{"id":1332,"date":"2023-07-26T20:21:26","date_gmt":"2023-07-26T20:21:26","guid":{"rendered":"https:\/\/statorials.org\/ja\/r-%e3%81%ae%e5%8a%a0%e9%87%8d%e6%9c%80%e5%b0%8f%e4%ba%8c%e4%b9%97\/"},"modified":"2023-07-26T20:21:26","modified_gmt":"2023-07-26T20:21:26","slug":"r-%e3%81%ae%e5%8a%a0%e9%87%8d%e6%9c%80%e5%b0%8f%e4%ba%8c%e4%b9%97","status":"publish","type":"post","link":"https:\/\/statorials.org\/ja\/r-%e3%81%ae%e5%8a%a0%e9%87%8d%e6%9c%80%e5%b0%8f%e4%ba%8c%e4%b9%97\/","title":{"rendered":"R \u3067\u52a0\u91cd\u6700\u5c0f\u4e8c\u4e57\u56de\u5e30\u3092\u5b9f\u884c\u3059\u308b\u65b9\u6cd5"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/ja\/\u7dda\u5f62\u56de\u5e30\u306e\u4eee\u5b9a\/\" target=\"_blank\" rel=\"noopener\">\u7dda\u5f62\u56de\u5e30\u306e\u91cd\u8981\u306a\u524d\u63d0<\/a>\u306e 1 \u3064\u306f\u3001\u4e88\u6e2c\u5909\u6570\u306e\u5404\u30ec\u30d9\u30eb\u3067<a href=\"https:\/\/statorials.org\/ja\/\u6b8b\u57fa\/\" target=\"_blank\" rel=\"noopener\">\u6b8b<\/a>\u5dee\u304c\u7b49\u3057\u3044\u5206\u6563\u3067\u5206\u5e03\u3057\u3066\u3044\u308b\u3068\u3044\u3046\u3053\u3068\u3067\u3059\u3002\u3053\u306e\u4eee\u5b9a\u306f<strong>\u7b49\u5206\u6563\u6027<\/strong>\u3068\u3057\u3066\u77e5\u3089\u308c\u3066\u3044\u307e\u3059\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u3053\u306e\u4eee\u5b9a\u304c\u5c0a\u91cd\u3055\u308c\u306a\u3044\u5834\u5408\u3001\u6b8b\u5dee\u306b<a href=\"https:\/\/statorials.org\/ja\/\u4e0d\u5747\u4e00\u5206\u6563\u6027\u56de\u5e30\/\" target=\"_blank\" rel=\"noopener\">\u4e0d\u5747\u4e00\u5206\u6563\u6027\u304c<\/a>\u5b58\u5728\u3059\u308b\u3068\u8a00\u308f\u308c\u307e\u3059\u3002\u3053\u308c\u304c\u8d77\u3053\u308b\u3068\u3001\u56de\u5e30\u7d50\u679c\u306f\u4fe1\u983c\u3067\u304d\u306a\u304f\u306a\u308a\u307e\u3059\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u3053\u306e\u554f\u984c\u3092\u89e3\u6c7a\u3059\u308b 1 \u3064\u306e\u65b9\u6cd5\u306f\u3001<strong>\u91cd\u307f\u4ed8\u304d\u6700\u5c0f\u4e8c\u4e57\u56de\u5e30<\/strong>\u3092\u4f7f\u7528\u3059\u308b\u3053\u3068\u3067\u3059\u3002\u3053\u308c\u306f\u3001\u8aa4\u5dee\u5206\u6563\u304c\u5c0f\u3055\u3044<a href=\"https:\/\/statorials.org\/ja\/\u7d71\u8a08\u306b\u304a\u3051\u308b\u89b3\u5bdf\/\" target=\"_blank\" rel=\"noopener\">\u89b3\u6e2c\u5024<\/a>\u306b\u306f\u3001\u3088\u308a\u5927\u304d\u306a\u8aa4\u5dee\u5206\u6563\u3092\u6301\u3064\u89b3\u6e2c\u5024\u3068\u6bd4\u8f03\u3057\u3066\u3088\u308a\u591a\u304f\u306e\u60c5\u5831\u304c\u542b\u307e\u308c\u308b\u305f\u3081\u3001\u3088\u308a\u591a\u304f\u306e\u91cd\u307f\u3092\u53d7\u3051\u53d6\u308b\u3088\u3046\u306b\u89b3\u6e2c\u5024\u306b\u91cd\u307f\u3092\u5272\u308a\u5f53\u3066\u307e\u3059\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u3053\u306e\u30c1\u30e5\u30fc\u30c8\u30ea\u30a2\u30eb\u3067\u306f\u3001R \u3067\u91cd\u307f\u4ed8\u304d\u6700\u5c0f\u4e8c\u4e57\u56de\u5e30\u3092\u5b9f\u884c\u3059\u308b\u65b9\u6cd5\u306e\u6bb5\u968e\u7684\u306a\u4f8b\u3092\u793a\u3057\u307e\u3059\u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u30b9\u30c6\u30c3\u30d7 1: \u30c7\u30fc\u30bf\u3092\u4f5c\u6210\u3059\u308b<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">\u6b21\u306e\u30b3\u30fc\u30c9\u306f\u300116 \u4eba\u306e\u5b66\u751f\u306e\u5b66\u7fd2\u6642\u9593\u6570\u3068\u5bfe\u5fdc\u3059\u308b\u8a66\u9a13\u306e\u30b9\u30b3\u30a2\u3092\u542b\u3080\u30c7\u30fc\u30bf \u30d5\u30ec\u30fc\u30e0\u3092\u4f5c\u6210\u3057\u307e\u3059\u3002<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong>df &lt;- data.frame(hours=c(1, 1, 2, 2, 2, 3, 4, 4, 4, 5, 5, 5, 6, 6, 7, 8),\n                 score=c(48, 78, 72, 70, 66, 92, 93, 75, 75, 80, 95, 97, 90, 96, 99, 99))\n<\/strong><\/pre>\n<h3><span style=\"color: #000000;\"><strong>\u30b9\u30c6\u30c3\u30d7 2: \u7dda\u5f62\u56de\u5e30\u3092\u5b9f\u884c\u3059\u308b<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">\u6b21\u306b\u3001 <strong>lm()<\/strong>\u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u3001\u4e88\u6e2c\u5909\u6570\u3068\u3057\u3066\u6642\u9593\u3092\u4f7f\u7528\u3057\u3001<a href=\"https:\/\/statorials.org\/ja\/\u5909\u6570\u306e\u8aac\u660e\u5fdc\u7b54\/\" target=\"_blank\" rel=\"noopener\">\u5fdc\u7b54\u5909\u6570<\/a>\u3068\u3057\u3066\u30b9\u30b3\u30a2\u3092\u4f7f\u7528\u3059\u308b<a href=\"https:\/\/statorials.org\/ja\/\u7dda\u5f62\u56de\u5e30-1\/\" target=\"_blank\" rel=\"noopener\">\u5358\u7d14\u306a\u7dda\u5f62\u56de\u5e30\u30e2\u30c7\u30eb<\/a>\u3092\u8fd1\u4f3c\u3057\u307e\u3059\u3002<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#fit simple linear regression model\n<\/span>model &lt;- lm(score ~ hours, data = df)\n\n<span style=\"color: #008080;\">#view summary of model\n<\/span>summary(model)\n\nCall:\nlm(formula = score ~ hours, data = df)\n\nResiduals:\n    Min 1Q Median 3Q Max \n-17,967 -5,970 -0.719 7,531 15,032 \n\nCoefficients:\n            Estimate Std. Error t value Pr(&gt;|t|)    \n(Intercept) 60,467 5,128 11,791 1.17e-08 ***\nhours 5,500 1,127 4,879 0.000244 ***\n---\nSignificant. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n\nResidual standard error: 9.224 on 14 degrees of freedom\nMultiple R-squared: 0.6296, Adjusted R-squared: 0.6032 \nF-statistic: 23.8 on 1 and 14 DF, p-value: 0.0002438\n<\/strong><\/pre>\n<h3><span style=\"color: #000000;\"><strong>\u30b9\u30c6\u30c3\u30d7 3: \u4e0d\u5747\u4e00\u5206\u6563\u6027\u3092\u30c6\u30b9\u30c8\u3059\u308b<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">\u6b21\u306b\u3001\u6b8b\u5dee\u3068\u8fd1\u4f3c\u5024\u306e\u30d7\u30ed\u30c3\u30c8\u3092\u4f5c\u6210\u3057\u3066\u3001\u4e0d\u5747\u4e00\u5206\u6563\u6027\u3092\u8996\u899a\u7684\u306b\u78ba\u8a8d\u3057\u307e\u3059\u3002<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#create residual vs. fitted plot\n<\/span>plot( <span style=\"color: #3366ff;\">fitted<\/span> (model), <span style=\"color: #3366ff;\">resid<\/span> (model), xlab=' <span style=\"color: #008000;\">Fitted Values<\/span> ', ylab=' <span style=\"color: #008000;\">Residuals<\/span> ')\n\n<span style=\"color: #008080;\">#add a horizontal line at 0 \n<\/span>abline(0,0)<\/strong> <\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-13025 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/wls1.png\" alt=\"\" width=\"429\" height=\"391\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p><span style=\"color: #000000;\">\u30b0\u30e9\u30d5\u304b\u3089\u3001\u6b8b\u5dee\u304c\u300c\u5186\u9310\u300d\u306e\u5f62\u72b6\u3092\u3057\u3066\u3044\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002\u6b8b\u5dee\u306f\u30b0\u30e9\u30d5\u5168\u4f53\u306b\u5747\u7b49\u306a\u5206\u6563\u3067\u5206\u5e03\u3057\u3066\u3044\u308b\u308f\u3051\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u4e0d\u5747\u4e00\u5206\u6563\u6027\u3092\u6b63\u5f0f\u306b\u30c6\u30b9\u30c8\u3059\u308b\u306b\u306f\u3001Breusch-Pagan \u30c6\u30b9\u30c8\u3092\u5b9f\u884c\u3067\u304d\u307e\u3059\u3002<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#load lmtest package\n<\/span><span style=\"color: #993300;\">library<\/span> (lmtest)\n\n<span style=\"color: #008080;\">#perform Breusch-Pagan test<\/span>\nbptest(model)\n\n\tstudentized Breusch-Pagan test\n\ndata: model\nBP = 3.9597, df = 1, p-value = 0.0466\n<\/strong><\/pre>\n<p> Breusch-Pagan \u691c\u5b9a\u3067\u306f\u3001<span style=\"color: #000000;\">\u6b21\u306e\u5e30\u7121\u4eee\u8aac\u3068\u5bfe\u7acb<\/span><span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/ja\/\u4eee\u8aac\u691c\u8a3c1\/\" target=\"_blank\" rel=\"noopener\">\u4eee\u8aac\u304c<\/a><\/span>\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002<\/p>\n<ul>\n<li><span style=\"color: #000000;\"><strong>\u5e30\u7121\u4eee\u8aac (H <sub>0<\/sub> ): \u7b49<\/strong>\u5206\u6563\u6027\u304c\u5b58\u5728\u3057\u307e\u3059 (\u6b8b\u5dee\u306f\u7b49\u5206\u6563\u3067\u5206\u5e03\u3057\u307e\u3059)<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong>\u5bfe\u7acb\u4eee\u8aac ( <sub>HA<\/sub> ):<\/strong>\u4e0d\u5747\u4e00\u5206\u6563\u304c\u5b58\u5728\u3057\u307e\u3059 (\u6b8b\u5dee\u306f\u7b49\u5206\u6563\u3067\u5206\u5e03\u3057\u3066\u3044\u307e\u305b\u3093)<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #000000;\">\u691c\u5b9a\u306e p \u5024\u306f<strong>0.0466<\/strong>\u3067\u3042\u308b\u305f\u3081\u3001\u5e30\u7121\u4eee\u8aac\u3092\u68c4\u5374\u3057\u3001\u3053\u306e\u30e2\u30c7\u30eb\u3067\u306f\u4e0d\u5747\u4e00\u5206\u6563\u6027\u304c\u554f\u984c\u3067\u3042\u308b\u3068\u7d50\u8ad6\u4ed8\u3051\u307e\u3059\u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u30b9\u30c6\u30c3\u30d7 4: \u52a0\u91cd\u6700\u5c0f\u4e8c\u4e57\u56de\u5e30\u3092\u5b9f\u884c\u3059\u308b<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">\u4e0d\u5747\u4e00\u5206\u6563\u6027\u304c\u5b58\u5728\u3059\u308b\u305f\u3081\u3001\u5206\u6563\u304c\u5c0f\u3055\u3044\u89b3\u6e2c\u5024\u304c\u3088\u308a\u591a\u304f\u306e\u91cd\u307f\u3092\u53d7\u3051\u53d6\u308b\u3088\u3046\u306b\u91cd\u307f\u3092\u8a2d\u5b9a\u3057\u3066\u3001\u91cd\u307f\u4ed8\u304d\u6700\u5c0f\u4e8c\u4e57\u6cd5\u3092\u5b9f\u884c\u3057\u307e\u3059\u3002<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #008080;\">#define weights to use\n<\/span>wt &lt;- 1 \/ lm( <span style=\"color: #3366ff;\">abs<\/span> (model$residuals) ~ model$fitted. <span style=\"color: #3366ff;\">values<\/span> )$fitted. <span style=\"color: #3366ff;\">values<\/span> ^2\n\n<span style=\"color: #008080;\">#perform weighted least squares regression\n<\/span>wls_model &lt;- lm(score ~ hours, data = df, weights=wt)\n\n<span style=\"color: #008080;\">#view summary of model\n<\/span>summary(wls_model)\n\nCall:\nlm(formula = score ~ hours, data = df, weights = wt)\n\nWeighted Residuals:\n    Min 1Q Median 3Q Max \n-2.0167 -0.9263 -0.2589 0.9873 1.6977 \n\nCoefficients:\n            Estimate Std. Error t value Pr(&gt;|t|)    \n(Intercept) 63.9689 5.1587 12.400 6.13e-09 ***\nhours 4.7091 0.8709 5.407 9.24e-05 ***\n---\nSignificant. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n\nResidual standard error: 1.199 on 14 degrees of freedom\nMultiple R-squared: 0.6762, Adjusted R-squared: 0.6531 \nF-statistic: 29.24 on 1 and 14 DF, p-value: 9.236e-05\n<\/strong><\/span><\/pre>\n<p><span style=\"color: #000000;\">\u7d50\u679c\u304b\u3089\u3001<em>\u6642\u9593<\/em>\u4e88\u6e2c\u5909\u6570\u306e\u4fc2\u6570\u63a8\u5b9a\u5024\u304c\u308f\u305a\u304b\u306b\u5909\u5316\u3057\u3001\u5168\u4f53\u7684\u306a\u30e2\u30c7\u30eb\u306e\u9069\u5408\u6027\u304c\u5411\u4e0a\u3057\u305f\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u52a0\u91cd\u6700\u5c0f\u4e8c\u4e57\u30e2\u30c7\u30eb\u306e\u6b8b\u5dee\u6a19\u6e96\u8aa4\u5dee\u306f<strong>1.199<\/strong>\u3067\u3059\u304c\u3001\u5143\u306e\u5358\u7d14\u7dda\u5f62\u56de\u5e30\u30e2\u30c7\u30eb\u306e\u6b8b\u5dee\u6a19\u6e96\u8aa4\u5dee\u306f<strong>9.224<\/strong>\u3067\u3059\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u3053\u308c\u306f\u3001\u91cd\u307f\u4ed8\u304d\u6700\u5c0f\u4e8c\u4e57\u30e2\u30c7\u30eb\u306b\u3088\u3063\u3066\u751f\u6210\u3055\u308c\u305f\u4e88\u6e2c\u5024\u304c\u3001\u5358\u7d14\u306a\u7dda\u5f62\u56de\u5e30\u30e2\u30c7\u30eb\u306b\u3088\u3063\u3066\u751f\u6210\u3055\u308c\u305f\u4e88\u6e2c\u5024\u3068\u6bd4\u8f03\u3057\u3066\u3001\u5b9f\u969b\u306e\u89b3\u6e2c\u5024\u306b\u306f\u308b\u304b\u306b\u8fd1\u3044\u3053\u3068\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u52a0\u91cd\u6700\u5c0f\u4e8c\u4e57\u30e2\u30c7\u30eb\u306e R \u4e8c\u4e57\u3082<strong>0.6762<\/strong>\u3067\u3059\u304c\u3001\u5143\u306e\u5358\u7d14\u7dda\u5f62\u56de\u5e30\u30e2\u30c7\u30eb\u306e R \u4e8c\u4e57\u306f<strong>0.6296<\/strong>\u3067\u3059\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u3053\u308c\u306f\u3001\u52a0\u91cd\u6700\u5c0f\u4e8c\u4e57\u30e2\u30c7\u30eb\u306e\u65b9\u304c\u3001\u5358\u7d14\u306a\u7dda\u5f62\u56de\u5e30\u30e2\u30c7\u30eb\u3088\u308a\u3082\u8a66\u9a13\u5f97\u70b9\u306e\u5206\u6563\u3092\u3088\u308a\u591a\u304f\u8aac\u660e\u3067\u304d\u308b\u3053\u3068\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u3053\u308c\u3089\u306e\u6e2c\u5b9a\u5024\u306f\u3001\u5358\u7d14\u306a\u7dda\u5f62\u56de\u5e30\u30e2\u30c7\u30eb\u3068\u6bd4\u8f03\u3057\u3066\u3001\u52a0\u91cd\u6700\u5c0f\u4e8c\u4e57\u30e2\u30c7\u30eb\u306e\u65b9\u304c\u30c7\u30fc\u30bf\u3078\u306e\u9069\u5408\u6027\u304c\u9ad8\u3044\u3053\u3068\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u8ffd\u52a0\u30ea\u30bd\u30fc\u30b9<\/strong><\/span><\/h3>\n<p><a href=\"https:\/\/statorials.org\/ja\/r-\u3066\u3099\u306e\u5358\u7d14\u306a\u7dda\u5f62\u56de\u5e30\/\" target=\"_blank\" rel=\"noopener\">R \u3067\u5358\u7d14\u306a\u7dda\u5f62\u56de\u5e30\u3092\u5b9f\u884c\u3059\u308b\u65b9\u6cd5<\/a><br \/><a href=\"https:\/\/statorials.org\/ja\/\u91cd\u7dda\u5f62\u56de\u5e30r\/\" target=\"_blank\" rel=\"noopener\">R \u3067\u91cd\u56de\u5e30\u3092\u5b9f\u884c\u3059\u308b\u65b9\u6cd5<\/a><br \/><a 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