{"id":1144,"date":"2020-06-16T11:00:00","date_gmt":"2020-06-16T02:00:00","guid":{"rendered":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/?p=1144"},"modified":"2020-07-30T10:36:30","modified_gmt":"2020-07-30T01:36:30","slug":"covariance","status":"publish","type":"post","link":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/covariance","title":{"rendered":"\u5171\u5206\u6563\u306e\u5b9a\u7fa9\u3010\u78ba\u7387\u5909\u6570\u306e\u5171\u5206\u6563\u3092\u77e5\u308b\u3011"},"content":{"rendered":"\n<p class=\"has-text-align-right\"><span style=\"text-decoration: underline;\">\u5b66\u7fd2\u30ec\u30d9\u30eb\uff1a\u9ad8\u6821\u751f\u3000\u96e3\u6613\u5ea6\uff1a\u2605\u2606\u2606\u2606\u2606<\/span><\/p>\n\n\n\n\n\n\n\n<p>\u5171\u5206\u6563\u306f\u3001\u30c7\u30fc\u30bf\u540c\u58eb\u306e\u76f8\u95a2\u95a2\u4fc2\u3092\u8868\u3057\u307e\u3059\u3002\u3053\u308c\u306f2\u7d44\u306e\u78ba\u7387\u5909\u6570\u3092\u5165\u624b\u3057\u305f\u6642\u30012\u7d44\u306e\u78ba\u7387\u5909\u6570\u306e\u9593\u306b\u3069\u306e\u3088\u3046\u306a\u95a2\u4fc2\u304c\u3042\u308b\u304b\u8868\u3059\u3082\u306e\u3067\u3059\uff08\u30c7\u30fc\u30bf\u306e\u76f8\u95a2\u95a2\u4fc2\u3068\u540c\u3058\u306a\u306e\u3067\u8a73\u3057\u304f\u306f<a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/correlation-coefficient\">\uff1c\u76f8\u95a2\u4fc2\u6570\u306e\u8a18\u4e8b\uff1e<\/a>\u3092\u3054\u89a7\u304f\u3060\u3055\u3044\uff09\u3002\u78ba\u7387\u5909\u6570\u304c\u8907\u6570\u5f97\u3089\u308c\u305f\u6642\u3001\u3088\u304f\u4f7f\u7528\u3055\u308c\u308b\u306e\u3067\u5171\u5206\u6563\u306e\u5b9a\u7fa9\u3060\u3051\u3067\u3082\u899a\u3048\u3066\u304a\u304d\u307e\u3057\u3087\u3046\uff01<\/p>\n\n\n\n<div id=\"toc_container\" class=\"toc_light_blue no_bullets\"><p class=\"toc_title\">\u76ee\u6b21<\/p><ul class=\"toc_list\"><li><a href=\"#i\"><span class=\"toc_number toc_depth_1\">1<\/span> \u5171\u5206\u6563\u306e\u5b9a\u7fa9<\/a><\/li><li><a href=\"#i-2\"><span class=\"toc_number toc_depth_1\">2<\/span> \u76f8\u95a2\u4fc2\u6570\u3068\u306f<\/a><\/li><li><a href=\"#i-3\"><span class=\"toc_number toc_depth_1\">3<\/span> \u76f8\u95a2\u4fc2\u6570\u306e\u89e3\u91c8\u306e\u4ed5\u65b9<\/a><\/li><li><a href=\"#i-4\"><span class=\"toc_number toc_depth_1\">4<\/span> \u5171\u5206\u6563\u306e\u307e\u3068\u3081<\/a><\/li><li><a href=\"#i-5\"><span class=\"toc_number toc_depth_1\">5<\/span> \u5171\u5206\u6563\u306e\u95a2\u9023\u8a18\u4e8b<\/a><\/li><\/ul><\/div>\n<h3><span id=\"i\">\u5171\u5206\u6563\u306e\u5b9a\u7fa9<\/span><\/h3>\n\n\n\n<div style=\"display: inline-block; background: #33cc33; padding: 5px 10px; color: #ffffff; border-radius: 5px 5px 0 0;\"><strong>\u5171\u5206\u6563(covariance)<\/strong><\/div>\n<div style=\"background: #ffffea; padding: 10px; border: 2px solid #33cc33;\">\u78ba\u7387\u5909\u6570\\((X,Y)\\)\u306e\u5171\u5206\u6563\u306f\u8a18\u53f7\\(\\mathrm{Cov}(X,Y)\\)\u3067\u8868\u3057\u3001\u4e0b\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002\n<div style=\"overflow-x: auto;\">\\begin{align}\n\\mathrm{Cov}(X,Y) &amp;= \\mathrm{E}[(X-\\mathrm{E}[X])(Y-\\mathrm{E}[Y])] \\\\\n&amp;= \\mathrm{E}[XY]-\\mathrm{E}[X]\\mathrm{E}[Y]\n\\end{align}<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n\n\n\n<div class=\"wp-block-liquid-speech-balloon liquid-speech-balloon-wrap liquid-speech-balloon-00  liquid-speech-balloon-short\"><div class=\"liquid-speech-balloon-avatar\"><\/div><div class=\"liquid-speech-balloon-text\" style=\"border-color:#d6ebf8;background-color:#d6ebf8;color:#000000\"><p>\u5171\u5206\u6563\u306b\u306f\u6b21\u306e\u610f\u5473\u304c\u3042\u308a\u307e\u3059\u3002<\/p><div class=\"liquid-speech-balloon-arrow\" style=\"border-color:transparent #d6ebf8 transparent transparent\"><\/div><\/div><\/div>\n\n\n\n<ul><li>\u5171\u5206\u6563\u304c\u300c\u6b63\u306e\u5024\u300d\u2192\\(X\\)\u304c\u5897\u52a0\u3059\u308b\u3068\\(Y\\)\u304c\u5897\u52a0\u3059\u308b\u50be\u5411\u304c\u3042\u308b\u3002\uff08\u6b63\u306e\u76f8\u95a2\uff09<\/li><li>\u5171\u5206\u6563\u304c\u300c\u8ca0\u306e\u5024\u300d\u2192\\(X\\)\u304c\u5897\u52a0\u3059\u308b\u3068\\(Y\\)\u304c\u6e1b\u5c11\u3059\u308b\u50be\u5411\u304c\u3042\u308b\u3002\uff08\u8ca0\u306e\u76f8\u95a2\uff09<\/li><li>\u5171\u5206\u6563\u304c0\u306b\u8fd1\u3044\u2192\\(X\\)\u3068\\(Y\\)\u306b\u306f\u3042\u307e\u308a\u95a2\u4fc2\u304c\u306a\u3044\u3002\uff08\u7121\u76f8\u95a2\uff09<\/li><li>\u5171\u5206\u6563\u304c0\u3067\u3042\u308b\u2192\\(X\\)\u3068\\(Y\\)\u306f\u72ec\u7acb\u3067\u3042\u308b\u3002<\/li><\/ul>\n\n\n\n<p>\u203b\u3000\u6b63\u306e\u76f8\u95a2\u30fb\u8ca0\u306e\u76f8\u95a2\u30fb\u7121\u76f8\u95a2\u306b\u3064\u3044\u3066\u306f<a class=\"aioseop-link\" href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/correlation\">\uff1c\u76f8\u95a2\u306e\u8a18\u4e8b\uff1e<\/a>\u3092\u3054\u89a7\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n\n<h3><span id=\"i-2\">\u76f8\u95a2\u4fc2\u6570\u3068\u306f<\/span><\/h3>\n\n\n\n<p>\u78ba\u7387\u5909\u6570\u306b\u3082\u76f8\u95a2\u4fc2\u6570\u3092\u5b9a\u7fa9\u3067\u304d\u307e\u3059\u3002\u30c7\u30fc\u30bf\u540c\u58eb\u306e\u76f8\u95a2\u4fc2\u6570\u540c\u69d8\u306b\u3001<strong>\u76f8\u95a2\u4fc2\u6570\u306f[\u76f8\u95a2\u306e\u7a2e\u985e]\u3068[\u76f8\u95a2\u306e\u5f37\u3055]\u3092\u8868\u3059\u57fa\u6e96<\/strong>\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<div style=\"display: inline-block; background: #33cc33; padding: 5px 10px; color: #ffffff; border-radius: 5px 5px 0 0;\"><strong>\u76f8\u95a2\u4fc2\u6570<\/strong><\/div>\n<div style=\"background: #ffffea; padding: 10px; border: 2px solid #33cc33;\">\u78ba\u7387\u5909\u6570\\((X,Y)\\)\u306e\u76f8\u95a2\u4fc2\u6570\u3092\\(\\rho(X,Y)\\)\u3067\u8868\u3057\u3001\u6b21\u306e\u5f0f\u3067\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002$$\\rho(X,Y)=\\frac{\\mathrm{Cov}(X,Y)}{\\sqrt{\\mathrm{Var}[X]}\\sqrt{\\mathrm{Var}[Y]}}$$<\/div>\n<p>&nbsp;<\/p>\n\n\n\n<p>\u203b\u3000\u5206\u6563\u306b\u3064\u3044\u3066\u306f<a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/variance\">\uff1c\u5206\u6563\u306e\u8a18\u4e8b\uff1e<\/a>\u3092\u3054\u89a7\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n\n<h3><span id=\"i-3\">\u76f8\u95a2\u4fc2\u6570\u306e\u89e3\u91c8\u306e\u4ed5\u65b9<\/span><\/h3>\n\n\n\n<p>\u76f8\u95a2\u4fc2\u6570\u3092\u8a08\u7b97\u3059\u308b\u3068\u5fc5\u305a\\(-1\uff5e1\\)\u306e\u9593\u306e\u5024\u3092\u3068\u308a\u307e\u3059\u3002\u307e\u305a\u76f8\u95a2\u4fc2\u6570\u304b\u3089\u3001\u76f8\u95a2\u306e\u7a2e\u985e\u306e\u5224\u65ad\u306b\u3064\u3044\u3066\u7d39\u4ecb\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<ul><li>\u76f8\u95a2\u4fc2\u6570\u304c\\(1\\)\u306b\u8fd1\u3044\u3068\u304d\uff1a\u6b63\u306e\u76f8\u95a2<\/li><li>\u76f8\u95a2\u4fc2\u6570\u304c\\(0\\)\u306b\u8fd1\u3044\u3068\u304d\uff1a\u7121\u76f8\u95a2<\/li><li>\u76f8\u95a2\u4fc2\u6570\u304c\\(-1\\)\u306b\u8fd1\u3044\u3068\u304d\uff1a\u8ca0\u306e\u76f8\u95a2<\/li><\/ul>\n\n\n\n<figure class=\"wp-block-table aligncenter\"><table><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\">\u76f8\u95a2\u4fc2\u6570\u306e\u7bc4\u56f2<\/td><td>\u8a55\u4fa1<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">\\(-1.0\uff5e-0.7\\)<\/td><td>\u5f37\u3044\u8ca0\u306e\u76f8\u95a2<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">\\(-0.7\uff5e-0.4\\)<\/td><td>\u8ca0\u306e\u76f8\u95a2<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">\\(-0.4\uff5e-0.2\\)<\/td><td>\u3084\u3084\u8ca0\u306e\u76f8\u95a2<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">\\(-0.2\uff5e0.2\\)<\/td><td>\u7121\u76f8\u95a2<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">\\(0.2\uff5e0.4\\)<\/td><td>\u3084\u3084\u6b63\u306e\u76f8\u95a2<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">\\(0.4\uff5e0.7\\)<\/td><td>\u6b63\u306e\u76f8\u95a2<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">\\(0.7\uff5e1.0\\)<\/td><td>\u5f37\u3044\u8ca0\u306e\u76f8\u95a2<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>\u76f8\u95a2\u4fc2\u6570\u3067\u6ce8\u610f\u3057\u306a\u3044\u3068\u3044\u3051\u306a\u3044\u3053\u3068\u306f\u3001\u76f8\u95a2\u95a2\u4fc2\u304c\u3042\u308b\u304b\u3089\u3068\u3044\u3063\u3066\u56e0\u679c\u95a2\u4fc2\u3092\u8868\u3059\u3082\u306e\u3067\u306f\u306a\u3044\u3053\u3068\u306b\u306f\u6ce8\u610f\u304c\u5fc5\u8981\u3067\u3042\u308b\uff08\u3053\u306e\u3088\u3046\u306a\u3053\u3068\u3092<strong>\u307f\u304b\u3051\u4e0a\u306e\u76f8\u95a2<\/strong>\u3068\u3044\u3044\u307e\u3059\uff09\u3002\u8a73\u3057\u304f\u306f<a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/correlation\" class=\"aioseop-link\">\uff1c\u76f8\u95a2\u306e\u8a18\u4e8b\uff1e<\/a>\u3092\u3054\u89a7\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n\n<h3><span id=\"i-4\">\u5171\u5206\u6563\u306e\u307e\u3068\u3081<\/span><\/h3>\n\n\n\n<p>\u5171\u5206\u6563\u306f\u78ba\u7387\u5909\u6570\u540c\u58eb\u306e\u76f8\u95a2\u95a2\u4fc2\u3092\u8868\u3057\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u5171\u5206\u6563\u306f\u30c7\u30fc\u30bf\u306b\u3088\u3063\u3066\u5024\u306e\u5927\u304d\u3055\u304c\u5909\u308f\u308b\u306e\u3067\u3001\u5224\u65ad\u306e\u57fa\u6e96\u304c\u660e\u78ba\u306b\u6c7a\u3081\u3089\u308c\u3066\u3044\u307e\u305b\u3093\u3002\u305d\u3053\u3067\u3001[\u76f8\u95a2\u306e\u7a2e\u985e]\u3068[\u76f8\u95a2\u306e\u5f37\u3055]\u3092\u6e2c\u308b\u305f\u3081\u306e\u57fa\u6e96\u3068\u3057\u3066\u76f8\u95a2\u4fc2\u6570\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<h3><span id=\"i-5\">\u5171\u5206\u6563\u306e\u95a2\u9023\u8a18\u4e8b<\/span><\/h3>\n\n\n\n<p>\u30fb<a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/variance\">\u5206\u6563\u306e\u5b9a\u7fa9<\/a>\uff1a\u5206\u6563\u3092\u5b9a\u7fa9\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u30fb<a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/conditional-variance\">\u6761\u4ef6\u4ed8\u304d\u5206\u6563<\/a>\uff1a\u6761\u4ef6\u4ed8\u304d\u78ba\u7387\u5909\u6570\u306e\u5206\u6563\u306e\u6c42\u3081\u65b9\u3092\u7d39\u4ecb\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u30fb<a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/variance-nature\">\u5206\u6563\u306e\u6027\u8cea<\/a>\uff1a\u5206\u6563\u306e\u6301\u3064\u6027\u8cea\u3092\u307e\u3068\u3081\u3066\u3044\u307e\u3059\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5b66\u7fd2\u30ec\u30d9\u30eb\uff1a\u9ad8\u6821\u751f\u3000\u96e3\u6613\u5ea6\uff1a\u2605\u2606\u2606\u2606\u2606 \u5171\u5206\u6563\u306f\u3001\u30c7\u30fc\u30bf\u540c\u58eb\u306e\u76f8\u95a2\u95a2\u4fc2\u3092\u8868\u3057\u307e\u3059\u3002\u3053\u308c\u306f2\u7d44\u306e\u78ba\u7387\u5909\u6570\u3092\u5165\u624b\u3057\u305f\u6642\u30012\u7d44\u306e\u78ba\u7387\u5909\u6570\u306e\u9593\u306b\u3069\u306e &#8230; <\/p>\n","protected":false},"author":1,"featured_media":829,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[74],"tags":[75,49],"jetpack_featured_media_url":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-content\/uploads\/2020\/05\/135-money-images.jpg","_links":{"self":[{"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/posts\/1144"}],"collection":[{"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/comments?post=1144"}],"version-history":[{"count":10,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/posts\/1144\/revisions"}],"predecessor-version":[{"id":2629,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/posts\/1144\/revisions\/2629"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/media\/829"}],"wp:attachment":[{"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/media?parent=1144"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/categories?post=1144"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/wp-json\/wp\/v2\/tags?post=1144"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}