{"id":708,"date":"2020-05-29T11:00:33","date_gmt":"2020-05-29T02:00:33","guid":{"rendered":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/?p=708"},"modified":"2020-06-30T21:09:22","modified_gmt":"2020-06-30T12:09:22","slug":"correlation-coefficient","status":"publish","type":"post","link":"https:\/\/develop-chronos.com\/statistics-top\/statistics\/correlation-coefficient","title":{"rendered":"\u76f8\u95a2\u4fc2\u6570\u3010\u30c7\u30fc\u30bf\u306e\u95a2\u4fc2\u3092\u6570\u5024\u5316\u3059\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><a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/correlation\" class=\"aioseop-link\">\u76f8\u95a2<\/a>\u3084<a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/scatter-diagram\" class=\"aioseop-link\">\u6563\u5e03\u56f3\u30fb\u30af\u30ed\u30b9\u8868<\/a>\u3067\u306f\u76f8\u95a2\u3068\u3044\u3046\u8a00\u8449\u306e\u5b9a\u7fa9\u3068\u76f8\u95a2\u95a2\u4fc2\u3092\u8996\u899a\u7684\u306b\u8868\u3059\u65b9\u6cd5\u3092\u7d39\u4ecb\u3057\u307e\u3057\u305f\u3002\u3057\u304b\u3057\u3001\u8996\u899a\u7684\u306b\u8a34\u3048\u3066\u3082\u5404\u500b\u4eba\u306e\u6349\u3048\u65b9\u306b\u3088\u3063\u3066\u9055\u3044\u304c\u51fa\u3066\u304d\u3066\u3057\u307e\u3044\u307e\u3059\u3002\u305d\u3053\u3067\u3053\u306e\u8a18\u4e8b\u3067\u306f\u3001\u30c7\u30fc\u30bf\u306e\u95a2\u4fc2\u6027\u3092\u6570\u5b57\u3067\u8868\u3059\u65b9\u6cd5\u3092\u7d39\u4ecb\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/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\u3068\u306f<\/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> \u76f8\u95a2\u4fc2\u6570\u306e\u307e\u3068\u3081<\/a><\/li><li><a href=\"#i-5\"><span class=\"toc_number toc_depth_1\">5<\/span> \u6563\u5e03\u56f3\u306e\u95a2\u9023\u8a18\u4e8b<\/a><\/li><\/ul><\/div>\n<h2><span id=\"i\">\u5171\u5206\u6563\u3068\u306f<\/span><\/h2>\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>\u30c7\u30fc\u30bf\u306e\u95a2\u4fc2\u3092\u6570\u5b57\u3067\u8868\u3059\u3001\u76f8\u95a2\u4fc2\u6570\u3092\u7d39\u4ecb\u3057\u3066\u3044\u304d\u307e\u3059\u3002<br>\u76f8\u95a2\u4fc2\u6570\u3092\u5b9a\u7fa9\u3059\u308b\u524d\u306b<strong>\u5171\u5206\u6563<\/strong>\u3068\u3044\u3046\u3082\u306e\u3092\u5b9a\u7fa9\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p><div class=\"liquid-speech-balloon-arrow\" style=\"border-color:transparent #d6ebf8 transparent transparent\"><\/div><\/div><\/div>\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;\">\u30c7\u30fc\u30bf\u6570\\(n\\)\u306e\u30c7\u30fc\u30bf\u7d44\\(\\{(x_{1},\\,y_{1}),\\,(x_{2},\\,y_{2}),\\cdots,(x_{n},\\,y_{n})\\}\\)\u306b\u3064\u3044\u3066<strong>\u5171\u5206\u6563\\(s_{xy}\\)<\/strong>\u306f\u6b21\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002<div style=\"overflow-x: auto;\">\\begin{align}<br>s_{xy} &amp;= \\frac{1}{n}\\left\\{ (x_{1}-\\bar{x})(y_{1}-\\bar{y})+\\cdots+(x_{n}-\\bar{x})(y_{n}-\\bar{y}) \\right\\} \\\\<br>&amp;=\\frac{1}{n}\\sum_{i=1}^{n}(x_{i}-\\bar{x})(y_{i}-\\bar{y})<br>\\end{align}<\/div><\/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><\/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 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<h2><span id=\"i-2\">\u76f8\u95a2\u4fc2\u6570\u3068\u306f<\/span><\/h2>\n\n\n\n<p>\u5171\u5206\u6563\u304b\u3089\u3001\u76f8\u95a2\u306e\u7a2e\u985e\u306e\u5224\u65ad\u306f\u3067\u304d\u307e\u3059\u304c\u3001\u76f8\u95a2\u306e\u5f37\u3055\u306f\u6e2c\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u305b\u3093\u3067\u3057\u305f\u3002<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(\u30d4\u30a2\u30bd\u30f3\u306e\u7a4d\u7387\u76f8\u95a2\u4fc2\u6570 correlation coefficient)<\/strong><\/div>\n<div style=\"background: #ffffea; padding: 10px; border: 2px solid #33cc33;\">\u30c7\u30fc\u30bf\u6570\\(n\\)\u306e\u30c7\u30fc\u30bf\u7d44\\(\\{(x_{1},\\,y_{1}),\\,(x_{2},\\,y_{2}),\\cdots,(x_{n},\\,y_{n})\\}\\)\u306b\u3064\u3044\u3066\u3001\\(\\{x_{1},\\cdots,x_{n}\\}\\)\u306e\u5206\u6563\u304c\\(s_{x}^{2}\\)\u3001\\(\\{y_{1},\\cdots,y_{n}\\}\\)\u306e\u5206\u6563\u304c\\(s_{y}^{2}\\)\u3067\u3042\u308a\u3001\\(x\\)\u3068\\(y\\)\u306e\u5171\u5206\u6563\u304c\\(s_{xy}\\)\u3067\u4e0e\u3048\u3089\u308c\u305f\u3068\u304d\u3001\\(x\\)\u3068\\(y\\)\u306e<strong>\u76f8\u95a2\u4fc2\u6570\\(r_{xy}\\)<\/strong>\u306f\u6b21\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002$$r_{xy}=\\frac{s_{xy}}{s_{x}s_{y}}$$<\/div>\n<p>\u00a0<\/p>\n\n\n\n<p>\u203b\u3000\u5206\u6563\u306b\u3064\u3044\u3066\u306f<a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/05241628\" class=\"aioseop-link\">\uff1c\u5206\u6563\u30fb\u6a19\u6e96\u504f\u5dee\u306e\u8a18\u4e8b\uff1e<\/a>\u3092\u3054\u89a7\u304f\u3060\u3055\u3044\u3002<\/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>\u76f8\u95a2\u4fc2\u6570\u306f\u6b21\u306e\u3088\u3046\u306b\u66f8\u304d\u63db\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p><div class=\"liquid-speech-balloon-arrow\" style=\"border-color:transparent #d6ebf8 transparent transparent\"><\/div><\/div><\/div>\n\n\n\n<p><div style=\"overflow-x: auto;\">\\begin{align}r_{xy}=\\frac{1}{n}\\sum_{i=1}^{n}\\frac{(x_{i}-\\bar{x})(y_{i}-\\bar{y})}{s_{x}s_{y}}=\\frac{1}{n}\\sum_{i=1}^{n}\\frac{(x_{i}-\\bar{x})}{s_{x}}\\cdot\\frac{(y_{i}-\\bar{y})}{s_{y}}\\end{align}<\/div><\/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>\u4e00\u756a\u3001\u53f3\u8fba\u3092\u6ce8\u76ee\u3057\u3066\u304f\u3060\u3055\u3044\uff01<br>\u3053\u306e\u5f0f\u304b\u3089<strong>\u76f8\u95a2\u4fc2\u6570\u306f\u6a19\u6e96\u5f97\u70b9\u3069\u3046\u3057\u306e\u5171\u5206\u6563\u306b\u306a\u3063\u3066\u3044\u308b<\/strong>\u3053\u3068\u304c\u308f\u304b\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<p>\u203b\u3000\u6a19\u6e96\u5f97\u70b9\u306b\u3064\u3044\u3066\u306f<a href=\"https:\/\/develop-chronos.com\/statistics-top\/statistics\/standard-score\" class=\"aioseop-link\">\uff1c\u6a19\u6e96\u5f97\u70b9\u306e\u8a18\u4e8b\uff1e<\/a>\u3092\u3054\u89a7\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n\n<h2><span id=\"i-3\">\u76f8\u95a2\u4fc2\u6570\u306e\u89e3\u91c8\u306e\u4ed5\u65b9<\/span><\/h2>\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<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>\u3057\u304b\u3057\u3001\u307e\u3060\u4e0d\u5b8c\u5168\u306a\u611f\u3058\u304c\u3057\u307e\u3059\u3088\u306d\uff01\uff1f<br>\u4f8b\u3048\u3070\u3001\u6b63\u306e\u76f8\u95a2\u3068\u7121\u76f8\u95a2\u306e\u5883\u76ee\u306f\u3069\u3053\u3089\u8fba\u304b\u7591\u554f\u306b\u601d\u3044\u307e\u305b\u3093\u304b\uff1f<br>\u6b21\u306b\u3082\u3046\u5c11\u3057\u8a73\u3057\u3044\u57fa\u6e96\u3092\u7d39\u4ecb\u3057\u307e\u3059\u3002<\/p><div class=\"liquid-speech-balloon-arrow\" style=\"border-color:transparent #d6ebf8 transparent transparent\"><\/div><\/div><\/div>\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<h2><span id=\"i-4\">\u76f8\u95a2\u4fc2\u6570\u306e\u307e\u3068\u3081<\/span><\/h2>\n\n\n\n<p>\u5171\u5206\u6563\u306f\u76f8\u95a2\u306e\u7a2e\u985e\u3092\u5224\u65ad\u3059\u308b\u3072\u3068\u3064\u306e\u6307\u6a19\u306b\u306a\u308a\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\u76f8\u95a2\u4fc2\u6570\u306f\u3069\u306e\u30c7\u30fc\u30bf\u306b\u7528\u3044\u3066\u3082\u5224\u65ad\u57fa\u6e96\u304c\u4e00\u5b9a\u306b\u306a\u308b\u306e\u3067\u3001\u30c7\u30fc\u30bf\u9593\u306e\u95a2\u4fc2\u3092\u8868\u3059\u305f\u3081\u306b\u3088\u304f\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<h2><span 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class=\"aioseop-link\">\u504f\u76f8\u95a2\u4fc2\u6570<\/a>\uff1a3\u3064\u4ee5\u4e0a\u306e\u30c7\u30fc\u30bf\u306b\u5bfe\u3057\u3066\u3001\u898b\u304b\u3051\u4e0a\u306e\u76f8\u95a2\u3092\u53d6\u308a\u9664\u304f\u624b\u6cd5\u3092\u7d39\u4ecb\u3057\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 \u76f8\u95a2\u3084\u6563\u5e03\u56f3\u30fb\u30af\u30ed\u30b9\u8868\u3067\u306f\u76f8\u95a2\u3068\u3044\u3046\u8a00\u8449\u306e\u5b9a\u7fa9\u3068\u76f8\u95a2\u95a2\u4fc2\u3092\u8996\u899a\u7684\u306b\u8868\u3059\u65b9\u6cd5\u3092\u7d39\u4ecb\u3057\u307e\u3057\u305f\u3002\u3057\u304b\u3057\u3001\u8996 &#8230; 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