4b\u95f4\u5171\u540c\u53d8\u5316\u7684\u7edf\u8ba1\u91cf\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u534f\u65b9\u5dee\u53ef\u4ee5\u8868\u793a\u4e00\u4e2a\u53d8\u91cf\u53d8\u52a8&#8230; <\/p>\n<div class=\"read-more navbutton\"><a href=\"https:\/\/t.n-years.com\/?p=6174\">\u9605\u8bfb\u66f4\u591a<i class=\"fa fa-angle-double-right\"><\/i><\/a><\/div>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[82],"class_list":["post-6174","post","type-post","status-publish","format-standard","hentry","category-5","tag-82"],"_links":{"self":[{"href":"https:\/\/t.n-years.com\/index.php?rest_route=\/wp\/v2\/posts\/6174","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/t.n-years.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/t.n-years.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/t.n-years.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/t.n-years.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=6174"}],"version-history":[{"count":1,"href":"https:\/\/t.n-years.com\/index.php?rest_route=\/wp\/v2\/posts\/6174\/revisions"}],"predecessor-version":[{"id":6175,"href":"https:\/\/t.n-years.com\/index.php?rest_route=\/wp\/v2\/posts\/6174\/revisions\/6175"}],"wp:attachment":[{"href":"https:\/\/t.n-years.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6174"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/t.n-years.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6174"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/t.n-years.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6174"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}