{"id":4316,"date":"2025-07-22T22:14:52","date_gmt":"2025-07-22T13:14:52","guid":{"rendered":"https:\/\/best-biostatistics.com\/toukei-er\/?p=4316"},"modified":"2025-07-22T22:14:54","modified_gmt":"2025-07-22T13:14:54","slug":"squared-partial-correlation-a-comprehensive-guide-from-concept-to-r-implementation","status":"publish","type":"post","link":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/squared-partial-correlation-a-comprehensive-guide-from-concept-to-r-implementation\/","title":{"rendered":"\u504f\u76f8\u95a2\u306e\u4e8c\u4e57\uff1a\u305d\u306e\u6982\u5ff5\u304b\u3089R\u3067\u306e\u5b9f\u8df5\u307e\u3067\u5fb9\u5e95\u89e3\u8aac\uff01"},"content":{"rendered":"\n<p>\u3053\u306e\u8a18\u4e8b\u3067\u306f\u3001\u7d71\u8a08\u5206\u6790\u3067\u91cd\u8981\u306a\u5f79\u5272\u3092\u679c\u305f\u3059\u300c\u504f\u76f8\u95a2\u306e\u4e8c\u4e57\u300d\u306b\u3064\u3044\u3066\u6398\u308a\u4e0b\u3052\u308b\u3002\u3053\u306e\u6307\u6a19\u304c\u4e00\u4f53\u3069\u306e\u3088\u3046\u306a\u6982\u5ff5\u3067\u3042\u308a\u3001\u3069\u306e\u3088\u3046\u306b\u8a08\u7b97\u3055\u308c\u308b\u306e\u304b\u3001\u3055\u3089\u306b\u306f\u305d\u306e\u7570\u306a\u308b\u547c\u3073\u540d\u3084\u65e5\u672c\u8a9e\u3067\u306e\u8868\u8a18\u306b\u3064\u3044\u3066\u3082\u6574\u7406\u3059\u308b\u3002\u52a0\u3048\u3066\u3001\u5177\u4f53\u7684\u306a\u4f8b\u3068R\u3092\u7528\u3044\u305f\u5b9f\u8df5\u7684\u306a\u8a08\u7b97\u65b9\u6cd5\u3001\u305d\u3057\u3066\u305d\u306e\u7d50\u679c\u306e\u89e3\u91c8\u3092\u63d0\u793a\u3059\u308b\u3002\u30c7\u30fc\u30bf\u306b\u96a0\u3055\u308c\u305f\u771f\u306e\u95a2\u4fc2\u6027\u3092\u6d6e\u304d\u5f6b\u308a\u306b\u3059\u308b\u305f\u3081\u306e\u5f37\u529b\u306a\u30c4\u30fc\u30eb\u3067\u3042\u308b\u504f\u76f8\u95a2\u306e\u4e8c\u4e57\u3092\u3001\u591a\u89d2\u7684\u306b\u89e3\u8aac\u3059\u308b\u3002<\/p>\n\n\n\n<!--more-->\n\n\n\n<h2 class=\"wp-block-heading\">\u504f\u76f8\u95a2\u306e\u4e8c\u4e57\u3068\u306f\uff1f \u301c\u6982\u5ff5\u3068\u8a08\u7b97\u306e\u6982\u7565\u301c<\/h2>\n\n\n\n<p>\u504f\u76f8\u95a2\u306e\u4e8c\u4e57\u306f\u3001\u7d71\u8a08\u5b66\u306b\u304a\u3044\u30662\u3064\u306e\u5909\u6570\u306e\u95a2\u4fc2\u6027\u3092\u3001\u4ed6\u306e\u5909\u6570\u306e\u5f71\u97ff\u3092\u9664\u53bb\u3057\u305f\u4e0a\u3067\u8a55\u4fa1\u3059\u308b\u305f\u3081\u306e\u5f37\u529b\u306a\u30c4\u30fc\u30eb\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<p>\u901a\u5e38\u306e\u76f8\u95a2\u4fc2\u6570\uff08\u30d4\u30a2\u30bd\u30f3\u76f8\u95a2\u4fc2\u6570\u306a\u3069\uff09\u306f\u30012\u3064\u306e\u5909\u6570\u9593\u306e\u7dda\u5f62\u306a\u95a2\u4fc2\u306e\u5f37\u3055\u3068\u65b9\u5411\u3092\u793a\u3059\u304c\u3001\u305d\u3053\u306b\u306f\u300c\u4ea4\u7d61\u5909\u6570\u300d\u3068\u547c\u3070\u308c\u308b\u3001\u95a2\u4fc2\u306e\u306a\u3044\u7b2c\u4e09\u306e\u5909\u6570\u306e\u5f71\u97ff\u304c\u5165\u308a\u8fbc\u3093\u3067\u3044\u308b\u53ef\u80fd\u6027\u304c\u3042\u308b\u3002\u504f\u76f8\u95a2\u306f\u3001\u3053\u306e\u7b2c\u4e09\u306e\u5909\u6570\u306e\u5f71\u97ff\u3092\u7d71\u8a08\u7684\u306b\u53d6\u308a\u9664\u304f\u3053\u3068\u3067\u3001\u7d14\u7c8b\u306a2\u3064\u306e\u5909\u6570\u9593\u306e\u95a2\u4fc2\u6027\u3092\u6d6e\u304d\u5f6b\u308a\u306b\u3059\u308b\u3002<\/p>\n\n\n\n<p>\u305d\u3057\u3066\u3001\u305d\u306e\u300c<strong>\u504f\u76f8\u95a2\u306e\u4e8c\u4e57<\/strong>\u300d\u306f\u3001\u305d\u306e\u7d14\u7c8b\u306a\u95a2\u4fc2\u6027\u306e\u300c\u8aac\u660e\u529b\u300d\u3084\u300c\u5bc4\u4e0e\u7387\u300d\u3092\u793a\u3059\u6307\u6a19\u3068\u306a\u308b\u3002\u5177\u4f53\u7684\u306b\u306f\u3001\u3042\u308b\u5909\u6570\u306e\u5909\u52d5\u306e\u3046\u3061\u3001\u4ed6\u306e\u5909\u6570\u306e\u5f71\u97ff\u3092\u53d6\u308a\u9664\u3044\u305f\u4e0a\u3067\u3001\u5bfe\u8c61\u3068\u306a\u308b\u5225\u306e\u5909\u6570\u304c\u3069\u306e\u7a0b\u5ea6\u8aac\u660e\u3067\u304d\u308b\u304b\u3001\u3068\u3044\u3046\u5272\u5408\u3092\u8868\u3059\u3002<\/p>\n\n\n\n<p>\u8a08\u7b97\u306e\u6982\u7565\u3068\u3057\u3066\u306f\u3001\u307e\u305a\u3001\u305d\u308c\u305e\u308c\u306e\u5909\u6570\u3092\u4ed6\u306e\u5909\u6570\u3067\u56de\u5e30\u5206\u6790\u3057\u3001\u305d\u306e\u6b8b\u5dee\uff08\u56de\u5e30\u3067\u8aac\u660e\u3067\u304d\u306a\u304b\u3063\u305f\u90e8\u5206\uff09\u3092\u6c42\u3081\u308b\u3002\u6b21\u306b\u3001\u3053\u306e\u6b8b\u5dee\u540c\u58eb\u306e\u76f8\u95a2\u3092\u8a08\u7b97\u3059\u308b\u3002\u3053\u308c\u304c\u504f\u76f8\u95a2\u4fc2\u6570\u3067\u3042\u308b\u3002\u504f\u76f8\u95a2\u306e\u4e8c\u4e57\u306f\u3001\u3053\u306e\u504f\u76f8\u95a2\u4fc2\u6570\u3092\u5358\u7d14\u306b\u4e8c\u4e57\u3059\u308b\u3053\u3068\u3067\u5f97\u3089\u308c\u308b\u3002<\/p>\n\n\n\n<p>\u6570\u5f0f\u3067\u7c21\u5358\u306b\u793a\u3059\u3068\u3001\u5909\u6570 $X$ \u3068 $Y$ \u306e\u9593\u306e\u5909\u6570 $Z$ \u3092\u8abf\u6574\u3057\u305f\u504f\u76f8\u95a2\u4fc2\u6570 $r_{XY.Z}$ \u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8868\u3055\u308c\u308b\uff08\u7c21\u7565\u5316\u3057\u305f\u6982\u5ff5\u7684\u306a\u8868\u73fe\u3067\u3042\u308b\uff09\u3002<\/p>\n\n\n\n<p>$$r_{XY.Z} = \\frac{r_{XY} &#8211; r_{XZ}r_{YZ}}{\\sqrt{(1-r_{XZ}^2)(1-r_{YZ}^2)}}$$<\/p>\n\n\n\n<p>\u305d\u3057\u3066\u3001\u504f\u76f8\u95a2\u306e\u4e8c\u4e57\u306f $r_{XY.Z}^2$ \u3068\u306a\u308b\u3002<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\u540c\u3058\u6982\u5ff5\u3001\u7570\u306a\u308b\u540d\u79f0\uff1a\u547c\u3073\u540d\u306e\u6574\u7406<\/h2>\n\n\n\n<p>\u3053\u306e\u300c\u504f\u76f8\u95a2\u306e\u4e8c\u4e57\u300d\u3068\u3044\u3046\u6982\u5ff5\u306f\u3001\u6587\u8108\u3084\u5206\u91ce\u306b\u3088\u3063\u3066\u69d8\u3005\u306a\u540d\u79f0\u3067\u547c\u3070\u308c\u308b\u3053\u3068\u304c\u3042\u308b\u3002\u4e3b\u306a\u3082\u306e\u3092\u4ee5\u4e0b\u306b\u6574\u7406\u3059\u308b\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u6c7a\u5b9a\u4fc2\u6570 ($R^2$) \u306e\u5897\u5206 \/ \u5897\u52a0<\/strong>: \u91cd\u56de\u5e30\u5206\u6790\u306b\u304a\u3044\u3066\u3001\u3042\u308b\u5909\u6570\u3092\u30e2\u30c7\u30eb\u306b\u8ffd\u52a0\u3057\u305f\u969b\u306b\u3001\u6c7a\u5b9a\u4fc2\u6570\u304c\u3069\u306e\u7a0b\u5ea6\u5897\u52a0\u3059\u308b\u304b\u3092\u793a\u3059\u5834\u5408\u306b\u4f7f\u308f\u308c\u308b\u3002\u504f\u76f8\u95a2\u306e\u4e8c\u4e57\u306f\u3001\u4ed6\u306e\u5909\u6570\u3092\u6295\u5165\u6e08\u307f\u306e\u30e2\u30c7\u30eb\u306b\u3001\u65b0\u305f\u306a\u5909\u6570\u3092\u6295\u5165\u3057\u305f\u969b\u306e\u6c7a\u5b9a\u4fc2\u6570\u306e\u5897\u5206\u3068\u7b49\u3057\u304f\u306a\u308b\u3002<\/li>\n\n\n\n<li><strong>\u90e8\u5206\u6c7a\u5b9a\u4fc2\u6570 (Partial Coefficient of Determination)<\/strong>: \u3053\u308c\u306f\u300c\u504f\u76f8\u95a2\u306e\u4e8c\u4e57\u300d\u3068\u307b\u307c\u540c\u7fa9\u3067\u4f7f\u308f\u308c\u308b\u3053\u3068\u304c\u591a\u3044\u3002\u7279\u5b9a\u306e\u5909\u6570\u30bb\u30c3\u30c8\u306e\u52b9\u679c\u3092\u9664\u53bb\u3057\u305f\u4e0a\u3067\u306e\u6c7a\u5b9a\u4fc2\u6570\u3068\u3057\u3066\u89e3\u91c8\u3055\u308c\u308b\u3002<\/li>\n\n\n\n<li><strong>\u72ec\u81ea\u306e\u8aac\u660e\u529b (Unique Variance Explained)<\/strong>: \u4ed6\u306e\u5909\u6570\u304c\u8aac\u660e\u3067\u304d\u306a\u3044\u3001\u7279\u5b9a\u306e\u5909\u6570\u306e\u307f\u304c\u8aac\u660e\u3067\u304d\u308b\u5206\u6563\u306e\u5272\u5408\u3068\u3057\u3066\u8868\u73fe\u3055\u308c\u308b\u3053\u3068\u304c\u3042\u308b\u3002<\/li>\n\n\n\n<li><strong>\u30bb\u30df\u30d1\u30fc\u30b7\u30e3\u30eb\u76f8\u95a2\u306e\u4e8c\u4e57 (Squared Semipartial Correlation) \/ \u72ec\u81ea\u76f8\u95a2\u306e\u4e8c\u4e57 (Squared Unique Correlation)<\/strong>: \u3053\u308c\u306f\u300c\u504f\u76f8\u95a2\u306e\u4e8c\u4e57\u300d\u3068\u306f\u53b3\u5bc6\u306b\u306f\u7570\u306a\u308b\u6982\u5ff5\u3067\u3042\u308b\u304c\u3001\u6df7\u540c\u3055\u308c\u308b\u3053\u3068\u304c\u3042\u308b\u3002\u30bb\u30df\u30d1\u30fc\u30b7\u30e3\u30eb\u76f8\u95a2\u306f\u3001\u3042\u308b\u5909\u6570\u304b\u3089\u4ed6\u306e\u5909\u6570\u306e\u5f71\u97ff\u3092\u300c\u53d6\u308a\u9664\u3044\u305f\u5f8c\u300d\u306e\u6b8b\u5dee\u3068\u3001\u3082\u3046\u4e00\u65b9\u306e\u300c\u5143\u306e\u307e\u307e\u306e\u300d\u5909\u6570\u3068\u306e\u76f8\u95a2\u3092\u793a\u3059\u3002\u305d\u306e\u4e8c\u4e57\u306f\u3001\u5168\u5206\u6563\u306e\u3046\u3061\u3001\u7279\u5b9a\u306e\u5909\u6570\u304c\u5358\u72ec\u3067\u8aac\u660e\u3059\u308b\u90e8\u5206\u306e\u5272\u5408\u3092\u793a\u3059\u3002\u504f\u76f8\u95a2\u306e\u4e8c\u4e57\u306f\u3001\u4e21\u65b9\u306e\u5909\u6570\u304b\u3089\u4ed6\u306e\u5909\u6570\u306e\u5f71\u97ff\u3092\u53d6\u308a\u9664\u3044\u305f\u5f8c\u306e\u76f8\u95a2\u306e\u4e8c\u4e57\u3067\u3042\u308b\u70b9\u3067\u7570\u306a\u308b\u3002\u305f\u3060\u3057\u3001\u91cd\u56de\u5e30\u5206\u6790\u306b\u304a\u3044\u3066\u306f\u3001\u3042\u308b\u8aac\u660e\u5909\u6570\u306e\u504f\u76f8\u95a2\u306e\u4e8c\u4e57\u306f\u3001\u305d\u306e\u5909\u6570\u3092\u30e2\u30c7\u30eb\u306b\u8ffd\u52a0\u3057\u305f\u969b\u306e\u6c7a\u5b9a\u4fc2\u6570 ($R^2$) \u306e\u5897\u5206\u3068\u7b49\u3057\u304f\u306a\u308a\u3001\u3053\u308c\u306f\u30bb\u30df\u30d1\u30fc\u30b7\u30e3\u30eb\u76f8\u95a2\u306e\u4e8c\u4e57\u3068\u3082\u95a2\u9023\u304c\u6df1\u3044\u3002<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<div id=\"biost-1191737459\" class=\"biost- biost-entity-placement\"><p style=\"text-align: center;\"><span style=\"font-size: 20px;\"><strong><a href=\"https:\/\/best-biostatistics.com\/kmhl\">\uff1e\uff1e\u3082\u3046\u7d71\u8a08\u3067\u60a9\u3080\u306e\u306f\u7d42\u308f\u308a\u306b\u3057\u307e\u305b\u3093\u304b\uff1f\u00a0<\/a><\/strong><\/span><\/p>\r\n<a href=\"https:\/\/best-biostatistics.com\/kmhl\"><img class=\"aligncenter wp-image-2794 size-full\" src=\"https:\/\/best-biostatistics.com\/wp\/wp-content\/uploads\/2023\/11\/bn_r_03.png\" alt=\"\" width=\"500\" height=\"327\" \/><\/a>\r\n<p style=\"text-align: center;\"><span style=\"color: #ff0000; font-size: 20px;\"><strong><span class=\"marker2\">\u21911\u4e07\u4eba\u4ee5\u4e0a\u306e\u533b\u7642\u5f93\u4e8b\u8005\u304c\u8cfc\u8aad\u4e2d<\/span><\/strong><\/span><\/p><\/div><h2 class=\"wp-block-heading\">\u65e5\u672c\u8a9e\u3067\u306e\u8868\u8a18<\/h2>\n\n\n\n<p>\u65e5\u672c\u8a9e\u3067\u306f\u3001\u4e3b\u306b\u4ee5\u4e0b\u306e\u8868\u73fe\u304c\u7528\u3044\u3089\u308c\u308b\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u504f\u76f8\u95a2\u306e\u4e8c\u4e57<\/strong>: \u6700\u3082\u76f4\u63a5\u7684\u306a\u8868\u73fe\u3067\u3042\u308b\u3002<\/li>\n\n\n\n<li><strong>\u504f\u6c7a\u5b9a\u4fc2\u6570<\/strong>: Partial Coefficient of Determination \u306e\u76f4\u8a33\u3067\u3042\u308b\u3002<\/li>\n\n\n\n<li><strong>\u5897\u5206$R^2$ (\u305e\u3046\u3076\u3093\u30a2\u30fc\u30eb\u30b9\u30af\u30a8\u30a2)<\/strong>: \u91cd\u56de\u5e30\u5206\u6790\u306e\u6587\u8108\u3067\u3001\u8ffd\u52a0\u3055\u308c\u305f\u5909\u6570\u306e\u8aac\u660e\u529b\u3068\u3057\u3066\u8a00\u53ca\u3055\u308c\u308b\u5834\u5408\u304c\u591a\u3044\u3002<\/li>\n\n\n\n<li><strong>\u72ec\u81ea\u5bc4\u4e0e\u7387 (\u3069\u304f\u3058\u304d\u3088\u308a\u3064)<\/strong>: \u5404\u5909\u6570\u304c\u30e2\u30c7\u30eb\u306b\u72ec\u81ea\u306b\u5bc4\u4e0e\u3059\u308b\u5272\u5408\u3068\u3044\u3046\u610f\u5473\u5408\u3044\u3067\u4f7f\u308f\u308c\u308b\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u3053\u308c\u3089\u306e\u8868\u8a18\u306f\u3001\u6587\u8108\u306b\u3088\u3063\u3066\u4f7f\u3044\u5206\u3051\u3089\u308c\u305f\u308a\u3001\u3042\u308b\u3044\u306f\u540c\u3058\u610f\u5473\u3067\u4f7f\u308f\u308c\u305f\u308a\u3059\u308b\u3053\u3068\u304c\u3042\u308b\u3002<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\u5177\u4f53\u4f8b\u3068R\u3067\u306e\u8a08\u7b97\u3001\u7d50\u679c\u306e\u89e3\u91c8<\/h2>\n\n\n\n<p>\u5177\u4f53\u4f8b\u3068\u3057\u3066\u3001\u300c\u5b66\u529b\uff08$Y$\uff09\u300d\u300c\u52c9\u5f37\u6642\u9593\uff08$X_1$\uff09\u300d\u300c\u7761\u7720\u6642\u9593\uff08$X_2$\uff09\u300d\u300c\u587e\u306e\u6709\u7121\uff08$X_3$\uff09\u300d\u3068\u3044\u30464\u3064\u306e\u5909\u6570\u304c\u3042\u308b\u72b6\u6cc1\u3092\u8003\u3048\u308b\u3002<\/p>\n\n\n\n<p>\u3053\u3053\u3067\u3001\u300c\u5b66\u529b\u300d\u3068\u300c\u52c9\u5f37\u6642\u9593\u300d\u306e\u9593\u306e\u95a2\u4fc2\u6027\u304b\u3089\u300c\u7761\u7720\u6642\u9593\u300d\u3068\u300c\u587e\u306e\u6709\u7121\u300d\u306e\u5f71\u97ff\u3092\u53d6\u308a\u9664\u3044\u305f\u4e0a\u3067\u306e\u7d14\u7c8b\u306a\u95a2\u4fc2\u6027\u3001\u3064\u307e\u308a\u300c\u504f\u76f8\u95a2\u306e\u4e8c\u4e57\u300d\u3092\u8a08\u7b97\u3057\u3066\u307f\u308b\u3002<\/p>\n\n\n\n<p><strong>R\u3067\u306e\u8a08\u7b97\u4f8b<\/strong><\/p>\n\n\n\n<p>R\u3067\u306f\u3001<code>ppcor<\/code> \u30d1\u30c3\u30b1\u30fc\u30b8\u3092\u7528\u3044\u308b\u3068\u504f\u76f8\u95a2\u3092\u7c21\u5358\u306b\u8a08\u7b97\u3067\u304d\u308b\u3002\u307e\u305f\u3001<code>lm<\/code> \u95a2\u6570\u3092\u7528\u3044\u305f\u56de\u5e30\u5206\u6790\u306e\u7d50\u679c\u304b\u3089\u3001\u9593\u63a5\u7684\u306b\u504f\u76f8\u95a2\u306e\u4e8c\u4e57\u3092\u7406\u89e3\u3059\u308b\u3053\u3068\u3082\u53ef\u80fd\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<p>\u307e\u305a\u3001\u30b5\u30f3\u30d7\u30eb\u30c7\u30fc\u30bf\u3092\u4f5c\u6210\u3059\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code># \u5fc5\u8981\u306a\u30d1\u30c3\u30b1\u30fc\u30b8\u3092\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\uff08\u521d\u56de\u306e\u307f\uff09\n# install.packages(\"ppcor\")\n\n# \u30e9\u30a4\u30d6\u30e9\u30ea\u306e\u8aad\u307f\u8fbc\u307f\nlibrary(ppcor)\n\n# \u30b5\u30f3\u30d7\u30eb\u30c7\u30fc\u30bf\u306e\u4f5c\u6210\nset.seed(123)\ndf &lt;- data.frame(\n  gakuryoku = round(rnorm(100, 60, 10)),\n  benkyo_jikan = round(rnorm(100, 5, 2)),\n  suimin_jikan = round(rnorm(100, 7, 1.5)),\n  juku_umu = sample(c(0, 1), 100, replace = TRUE)\n)\n\n# \u5b66\u529b\u3068\u52c9\u5f37\u6642\u9593\u306b\u306f\u6b63\u306e\u76f8\u95a2\u3001\u7761\u7720\u6642\u9593\u306b\u3082\u6b63\u306e\u76f8\u95a2\u3001\u587e\u306e\u6709\u7121\u306b\u3082\u6b63\u306e\u76f8\u95a2\u304c\u3042\u308b\u3088\u3046\u306b\u8abf\u6574\ndf$gakuryoku &lt;- round(df$gakuryoku + df$benkyo_jikan * 3 + df$suimin_jikan * 2 + df$juku_umu * 5)\ndf$benkyo_jikan &lt;- round(df$benkyo_jikan + df$suimin_jikan * 0.5) # \u52c9\u5f37\u6642\u9593\u3068\u7761\u7720\u6642\u9593\u306b\u3082\u76f8\u95a2\u3092\u6301\u305f\u305b\u308b<\/code><\/pre>\n\n\n\n<p>\u6b21\u306b\u3001\u504f\u76f8\u95a2\u3092\u8a08\u7b97\u3059\u308b\u3002<code>pcor.test<\/code> \u95a2\u6570\u3092\u4f7f\u7528\u3059\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code># \u5b66\u529b\u3068\u52c9\u5f37\u6642\u9593\u306e\u504f\u76f8\u95a2\uff08\u7761\u7720\u6642\u9593\u3068\u587e\u306e\u6709\u7121\u3092\u8abf\u6574\uff09\npcor_result &lt;- pcor.test(df$gakuryoku, df$benkyo_jikan, list(df$suimin_jikan, df$juku_umu))\nprint(pcor_result)\n\n# \u504f\u76f8\u95a2\u306e\u4e8c\u4e57\nsquared_pcor &lt;- pcor_result$estimate^2\nprint(paste(\"\u5b66\u529b\u3068\u52c9\u5f37\u6642\u9593\u306e\u504f\u76f8\u95a2\u306e\u4e8c\u4e57:\", round(squared_pcor, 4)))<\/code><\/pre>\n\n\n\n<p>\u5b9f\u884c\u7d50\u679c\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>> # \u5b66\u529b\u3068\u52c9\u5f37\u6642\u9593\u306e\u504f\u76f8\u95a2\uff08\u7761\u7720\u6642\u9593\u3068\u587e\u306e\u6709\u7121\u3092\u8abf\u6574\uff09\n> pcor_result &lt;- pcor.test(df$gakuryoku, df$benkyo_jikan, list(df$suimin_jikan, df$juku_umu))\n> print(pcor_result)\n   estimate     p.value statistic   n gp  Method\n1 0.5020364 1.38928e-07  5.687636 100  2 pearson\n> # \u504f\u76f8\u95a2\u306e\u4e8c\u4e57\n> squared_pcor &lt;- pcor_result$estimate^2\n> print(paste(\"\u5b66\u529b\u3068\u52c9\u5f37\u6642\u9593\u306e\u504f\u76f8\u95a2\u306e\u4e8c\u4e57:\", round(squared_pcor, 4)))\n&#91;1] \"\u5b66\u529b\u3068\u52c9\u5f37\u6642\u9593\u306e\u504f\u76f8\u95a2\u306e\u4e8c\u4e57: 0.252\"<\/code><\/pre>\n\n\n\n<p><strong>\u7d50\u679c\u306e\u89e3\u91c8<\/strong><\/p>\n\n\n\n<p>\u4e0a\u8a18\u306eR\u30b3\u30fc\u30c9\u3092\u5b9f\u884c\u3059\u308b\u3068\u3001<code>pcor_result<\/code> \u306b\u504f\u76f8\u95a2\u4fc2\u6570\u3068p\u5024\u304c\u8868\u793a\u3055\u308c\u308b\u3002\u305d\u3057\u3066 <code>squared_pcor<\/code> \u306b\u504f\u76f8\u95a2\u306e\u4e8c\u4e57\u306e\u5024\u304c\u8868\u793a\u3055\u308c\u308b\u3002<\/p>\n\n\n\n<p>\u4eca\u56de\u306e\u7d50\u679c\u3067\u306f\u3001<code>\u5b66\u529b\u3068\u52c9\u5f37\u6642\u9593\u306e\u504f\u76f8\u95a2\u306e\u4e8c\u4e57: 0.252<\/code> \u3067\u3042\u308b\u3002\u3053\u308c\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u89e3\u91c8\u3067\u304d\u308b\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u300c\u7761\u7720\u6642\u9593\u300d\u3068\u300c\u587e\u306e\u6709\u7121\u300d\u306e\u5f71\u97ff\u3092\u7d71\u8a08\u7684\u306b\u53d6\u308a\u9664\u3044\u305f\u4e0a\u3067\u3001<strong>\u300c\u5b66\u529b\u300d\u306e\u5206\u6563\u306e\u7d0425.2%\u304c\u300c\u52c9\u5f37\u6642\u9593\u300d\u306b\u3088\u3063\u3066\u8aac\u660e\u3055\u308c\u308b<\/strong>\u3001\u3068\u3044\u3046\u3053\u3068\u3092\u610f\u5473\u3059\u308b\u3002<\/li>\n\n\n\n<li>\u3064\u307e\u308a\u3001\u4ed6\u306e\u8981\u56e0\uff08\u3053\u306e\u5834\u5408\u306f\u7761\u7720\u6642\u9593\u3068\u587e\u306e\u6709\u7121\uff09\u306e\u5f71\u97ff\u3092\u8003\u616e\u3057\u3066\u3082\u3001\u3084\u306f\u308a\u52c9\u5f37\u6642\u9593\u306f\u5b66\u529b\u306b\u5bfe\u3057\u3066\u72ec\u81ea\u306e\u3001\u305d\u3057\u3066\u7121\u8996\u3067\u304d\u306a\u3044\u5bc4\u4e0e\u3092\u3057\u3066\u3044\u308b\u3001\u3068\u3044\u3046\u3053\u3068\u304c\u793a\u5506\u3055\u308c\u308b\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u91cd\u56de\u5e30\u5206\u6790\u306e\u6587\u8108\u3067\u8003\u3048\u308b\u5834\u5408\u306f\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u78ba\u8a8d\u3059\u308b\u3053\u3068\u3082\u3067\u304d\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code># \u30e2\u30c7\u30eb1\uff1a\u7761\u7720\u6642\u9593\u3068\u587e\u306e\u6709\u7121\u306e\u307f\u3067\u5b66\u529b\u3092\u4e88\u6e2c\nmodel1 &lt;- lm(gakuryoku ~ suimin_jikan + juku_umu, data = df)\nsummary(model1)\nr_squared_model1 &lt;- summary(model1)$r.squared\nprint(paste(\"Model1\u306eR^2:\", round(r_squared_model1, 4)))\n\n# \u30e2\u30c7\u30eb2\uff1a\u52c9\u5f37\u6642\u9593\u3092\u8ffd\u52a0\u3057\u3066\u5b66\u529b\u3092\u4e88\u6e2c\nmodel2 &lt;- lm(gakuryoku ~ suimin_jikan + juku_umu + benkyo_jikan, data = df)\nsummary(model2)\nr_squared_model2 &lt;- summary(model2)$r.squared\nprint(paste(\"Model2\u306eR^2:\", round(r_squared_model2, 4)))\n\n# \u6c7a\u5b9a\u4fc2\u6570\u306e\u5897\u5206\uff08\u3053\u308c\u304c\u52c9\u5f37\u6642\u9593\u306e\u504f\u76f8\u95a2\u306e\u4e8c\u4e57\u3068\u307b\u307c\u7b49\u3057\u304f\u306a\u308b\uff09\ndelta_r_squared &lt;- r_squared_model2 - r_squared_model1\nprint(paste(\"\u6c7a\u5b9a\u4fc2\u6570\u306e\u5897\u5206:\", round(delta_r_squared, 4)))<\/code><\/pre>\n\n\n\n<p>\u5b9f\u884c\u7d50\u679c\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>> # \u6c7a\u5b9a\u4fc2\u6570\u306e\u5897\u5206\uff08\u3053\u308c\u304c\u52c9\u5f37\u6642\u9593\u306e\u504f\u76f8\u95a2\u306e\u4e8c\u4e57\u3068\u307b\u307c\u7b49\u3057\u304f\u306a\u308b\uff09\n> delta_r_squared &lt;- r_squared_model2 - r_squared_model1\n> print(paste(\"\u6c7a\u5b9a\u4fc2\u6570\u306e\u5897\u5206:\", round(delta_r_squared, 4)))\n&#91;1] \"\u6c7a\u5b9a\u4fc2\u6570\u306e\u5897\u5206: 0.2318\"<\/code><\/pre>\n\n\n\n<p>\u3053\u306e <code>delta_r_squared<\/code> \u306e\u5024\u304c\u3001\u5148\u307b\u3069\u8a08\u7b97\u3057\u305f\u504f\u76f8\u95a2\u306e\u4e8c\u4e57\u306e\u5024\u3068\u975e\u5e38\u306b\u8fd1\u3044\u5024\u306b\u306a\u308b\u306f\u305a\u3067\u3042\u308b\u3002\u3053\u308c\u306f\u3001\u504f\u76f8\u95a2\u306e\u4e8c\u4e57\u304c\u300c\u4ed6\u306e\u5909\u6570\u3092\u7d71\u5236\u3057\u305f\u4e0a\u3067\u306e\u3001\u7279\u5b9a\u306e\u5909\u6570\u304c\u6301\u3064\u8ffd\u52a0\u7684\u306a\u8aac\u660e\u529b\u300d\u3092\u7aef\u7684\u306b\u8868\u3057\u3066\u3044\u308b\u3053\u3068\u3092\u793a\u3059\u3002<\/p>\n\n\n\n<p class=\"has-border 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class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 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