{"id":1060,"date":"2023-07-27T19:30:41","date_gmt":"2023-07-27T19:30:41","guid":{"rendered":"https:\/\/statorials.org\/ja\/%e6%ae%8b%e7%95%99%e6%a8%99%e6%ba%96%e8%aa%a4%e5%b7%ae-r\/"},"modified":"2023-07-27T19:30:41","modified_gmt":"2023-07-27T19:30:41","slug":"%e6%ae%8b%e7%95%99%e6%a8%99%e6%ba%96%e8%aa%a4%e5%b7%ae-r","status":"publish","type":"post","link":"https:\/\/statorials.org\/ja\/%e6%ae%8b%e7%95%99%e6%a8%99%e6%ba%96%e8%aa%a4%e5%b7%ae-r\/","title":{"rendered":"R \u306e\u6b8b\u5dee\u6a19\u6e96\u8aa4\u5dee\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">R \u3067\u7dda\u5f62\u56de\u5e30\u30e2\u30c7\u30eb\u3092\u8fd1\u4f3c\u3059\u308b\u3068\u3001\u30e2\u30c7\u30eb\u306f\u6b21\u306e\u5f62\u5f0f\u306b\u306a\u308a\u307e\u3059\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\">Y = \u03b2 <sub>0<\/sub> + \u03b2 <sub>1<\/sub> X + \u2026 + \u03b2 <sub>i<\/sub><\/span><\/p>\n<p><span style=\"color: #000000;\">\u3053\u3053\u3067\u3001\u03f5 \u306f X \u304b\u3089\u72ec\u7acb\u3057\u305f\u8aa4\u5dee\u9805\u3067\u3059\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\">X \u3092\u3069\u306e\u3088\u3046\u306b\u4f7f\u7528\u3057\u3066 Y \u306e\u5024\u3092\u4e88\u6e2c\u3067\u304d\u308b\u304b\u306b\u95a2\u4fc2\u306a\u304f\u3001\u30e2\u30c7\u30eb\u306b\u306f\u5e38\u306b\u30e9\u30f3\u30c0\u30e0\u306a\u8aa4\u5dee\u304c\u5b58\u5728\u3057\u307e\u3059\u3002\u3053\u306e\u30e9\u30f3\u30c0\u30e0\u8aa4\u5dee\u306e\u5206\u6563\u3092\u6e2c\u5b9a\u3059\u308b 1 \u3064\u306e\u65b9\u6cd5\u306f\u3001<strong>\u6b8b\u5dee\u6a19\u6e96\u8aa4\u5dee<\/strong>\u3092\u4f7f\u7528\u3059\u308b\u3053\u3068\u3067\u3059\u3002\u3053\u308c\u306f\u3001\u6b8b\u5dee \u03f5 \u306e\u6a19\u6e96\u504f\u5dee\u3092\u6e2c\u5b9a\u3059\u308b\u65b9\u6cd5\u3067\u3059\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\">\u56de\u5e30\u30e2\u30c7\u30eb\u306e\u6b8b\u5dee\u6a19\u6e96\u8aa4\u5dee\u306f\u6b21\u306e\u3088\u3046\u306b\u8a08\u7b97\u3055\u308c\u307e\u3059\u3002<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>\u6b8b\u5dee\u6a19\u6e96\u8aa4\u5dee = \u221a <span style=\"border-top: 1px solid black;\">SS<sub>\u6b8b\u5dee<\/sub>\/ df<sub>\u6b8b\u5dee<\/sub><\/span><\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">\u91d1\uff1a<\/span><\/p>\n<ul>\n<li><span style=\"color: #000000;\"><strong><sub>\u6b8b\u5dee<\/sub>SS<\/strong> : \u6b8b\u5dee\u4e8c\u4e57\u548c\u3002<\/span><\/li>\n<li><span style=\"color: #000000;\"><strong><sub>\u6b8b\u5dee<\/sub>df<\/strong> : \u6b8b\u5dee\u81ea\u7531\u5ea6\u3002n \u2013 k \u2013 1 \u3068\u3057\u3066\u8a08\u7b97\u3055\u308c\u307e\u3059\u3002\u3053\u3053\u3067\u3001n = \u89b3\u6e2c\u5024\u306e\u5408\u8a08\u6570\u3001k = \u30e2\u30c7\u30eb \u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u306e\u5408\u8a08\u6570\u3067\u3059\u3002<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">R \u306e\u56de\u5e30\u30e2\u30c7\u30eb\u306e\u6b8b\u5dee\u6a19\u6e96\u8aa4\u5dee\u3092\u8a08\u7b97\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3067\u304d\u308b\u65b9\u6cd5\u306f 3 \u3064\u3042\u308a\u307e\u3059\u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u65b9\u6cd5 1: \u30e2\u30c7\u30eb\u306e\u6982\u8981\u3092\u5206\u6790\u3059\u308b<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">\u6b8b\u5dee\u6a19\u6e96\u8aa4\u5dee\u3092\u53d6\u5f97\u3059\u308b\u6700\u521d\u306e\u65b9\u6cd5\u306f\u3001\u5358\u7d14\u306b\u7dda\u5f62\u56de\u5e30\u30e2\u30c7\u30eb\u3092\u8fd1\u4f3c\u3057\u3001\u6b21\u306b<strong>summary()<\/strong>\u30b3\u30de\u30f3\u30c9\u3092\u4f7f\u7528\u3057\u3066\u30e2\u30c7\u30eb\u306e\u7d50\u679c\u3092\u53d6\u5f97\u3059\u308b\u3053\u3068\u3067\u3059\u3002\u6b21\u306b\u3001\u51fa\u529b\u306e\u4e0b\u90e8\u306b\u3042\u308b\u300c\u6b8b\u308a\u306e\u6a19\u6e96\u8aa4\u5dee\u300d\u3092\u63a2\u3057\u307e\u3059\u3002<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#load built-in <em>mtcars<\/em> dataset<\/span>\ndata(mtcars)\n\n<span style=\"color: #008080;\">#fit regression model\n<\/span>model &lt;- lm(mpg~disp+hp, data=mtcars)\n\n<span style=\"color: #008080;\">#view model summary\n<\/span>summary(model)\n\nCall:\nlm(formula = mpg ~ disp + hp, data = mtcars)\n\nResiduals:\n    Min 1Q Median 3Q Max \n-4.7945 -2.3036 -0.8246 1.8582 6.9363 \n\nCoefficients:\n             Estimate Std. Error t value Pr(&gt;|t|)    \n(Intercept) 30.735904 1.331566 23.083 &lt; 2nd-16 ***\navailable -0.030346 0.007405 -4.098 0.000306 ***\nhp -0.024840 0.013385 -1.856 0.073679 .  \n---\nSignificant. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n\nResidual standard error: <span style=\"color: #008000;\">3.127<\/span> on 29 degrees of freedom\nMultiple R-squared: 0.7482, Adjusted R-squared: 0.7309 \nF-statistic: 43.09 on 2 and 29 DF, p-value: 2.062e-09<\/strong><\/pre>\n<p><span style=\"color: #000000;\">\u6b8b\u5dee\u6a19\u6e96\u8aa4\u5dee\u304c<strong>3.127<\/strong>\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u65b9\u6cd5 2: \u5358\u7d14\u306a\u6570\u5f0f\u3092\u4f7f\u7528\u3059\u308b<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">\u6b8b\u5dee\u6a19\u6e96\u8aa4\u5dee (RSE) \u3092\u53d6\u5f97\u3059\u308b\u3082\u3046 1 \u3064\u306e\u65b9\u6cd5\u306f\u3001\u7dda\u5f62\u56de\u5e30\u30e2\u30c7\u30eb\u3092\u8fd1\u4f3c\u3057\u3001\u6b21\u306e\u5f0f\u3092\u4f7f\u7528\u3057\u3066 RSE \u3092\u8a08\u7b97\u3059\u308b\u3053\u3068\u3067\u3059\u3002<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong>sqrt( <span style=\"color: #3366ff;\">deviance<\/span> (model)\/df. <span style=\"color: #3366ff;\">residual<\/span> (model))\n<\/strong><\/pre>\n<p><span style=\"color: #000000;\">\u3053\u306e\u5f0f\u3092 R \u3067\u5b9f\u88c5\u3059\u308b\u65b9\u6cd5\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#load built-in <em>mtcars<\/em> dataset<\/span>\ndata(mtcars)\n\n<span style=\"color: #008080;\">#fit regression model\n<\/span>model &lt;- lm(mpg~disp+hp, data=mtcars)\n\n<span style=\"color: #008080;\">#calculate residual standard error\n<\/span>sqrt( <span style=\"color: #3366ff;\">deviance<\/span> (model)\/df. <span style=\"color: #3366ff;\">residual<\/span> (model))\n\n[1] 3.126601\n<\/strong><\/pre>\n<p><span style=\"color: #000000;\">\u6b8b\u5dee\u6a19\u6e96\u8aa4\u5dee\u304c<strong>3.126601<\/strong>\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u65b9\u6cd5 3: \u6bb5\u968e\u7684\u306a\u5f0f\u3092\u4f7f\u7528\u3059\u308b<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">\u6b8b\u5dee\u6a19\u6e96\u8aa4\u5dee\u3092\u53d6\u5f97\u3059\u308b\u3082\u3046 1 \u3064\u306e\u65b9\u6cd5\u306f\u3001\u7dda\u5f62\u56de\u5e30\u30e2\u30c7\u30eb\u3092\u8fd1\u4f3c\u3057\u3001\u6bb5\u968e\u7684\u306a\u30a2\u30d7\u30ed\u30fc\u30c1\u3092\u4f7f\u7528\u3057\u3066 RSE \u5f0f\u306e\u500b\u3005\u306e\u30b3\u30f3\u30dd\u30fc\u30cd\u30f3\u30c8\u3092\u8a08\u7b97\u3059\u308b\u3053\u3068\u3067\u3059\u3002<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#load built-in <em>mtcars<\/em> dataset<\/span>\ndata(mtcars)\n\n<span style=\"color: #008080;\">#fit regression model\n<\/span>model &lt;- lm(mpg~disp+hp, data=mtcars)\n\n<span style=\"color: #008080;\">#calculate the number of model parameters - 1\n<\/span>k=length(model$ <span style=\"color: #3366ff;\">coefficients<\/span> )-1\n\n<span style=\"color: #008080;\">#calculate sum of squared residuals<\/span>\nSSE=sum(model$ <span style=\"color: #3366ff;\">residuals<\/span> **2)\n\n<span style=\"color: #008080;\">#calculate total observations in dataset<\/span>\nn=length(model$ <span style=\"color: #3366ff;\">residuals<\/span> )\n\n<span style=\"color: #008080;\">#calculate residual standard error<\/span>\nsqrt(SSE\/(n-(1+k)))\n\n[1] 3.126601\n<\/strong><\/pre>\n<p><span style=\"color: #000000;\">\u6b8b\u5dee\u6a19\u6e96\u8aa4\u5dee\u304c<strong>3.126601<\/strong>\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002<\/span><\/p>\n<h3><span style=\"color: #000000;\"><strong>\u6b8b\u5dee\u6a19\u6e96\u8aa4\u5dee\u306e\u89e3\u91c8\u65b9\u6cd5<\/strong><\/span><\/h3>\n<p><span style=\"color: #000000;\">\u524d\u8ff0\u3057\u305f\u3088\u3046\u306b\u3001\u6b8b\u5dee\u6a19\u6e96\u8aa4\u5dee (RSE) \u306f\u3001\u56de\u5e30\u30e2\u30c7\u30eb\u306e\u6b8b\u5dee\u306e\u6a19\u6e96\u504f\u5dee\u3092\u6e2c\u5b9a\u3059\u308b\u65b9\u6cd5\u3067\u3059\u3002<\/span><\/p>\n<p> <span style=\"color: #000000;\">CSR \u5024\u304c\u4f4e\u3044\u307b\u3069\u3001\u30e2\u30c7\u30eb\u306f\u30c7\u30fc\u30bf\u3092\u3088\u308a\u9069\u5207\u306b\u9069\u5408\u3067\u304d\u307e\u3059 (\u305f\u3060\u3057\u3001 <a href=\"https:\/\/statorials.org\/ja\/\u6a5f\u68b0\u5b66\u7fd2\u306e\u904e\u5b66\u7fd2\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u904e\u5270\u9069\u5408<\/a>\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044)\u3002\u3053\u308c\u306f\u30012 \u3064\u4ee5\u4e0a\u306e\u30e2\u30c7\u30eb\u3092\u6bd4\u8f03\u3057\u3066\u3069\u306e\u30e2\u30c7\u30eb\u304c\u30c7\u30fc\u30bf\u306b\u6700\u3082\u9069\u5408\u3059\u308b\u304b\u3092\u5224\u65ad\u3059\u308b\u3068\u304d\u306b\u4f7f\u7528\u3059\u308b\u3068\u4fbf\u5229\u306a\u30e1\u30c8\u30ea\u30c3\u30af\u3068\u306a\u308a\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\/\u6b8b\u5dee\u6a19\u6e96\u8aa4\u5dee\u3092\u89e3\u91c8\u3059\u308b\u65b9\u6cd5\/\">\u6b8b\u5dee\u6a19\u6e96\u8aa4\u5dee\u306e\u89e3\u91c8\u65b9\u6cd5<\/a><br \/><a href=\"https:\/\/statorials.org\/ja\/\u91cd\u7dda\u5f62\u56de\u5e30r\/\" target=\"_blank\" rel=\"noopener noreferrer\">R \u3067\u91cd\u56de\u5e30\u3092\u5b9f\u884c\u3059\u308b\u65b9\u6cd5<\/a><br \/><a href=\"https:\/\/statorials.org\/ja\/r-\u3066\u3099\u30e2\u30c6\u3099\u30eb\u306e\u30cf\u309a\u30d5\u30a9\u30fc\u30de\u30f3\u30b9\u306e\u76f8\u4e92\u691c\u8a3c\u3092\u5b9f\u884c\u3059\u308b\u65b9\u6cd5\/\" target=\"_blank\" rel=\"noopener noreferrer\">R \u3067\u30e2\u30c7\u30eb\u306e\u30d1\u30d5\u30a9\u30fc\u30de\u30f3\u30b9\u3092\u76f8\u4e92\u691c\u8a3c\u3059\u308b\u65b9\u6cd5<\/a><br \/><a href=\"https:\/\/statorials.org\/ja\/r\u306e\u6a19\u6e96\u504f\u5dee\/\" target=\"_blank\" rel=\"noopener noreferrer\">R \u306e\u6a19\u6e96\u504f\u5dee\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>R \u3067\u7dda\u5f62\u56de\u5e30\u30e2\u30c7\u30eb\u3092\u8fd1\u4f3c\u3059\u308b\u3068\u3001\u30e2\u30c7\u30eb\u306f\u6b21\u306e\u5f62\u5f0f\u306b\u306a\u308a\u307e\u3059\u3002 Y = \u03b2 0 + \u03b2 1 X + \u2026 + \u03b2 i \u3053\u3053\u3067\u3001\u03f5 \u306f X \u304b\u3089\u72ec\u7acb\u3057\u305f\u8aa4\u5dee\u9805\u3067\u3059\u3002 X \u3092\u3069\u306e\u3088\u3046\u306b\u4f7f\u7528\u3057\u3066 Y \u306e\u5024\u3092\u4e88\u6e2c\u3067\u304d\u308b\u304b\u306b\u95a2\u4fc2\u306a\u304f [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[16],"tags":[],"class_list":["post-1060","post","type-post","status-publish","format-standard","hentry","category-16"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - 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