{"id":616,"date":"2023-11-12T08:09:33","date_gmt":"2023-11-11T23:09:33","guid":{"rendered":"https:\/\/bunseki-data.com\/r-onlinecourse\/?p=616"},"modified":"2023-11-12T08:33:16","modified_gmt":"2023-11-11T23:33:16","slug":"index-knit-md-2","status":"publish","type":"post","link":"https:\/\/bunseki-data.com\/r-onlinecourse\/2023\/11\/12\/index-knit-md-2\/","title":{"rendered":"\u91cd\u56de\u5e30\u5206\u6790\u306e\u30e2\u30c7\u30eb\u30c1\u30a7\u30c3\u30af\uff08\u7dda\u5f62\u6027\u306e\u78ba\u8a8d\uff09\u306e\u52c9\u5f37\u30e1\u30e2"},"content":{"rendered":"\n<pre class=\"wp-block-code\"><code>library(tidyverse)\nlibrary(gtsummary)<\/code><\/pre>\n\n\n\n<pre class=\"wp-block-code\"><code>#wordpress\u3067\u306e\u51fa\u529b\u3067gtsummary\u304c\u3046\u307e\u304f\u52d5\u304b\u306a\u304b\u3063\u305f\u305f\u3081\u3001\u30e2\u30c7\u30eb\u3092\u4e26\u3079\u308b\u81ea\u4f5c\u95a2\u6570\u3092\u4f5c\u6210\ncompare_models &lt;- function(models, labels){\n  procamod &lt;- function(amodel, alabel){\n    broom::tidy(amodel, conf.int = TRUE) |&gt; \n    mutate(across(c(estimate, conf.low, conf.high), ~{\n      scales::number(., accuracy = 0.01)\n    })) |&gt; \n    #mutate(p.value = scales::number(p.value, 0.0001)) |&gt; \n    mutate(res = str_glue(\"{estimate}({conf.low} - {conf.high})\")) |&gt; \n    select(term, res) |&gt; \n    rename(!!rlang::sym(alabel) := res)\n  }\n\n  map2(models, labels, procamod) |&gt; \n    reduce(~full_join(.x,.y,by=\"term\"))\n}<\/code><\/pre>\n\n\n\n<h2 class=\"wp-block-heading\">\u306f\u3058\u3081\u306b<\/h2>\n\n\n\n<p>\u4ed5\u4e8b\u95a2\u4fc2\u3067\u3001\u91cd\u56de\u5e30\u5206\u6790\u3092\u7523\u696d\u4fdd\u5065\u8077\u3084\u4eba\u4e8b\u90e8\u306e\u8208\u5473\u304c\u3042\u308b\u4eba\u306b\u6559\u3048\u305f\u3044\u3068\u601d\u3044\u7acb\u3061\uff08\u672c\u696d\u306f\u5b9f\u306f\uff01\uff1f\u7523\u696d\u533b\u3067\u3059\uff09\u3001\u6539\u3081\u3066\u91cd\u56de\u5e30\u5206\u6790\u3092\u3061\u3083\u3093\u3068\u3084\u308b\u65b9\u6cd5\u3092\u52c9\u5f37\u3057\u305f\u306a\u304b\u3067\u3001\u30e2\u30c7\u30eb\u30c1\u30a7\u30c3\u30af\u306e\u65b9\u6cd5\u306b\u3064\u3044\u3066\u5b9f\u306f\u305d\u3093\u306a\u306b\u6df1\u304f\u7406\u89e3\u3067\u304d\u3066\u3044\u306a\u3044\u3068\u3044\u3046\u3053\u3068\u306b\u6c17\u3065\u304d\u3001\u52c9\u5f37\u3057\u305f\u3053\u3068\u3092\u307e\u3068\u3081\u3066\u307f\u307e\u3057\u305f\u3002\u3053\u306e\u8a18\u4e8b\u3001\u304b\u306a\u308a\u52c9\u5f37\u30ce\u30fc\u30c8\u3068\u304b\u30e1\u30e2\u306b\u8fd1\u3044\u5f62\u306a\u306e\u3092\u3054\u7559\u610f\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n\n<p>\u5168\u4f53\u50cf\u3068\u3057\u3066\u306f\u3001<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u4eee\u5b9a\u306e\u7f85\u5217\u3068\u6559\u79d1\u66f8\u306e\u8aac\u660e\u306e\u629c\u7c8b<\/li>\n\n\n\n<li>R\u3067\u30c7\u30fc\u30bf\u3068\u30e2\u30c7\u30eb\u3092\u4f5c\u6210\u3059\u308b<\/li>\n\n\n\n<li>car\u30d1\u30c3\u30b1\u30fc\u30b8\u306eDiagnosticPlot\u3092\u8abf\u3079\u305f\u5185\u5bb9\u306e\u8a18\u8f09<\/li>\n\n\n\n<li>\u8abf\u3079\u305f\u5185\u5bb9\u304b\u3089\u3001ggplot2\u3067car::residualPlots, car::avPlots, car::crPlots\u306e\uff13\u3064\u306e\u30d7\u30ed\u30c3\u30c8\u3092\u518d\u73fe\u3059\u308b\u95a2\u6570\u3092\u4f5c\u6210<\/li>\n\n\n\n<li>\u4f5c\u6210\u3057\u305f\u30c7\u30fc\u30bf\u306b\u5bfe\u3057\u3066car\u30d1\u30c3\u30b1\u30fc\u30b8\u306eDiagnostic Plot\u3068\u81ea\u4f5c\u95a2\u6570\u3092\u9069\u5fdc\u3057\u3066\u3001\u30e2\u30c7\u30eb\u3092\u9593\u9055\u3048\u3066\u6307\u5b9a\u3057\u305f\u5834\u5408\u306b\u5404\u30d7\u30ed\u30c3\u30c8\u304c\u3069\u306e\u3088\u3046\u306a\u3075\u308b\u307e\u3044\u3092\u3059\u308b\u304b\u3092\u898b\u3066\u307f\u308b\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u3068\u3044\u3046\u6d41\u308c\u3067\u3059\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u8b1d\u8f9e<\/h2>\n\n\n\n<p>\u3053\u306e\u8a18\u4e8b\u306f\u3001\u79c1\u304cTwiter\u306b\u3064\u3076\u3084\u3044\u305f\u7591\u554f\u306b\u591a\u304f\u306e\u65b9\u304c\u304a\u8fd4\u4e8b\u3044\u305f\u3060\u3044\u305f\u3053\u3068\u304b\u3089\u3001\u4f5c\u6210\u3057\u3088\u3046\u3068\u8003\u3048\u307e\u3057\u305f\u3002\u30b3\u30e1\u30f3\u30c8\u3092\u3044\u305f\u3060\u3044\u305f\u5168\u3066\u306e\u65b9\u306b\u6df1\u3044\u611f\u8b1d\u3092\u7533\u3057\u4e0a\u3052\u307e\u3059\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u53c2\u8003\u56f3\u66f8<\/h2>\n\n\n\n<p>\u3053\u306e\u8a18\u4e8b\u3092\u66f8\u304f\u306b\u3042\u305f\u308a\u3001\u6b21\u306e\u6559\u79d1\u66f8\u3092\u53c2\u8003\u306b\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>\u9ad8\u6a4b \u5c06\u5b9c(2022)\u300e\u7d71\u8a08\u7684\u56e0\u679c\u63a8\u8ad6\u306e\u7406\u8ad6\u3068\u5b9f\u88c5\u2015\u6f5c\u5728\u7684\u7d50\u679c\u5909\u6570\u3068\u6b20\u6e2c\u30c7\u30fc\u30bf\u2015\u300f\u5171\u7acb\u51fa\u7248<\/p>\n\n\n\n<p>Fox, John, Sanford Weisberg. An R Companion to Applied Regression. Third edition. Los Angeles: SAGE, 2019<\/p>\n\n\n\n<p>Jeffrey M Wooldridge. Introductory EconomEtrIcs A modern Approach 7e<\/p>\n\n\n\n<p>Fox, John, Regression Diagnostics An Introduction Second Edition.<\/p>\n<\/blockquote>\n\n\n\n<p>\u3068\u304f\u306b\u3001\u9ad8\u6a4b\u5148\u751f\u306e\u672c\u3001\u5165\u624b\u3057\u3066\u3044\u305f\u306e\u306b\u3001\u6700\u521d\u306e\u90e8\u5206\u3092\u8aad\u307f\u98db\u3070\u3057\u3066\u3044\u3066\u3001\u53cd\u7701\u3057\u3066\u3044\u307e\u3059\u3002\u3082\u306e\u3059\u3054\u304f\u5206\u304b\u308a\u3084\u3059\u3044\u672c\u306a\u306e\u3067\u3001R User\u3067\u306a\u304f\u3066\u3082\u30aa\u30b9\u30b9\u30e1\u3067\u3059\u3002<\/p>\n\n\n\n<iframe sandbox=\"allow-popups allow-scripts allow-modals allow-forms allow-same-origin\" style=\"width:120px;height:240px;\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"no\" frameborder=\"0\" src=\"\/\/rcm-fe.amazon-adsystem.com\/e\/cm?lt1=_blank&#038;bc1=000000&#038;IS2=1&#038;bg1=FFFFFF&#038;fc1=000000&#038;lc1=0000FF&#038;t=ma06063-22&#038;language=ja_JP&#038;o=9&#038;p=8&#038;l=as4&#038;m=amazon&#038;f=ifr&#038;ref=as_ss_li_til&#038;asins=4320112458&#038;linkId=a9d5f35a296e6742f61a8ce9df19c48e\"><\/iframe>\n\n\n\n<p><iframe style=\"width: 120px; height: 240px;\" sandbox=\"allow-popups allow-scripts allow-modals allow-forms allow-same-origin\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"no\" frameborder=\"0\" src=\"\/\/rcm-fe.amazon-adsystem.com\/e\/cm?lt1=_blank&amp;bc1=000000&amp;IS2=1&amp;bg1=FFFFFF&amp;fc1=000000&amp;lc1=0000FF&amp;t=ma06063-22&amp;language=ja_JP&amp;o=9&amp;p=8&amp;l=as4&amp;m=amazon&amp;f=ifr&amp;ref=as_ss_li_til&amp;asins=4320112458&amp;linkId=a9d5f35a296e6742f61a8ce9df19c48e\"><\/iframe><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u30e2\u30c7\u30eb\u30c1\u30a7\u30c3\u30af<\/h2>\n\n\n\n<p>\u91cd\u56de\u5e30\u5206\u6790\u3092\u884c\u3046\u969b\u306b\u3001\u9069\u5207\u306a\u5206\u6790\u304c\u884c\u3048\u3066\u3044\u308b\u304b\u3092\u8abf\u3079\u308b\u305f\u3081\u306e\u300c\u30e2\u30c7\u30eb\u30c1\u30a7\u30c3\u30af\u300d\u3092\u884c\u3046\u3053\u3068\u306f\u91cd\u8981\u3067\u3059\u3002\u3053\u306e\u8a18\u4e8b\u3067\u306f\u3001\u91cd\u56de\u5e30\u5206\u6790\u304c\u9069\u5fdc\u3057\u3066\u3044\u308b\u30c7\u30fc\u30bf\u306b\u5bfe\u3057\u3066\u3001\u9069\u5207\u306b\u7528\u3044\u308b\u3053\u3068\u304c\u3067\u304d\u3066\u3044\u308b\u304b\u3001\u7279\u306b\u7dda\u5f62\u6027\u306e\u78ba\u8a8d\u306b\u3064\u3044\u3066\u3092\uff32\u3067\u8abf\u3079\u308b\u65b9\u6cd5\u3092\u89e3\u8aac\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u8868\u8a18<\/h2>\n\n\n\n<p>\u6b21\u306e\u3088\u3046\u306a\u30c7\u30fc\u30bf$n$\u500b\uff08\u884c\uff09\u306e\u30b5\u30f3\u30d7\u30eb\u3092\u542b\u3080\u30c7\u30fc\u30bf\u304c\u3042\u308b\u3068\u3057\u3066\u3001$i$\u756a\uff08\u884c\uff09\u76ee\u306e\u76ee\u7684\u5909\u6570\u3092$y<em>i$\u3068\u8868\u8a18\u3057\u307e\u3059\u3002$k$\u500b\u306e\u8aac\u660e\u5909\u6570\u304c\u3042\u308b\u3068\u3057\u3066\u3001$i$\u884c\u76ee\u306e\u8aac\u660e\u5909\u6570\u3092\u3001$x<\/em>{i1}, x<em>{i2}, \\cdots x<\/em>{ik}$\u306e\u3088\u3046\u306b\u8868\u8a18\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>$Y$<\/td><td>$X_1$<\/td><td>$X_2$<\/td><td>$\\cdots$<\/td><td>$X_k$<\/td><\/tr><tr><td>$y_1$<\/td><td>$x_{11}$<\/td><td>$x_{12}$<\/td><td>$\\cdots$<\/td><td>$x_{1k}$<\/td><\/tr><tr><td>$y_1$<\/td><td>$x_{21}$<\/td><td>$x_{22}$<\/td><td>$\\cdots$<\/td><td>$x_{2k}$<\/td><\/tr><tr><td>$\\vdots$<\/td><td>$\\vdots$<\/td><td>$\\vdots$<\/td><td>$\\ddots$<\/td><td>$\\vdots$<\/td><\/tr><tr><td>$y_i$<\/td><td>$x_{i1}$<\/td><td>$x_{i2}$<\/td><td>$\\cdots$<\/td><td>$x_{ik}$<\/td><\/tr><tr><td>$\\vdots$<\/td><td>$\\vdots$<\/td><td>$\\vdots$<\/td><td>$\\ddots$<\/td><td>$\\vdots$<\/td><\/tr><tr><td>$y_n$<\/td><td>$x_{n1}$<\/td><td>$x_{n2}$<\/td><td>$\\cdots$<\/td><td>$x_{nk}$<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">\u91cd\u56de\u5e30\u5206\u6790\u306eAssumption\uff08\u4eee\u5b9a\uff09<\/h2>\n\n\n\n<p>\u91cd\u56de\u5e30\u5206\u6790\u306e\u30e2\u30c7\u30eb\uff1a<\/p>\n\n\n\n<p>\\[y_i = \\beta_0 + \\beta_<em>1_x<\/em>{i1} + \\cdots + \\beta_<em>k_x<\/em>{ik} + \\epsilon_i\\]<\/p>\n\n\n\n<p>\u306b\u304a\u3044\u3066\u3001\u8272\u3005\u306a\u4eee\u5b9a\u304c\u304a\u304b\u308c\u3066\u3044\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u4eee\u5b9a\u306f\u7d50\u69cb\u5f37\u3044\u4eee\u5b9a\u306a\u306e\u3067\u3001\u30e2\u30c7\u30eb\u3092\u4f5c\u6210\u3057\u305f\u3068\u304d\u306b\u3001\u305d\u308c\u3092\u691c\u8a3c\u3059\u308b\u5fc5\u8981\u304c\u3067\u3066\u304d\u307e\u3059\u3002\u4eee\u5b9a\u306f\u3001\u9ad8\u6a4b\u5148\u751f\u306e\u6559\u79d1\u66f8\u3068Wooldridge\u5148\u751f\u306e\u6559\u79d1\u66f8\u304b\u3089\u629c\u7c8b\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u4eee\u5b9a\uff11\uff1a\u8aa4\u5dee\u9805\u306e\u671f\u5f85\u5024\u30bc\u30ed<\/li>\n\n\n\n<li>\u4eee\u5b9a\uff12\uff1a\u30d1\u30e9\u30e1\u30fc\u30bf\uff08\u6bcd\u6570\uff09\u306b\u304a\u3051\u308b\u7dda\u5f62\u6027<\/li>\n\n\n\n<li>\u4eee\u5b9a\uff13\uff1a\u8aa4\u5dee\u9805\u306e\u6761\u4ef6\u4ed8\u304d\u671f\u5f85\u5024\u30bc\u30ed<\/li>\n\n\n\n<li>\u4eee\u5b9a\uff14\uff1a\u5b8c\u5168\u306a\u591a\u91cd\u5171\u7dda\u6027\u304c\u306a\u3044\u3053\u3068<\/li>\n\n\n\n<li>\u4eee\u5b9a\uff15\uff1a\u8aa4\u5dee\u9805\u306e\u5206\u6563\u5747\u4e00\u6027<\/li>\n\n\n\n<li>\u4eee\u5b9a\uff16\uff1a\u8aa4\u5dee\u9805\u306e\u6b63\u898f\u6027<\/li>\n<\/ul>\n\n\n\n<p>\u5c1a\u3001Wooldridge\u306e\u6559\u79d1\u66f8\u3067\u306f\u3001\u63a8\u5b9a\u5024$\\beta_j$\u304c\u3001\u4eee\u5b9a\uff12\uff0d\uff15\u3067\u304c\u30d0\u30a4\u30a2\u30b9\u306a\u304f\u63a8\u5b9a\u3067\u304d\u308b\u3053\u3068\u3001\u4eee\u5b9a\uff16\u3067\u5206\u6563\u304c\u63a8\u5b9a\u3067\u304d\u308b\u3068\u306e\u8a18\u8f09\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u4eee\u5b9a\uff11\uff1a\u8aa4\u5dee\u9805\u306e\u671f\u5f85\u5024\u30bc\u30ed<\/h2>\n\n\n\n<p>\u8aa4\u5dee\u9805\u306e\u671f\u5f85\u5024\u30bc\u30ed(\u4eee\u5b9a1)\u306f\u3001\u6e80\u305f\u3057\u3066\u3044\u306a\u3044\u5834\u5408\u306f\u3001\u5207\u7247\u9805($\\beta_0$) \u306b\u5f71\u97ff\u3092\u4e0e\u3048\u308b\u3002\u305f\u3060\u3001\u305d\u308c\u4ee5\u5916\u306e$\\beta_1 \\cdots \\beta_k$\u306b\u306f\u5f71\u97ff\u3092\u4e0e\u3048\u306a\u3044\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>#\u30c7\u30fc\u30bf\u306e\u4f5c\u6210\ndata1 &lt;- tibble(x1 = runif(100,0,10)) |&gt; \n  mutate(\n    y1 = 10 + 3*x1 + rnorm(100, 0,1),   #epsilon ~ N(0 ,1)\n    y2 = 10 + 3*x1 + rnorm(100,10,1)    #epsilon ~ N(10,1)\n  )<\/code><\/pre>\n\n\n\n<p>\u4f5c\u6210\u3057\u305f\u30c7\u30fc\u30bf\u306fy1\u5909\u6570\u304c\u8aa4\u5dee\u9805\u304c\u5e73\u57470\u3001SD1\u306e\u6b63\u898f\u5206\u5e03\u306b\u3057\u305f\u304c\u3044\u3001y2\u306f\u5e73\u574710<br>\u8aa4\u5dee\u98051\u306e\u6b63\u898f\u5206\u5e03\u306b\u5f93\u3046\u3002\u3069\u3061\u3089\u306e\u76ee\u7684\u5909\u6570\u3082\u3001\u03b2\u306e\u5024\u306f\u540c\u3058\u3067\u3042\u308a\u3001$\\beta_0=10$,$\\beta_1 = 3$\u3068\u8a2d\u5b9a\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u30b0\u30e9\u30d5\u306b\u3059\u308b\u3068\u3053\u3093\u306a\u611f\u3058\u3067\u3059\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>data1 |&gt; \n  pivot_longer(cols = !x1, names_to = \"response\", values_to = \"yval\") |&gt; \nggplot() +\n  geom_point(aes(x = x1, y = yval, color = response)) +\n  labs(x = \"x1\", y = \"y\", color = \"\u76ee\u7684\u5909\u6570\")<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/bunseki-data.com\/r-onlinecourse\/wp-content\/uploads\/2023\/11\/unnamed-chunk-3-1-3.png\" alt=\"\"\/><\/figure>\n\n\n\n<p>\u3053\u306e\u30c7\u30fc\u30bf\u304b\u3089\u30e2\u30c7\u30eb\u3092\u4e8c\u3064\u4f5c\u6210\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>mod1 &lt;- lm(y1 ~ x1, data = data1)  \nmod2 &lt;- lm(y2 ~ x1, data = data1) \n\ncompare_models(list(mod1,mod2),list(\"y1=x1+N(0,1)\",\"y2=x1+N(10,1)\"))<\/code><\/pre>\n\n\n\n<pre class=\"wp-block-code\"><code>## # A tibble: 2 \u00d7 3\n##   term        `y1=x1+N(0,1)`     `y2=x1+N(10,1)`     \n##   &lt;chr&gt;       &lt;glue&gt;             &lt;glue&gt;              \n## 1 (Intercept) 9.95(9.56 - 10.34) 20.13(19.76 - 20.50)\n## 2 x1          3.03(2.96 - 3.09)  2.94(2.88 - 3.01)<\/code><\/pre>\n\n\n\n<p>\u8aa4\u5dee\u9805\u306e\u5e73\u5747\u306b\u5dee\u304c\u3042\u308b\u305f\u3081\u3001\u5207\u7247\u306e$\\beta$\u306e\u5024\u306f\u9055\u3063\u3066\u3044\u308b\u304c\u3001x1\u306e\u4fc2\u6570\u3001$\\beta_1$\u306f\u4e8c\u3064\u3067\u540c\u3058\u5024\u306e\u7d50\u679c\u3068\u306a\u3063\u3066\u3044\u307e\u3059\u3002\uff08\u30b0\u30e9\u30d5\u304b\u3089\u306f\u660e\u3089\u304b\u3067\u3059\u306d\uff09<\/p>\n\n\n\n<p>\u8aa4\u5dee\u9805\u306e\u5e73\u5747\u5024\u304c\u30bc\u30ed\u304b\u3069\u3046\u304b\u3092\u30c1\u30a7\u30c3\u30af\u3059\u308b\u65b9\u6cd5\u306b\u3064\u3044\u3066\u306f\u3001\u8aa4\u5dee\u9805\u306e\u30c7\u30fc\u30bf\u305d\u306e\u3082\u306e\u304c\u5165\u624b\u3067\u304d\u306a\u3044\u3053\u3068\u3084\u3001\u5207\u7247\u4fc2\u6570\u306e\u5024\u3092\u6700\u521d\u304b\u3089\u77e5\u3063\u3066\u3044\u306a\u3044\u3068\u30ba\u30ec\u304c\u751f\u3058\u3066\u3044\u308b\u304b\u3092\u8abf\u3079\u308b\u3053\u3068\u304c\u4e0d\u53ef\u80fd\uff1f\u306a\u305f\u3081\u3001\u6559\u79d1\u66f8\u7684\u306b\u306f\u8a00\u53ca\u304c\u3042\u308a\u307e\u305b\u3093\u3067\u3057\u305f\u3002\uff08\u898b\u843d\u3068\u3057\u3066\u3044\u305f\u3089\u7533\u3057\u8a33\u3042\u308a\u307e\u305b\u3093\uff09<\/p>\n\n\n\n<p>\u5168\u4f53\u7684\u306b\u8aa4\u5dee\u9805\u304c\u305a\u308c\u3066\u3044\u308b\u3068\u3044\u3046\u3053\u3068\u306f\u3001\u4f55\u304b\u3057\u3089\u306e\u91cd\u8981\u306a\u5909\u6570\u3092\u53d6\u308a\u3053\u307c\u3057\u3066\u3044\u308b\u53ef\u80fd\u6027\u304c\u793a\u5506\u3055\u308c\u307e\u3059\u304c\u3001\u3053\u3061\u3089\u3082\u30c1\u30a7\u30c3\u30af\u3059\u308b\u306e\u306f\u56f0\u96e3\u3068\u8003\u3048\u3089\u308c\u308b\u306e\u3067\u3001\u3053\u306e\u4eee\u5b9a\u306b\u3064\u3044\u3066\u306f\u8aa4\u5dee\u9805\u306e\u5e73\u5747\u304c\u30bc\u30ed\u3067\u306a\u3044\u5834\u5408\u306f\u5207\u7247\u9805\u306b\u306e\u307f\u5f71\u97ff\u304c\u3067\u308b\u3068\u3044\u3046\u7406\u89e3\u3067\u3088\u3044\u306e\u3060\u3068\u601d\u3044\u307e\u3059\u3002\uff08\u306a\u306b\u304b\u3054\u5b58\u3058\u306e\u65b9\u304c\u3044\u3089\u3063\u3057\u3083\u3063\u305f\u3089\u304a\u6559\u3048\u304f\u3060\u3055\u3044\u3002\uff09<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u4eee\u5b9a\uff12\uff1a\u30d1\u30e9\u30e1\u30fc\u30bf\uff08\u6bcd\u6570\uff09\u306b\u304a\u3051\u308b\u7dda\u5f62\u6027<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">\u52d8\u9055\u3044<\/h3>\n\n\n\n<p>\u3053\u3061\u3089\u304c\u3001Linearity\u3068\u3044\u3046\u4eee\u5b9a\u3067\u82f1\u8a9e\u570f\u306e\u8a18\u4e8b\u306a\u3069\u3067\u7d39\u4ecb\u3055\u308c\u305f\u3001\u300c\u5358\u7d14\u306a\u6563\u5e03\u56f3\u3092\u66f8\u3044\u3066\u3001\u7dda\u5f62\u6027\u3092\u78ba\u304b\u3081\u308b\u300d\u3053\u3068\u304c\u9593\u9055\u3044\u306a\u306e\u3067\u306f\u306a\u3044\u3067\u3057\u3087\u3046\u304b\uff1f\u3068Tweet\u3057\u305f\u5185\u5bb9\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>\u91cd\u56de\u5e30\u5206\u6790\u306eAssumption\u3067\u8aac\u660e\u5909\u6570\u306e\u300c\u7dda\u5f62\u6027\u306e\u78ba\u8a8d\u300d\u3067\u3001\u8aac\u660e\u5909\u6570\u3068\u76ee\u7684\u5909\u6570\u306e\u6563\u5e03\u56f3\u3092\u66f8\u3044\u3066\u8996\u899a\u7684\u306b\u7dda\u5f62\u6027\u304c\u3042\u308b\u304b\u3092\u78ba\u8a8d\u3059\u308b\u3002<\/p>\n\n\n\n<p>\u306e\u3088\u3046\u306a\u8aac\u660e\u3092\u3088\u304f\u898b\u308b\u306e\u3067\u3059\u304c\u3001\u4ed6\u306e\u8aac\u660e\u5909\u6570\u306e\u5f71\u97ff\u3092\u53d7\u3051\u3066\u3044\u308b\u5834\u5408\u3001\u6563\u5e03\u56f3\u3067\u307f\u3066\u3082\u7dda\u5f62\u6027\u306e\u78ba\u8a8d\u306f\u3067\u304d\u306a\u3044\u3068\u601d\u3046\u306e\u3067\u3059\u304c\u3001\u9593\u9055\u3063\u305f\u8003\u3048\u65b9\u3067\u3057\u3087\u3046\u304b\uff1f<\/p>\n\n\n\n<p>\u2014 Norimitsu Nishida (@NorimitsuNishi1) <a href=\"https:\/\/twitter.com\/NorimitsuNishi1\/status\/1626342801473699841?ref_src=twsrc%5Etfw\">February 16, 2023<\/a><\/p>\n<\/blockquote>\n\n\n\n<pre class=\"wp-block-preformatted\">\n<\/pre>\n\n\n\n<p>\u3053\u308c\u306f\u79c1\u304c\u7406\u89e3\u3057\u3066\u3044\u306a\u304b\u3063\u305f\u3060\u3051\u306a\u306e\u3067\u3059\u304c\u3001\u7dda\u5f62\u6027\u306e\u4eee\u5b9a\u306f\u3001\u300c\u30a2\u30a6\u30c8\u30ab\u30e0\u304c\u8aac\u660e\u5909\u6570\u3068\u305d\u306e\u56de\u5e30\u4fc2\u6570\u3068\u3001\u8aa4\u5dee\u9805\u3068\u306e\u7dda\u5f62\u7d50\u5408\u3067\u3042\u308b\u300d\u3068\u3044\u3046\u610f\u5473\u5408\u3044\u3067\u3001\u4e00\u3064\u4e00\u3064\u306e\u8aac\u660e\u5909\u6570\u306e\u5909\u5316\uff08\u3053\u3053\u3067\u3001$x,x^2,log(x)$\u306a\u3069\u306e\u5909\u5f62\u3092\u542b\u307f\uff09\u304c\u76ee\u7684\u5909\u6570\u3092\u4e00\u5b9a\u306b\u5909\u5316\u3055\u305b\u308b\u3068\u3044\u3046\u610f\u5473\u5408\u3044\u3068\u306f\u9055\u3046\u3053\u3068\u3067\u3059\uff08\u3068\u306f\u3044\u3048\u3001\u7dda\u5f62\u7d50\u5408\u3067\u3042\u308b\u305f\u3081\u306b\u306f\u305d\u3046\u3042\u308b\u3053\u3068\u3082\u5fc5\u8981\uff08\u3060\u3051\u3069\u76ee\u7684\u5909\u6570\u3092\u5909\u63db\u3059\u308b\u5834\u5408\u306f\u3061\u3087\u3063\u3068\u9055\u3046\uff09\uff09<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u4eee\u5b9a\u306e\u5185\u5bb9<\/h3>\n\n\n\n<p>\u6a2a\u9053\u306b\u305d\u308c\u307e\u3057\u305f\u304c\u3001Fox\u306eRegression Diagnostics&#8230;(P39)\u3067\u306f\u3001<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>\u76ee\u7684\u5909\u6570\u306e\u6761\u4ef6\u4ed8\u304d\u671f\u5f85\u5024\uff08$u_i$)\u304c\u30d1\u30e9\u30e1\u30fc\u30bf\uff08$\\beta$\uff09\u3068\u8aac\u660e\u5909\u6570\u306e\u7dda\u5f62\u7d50\u5408\u3067\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u308b\u3053\u3068\uff08\u610f\u8a33\uff09<\/p>\n<\/blockquote>\n\n\n\n<p>\\[u_i = E[y_i|\\beta_0 + \\beta<em>1 x<\/em>{i1} + \\cdots + \\beta<em>k x<\/em>{ik}]=\\beta_0 + \\beta<em>1 x<\/em>{i1} + \\cdots + \\beta<em>k x<\/em>{ik} \\]<\/p>\n\n\n\n<p>\u3068\u8aac\u660e\u3055\u308c\u3066\u304a\u308a\u3001\u307e\u305fWooldridge\u306e\u6559\u79d1\u66f8(P80)\u3067\u306f\u3001<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>\u30e2\u30c7\u30eb\u304c\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc($\\beta_0, \\beta_1, \\cdots \\beta_k$)\u306b\u304a\u3044\u3066\u7dda\u5f62\u3067\u3042\u308b\u3053\u3068\u3002\u3053\u308c\u306f\u76ee\u7684\u5909\u6570\u3068\u8aac\u660e\u5909\u6570\u304c\u30ed\u30b0\u3084\u4e8c\u4e57\u306a\u3069\u306e\u4efb\u610f\u306e\u95a2\u6570\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u305f\u3081\u3001\u975e\u5e38\u306b\u67d4\u8edf\u3067\u3042\u308b\u3002\uff08\u610f\u8a33\uff09<\/p>\n<\/blockquote>\n\n\n\n<p>\u3068\u89e3\u8aac\u3055\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u3053\u308c\u3089\u306b\u3064\u3044\u3066\u3001\u81ea\u5206\u306e\u8a00\u8449\u3067\u89e3\u8aac\u3059\u308b\u3068\u3001\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u300c\u76ee\u7684\u5909\u6570\u306e\u4f55\u3089\u304b\u306e\u95a2\u6570=$\\beta_0$ + $\\beta_1$($x_1$\u306e\u4f55\u3089\u304b\u306e\u95a2\u6570) + $\\beta_2$($x_2$\u306e\u4f55\u3089\u304b\u306e\u95a2\u6570) + $\\cdots$ + $\\beta_k$($x_k$\u306e\u4f55\u3089\u304b\u306e\u95a2\u6570)\u300d<\/p>\n\n\n\n<p>\u3068\u3044\u3046\u5f62\u3067\u3042\u308c\u3070\u7dda\u5f62\u6027\u3092\u6e80\u305f\u3057\u3066\u3044\u308b\u3068\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u306a\u306e\u3067\u3001R\u306eformula\u3067\u8868\u8a18\u3059\u308b\u3068<\/p>\n\n\n\n<p>\\[Y \\sim X1 + X2\\]<\/p>\n\n\n\n<p>\\[Y \\sim log(X1) + (X2)^2\\]<\/p>\n\n\n\n<p>\\[Y \\sim X1 + (X1)^2 + \\sqrt{X2}\\]<\/p>\n\n\n\n<p>\\[log(Y) \\sim X1 + X2 \\Leftrightarrow Y \\sim \\exp(X1+X2)\\]<\/p>\n\n\n\n<p>\u306a\u3069\u306e\u30e2\u30c7\u30eb\u304c\u7dda\u5f62\u6027\u304c\u4fdd\u305f\u308c\u3066\u3044\u308b\u30e2\u30c7\u30eb\u3067\u3042\u308b\u3068\u3044\u3046\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u4eee\u5b9a\uff13\uff1a\u8aa4\u5dee\u9805\u306e\u6761\u4ef6\u4ed8\u304d\u671f\u5f85\u5024\u30bc\u30ed<\/h2>\n\n\n\n<p>Wooldridge\u306e\u6559\u79d1\u66f8(P82)\u306b\u306f\u6b21\u306e\u3088\u3046\u306b\u8a18\u8f09\u3055\u308c\u3066\u3044\u307e\u3059<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>\u8aa4\u5dee\u9805\u306f\u3001\u3069\u306e\u3088\u3046\u306a\u8aac\u660e\u5909\u6570\u3092\u4e0e\u3048\u3089\u308c\u3066\u3082\u305d\u306e\u671f\u5f85\u5024\u304c\u30bc\u30ed\u3068\u306a\u308b\u3053\u3068<\/p>\n<\/blockquote>\n\n\n\n<p>\\[E[\\epsilon|x_1,x_2,\\cdots,x_k]=0 \\]<br>\u4eee\u5b9a2\u3067\u8003\u3048\u305f\u30e2\u30c7\u30eb\u304c\u8aa4\u3063\u3066\u3044\u308b\u5834\u5408\u306b\u3001\u3053\u306e\u4eee\u5b9a\u304c\u6210\u308a\u7acb\u305f\u3061\u307e\u305b\u3093\u3002\u307e\u305f\u3001\u91cd\u8981\u306a\u5909\u6570\u3092\u30e2\u30c7\u30eb\u306b\u7d44\u307f\u8fbc\u3093\u3067\u3044\u306a\u3044\u5834\u5408\u3082\u3001\u540c\u69d8\u306b\u306a\u308a\u305f\u3061\u307e\u305b\u3093\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u4eee\u5b9a\uff14\uff1a\u5b8c\u5168\u306a\u5171\u7dda\u6027\u304c\u306a\u3044\u3053\u3068<\/h2>\n\n\n\n<p>\u3053\u308c\u306f\u3001\u8907\u6570\u306e\u5909\u6570\u304c\u5b8c\u5168\u306a\u76f8\u95a2\u3092\u3057\u3066\u3044\u308b\u5834\u5408\u3001\u4e00\u3064\u3067\u3082\u5909\u6570\u304c\u5b9a\u6570\u3067\u3042\u308b\u5834\u5408\u306b\u4eee\u5b9a\u3092\u6e80\u305f\u3055\u306a\u3044\u7d50\u679c\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u4eee\u5b9a\uff15\uff1a\u8aa4\u5dee\u9805\u306e\u5206\u6563\u5747\u4e00\u6027<\/h2>\n\n\n\n<p>Homoskedasticity\uff08\u7b49\u5206\u6563\u6027\uff09\u3002Homo-\u540c\u3058\u3001skedastic-\u8aa4\u5dee\u306e\u6563\u3089\u3070\u308a\u3002\u3068\u3044\u3046\u610f\u5473\u3089\u3057\u3044\uff1f\u3002<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>\u8aa4\u5dee\u3001\u03b5\u304c\u3069\u306e\u76ee\u7684\u5909\u6570\u306e\u3082\u3068\u3082\u540c\u3058\u5206\u6563\u3067\u3042\u308b\u3053\u3068<\/p>\n<\/blockquote>\n\n\n\n<p>\\[Var(\\epsilon|x_1, x_2, \\cdots, x_k)=\\sigma^2\\]<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u4eee\u5b9a\uff16\uff1a\u8aa4\u5dee\u9805\u306e\u6b63\u898f\u6027<\/h2>\n\n\n\n<p>\u8aa4\u5dee\u9805\u306f\u4eee\u5b9a\uff11\u3088\u308a\u3001\u305d\u306e\u5e73\u5747\u306f\uff10\u3067\u3001\u4eee\u5b9a\uff15\u3088\u308a\u305d\u306e\u5206\u6563\u306f\u4e00\u5b9a\u3067\u3001<\/p>\n\n\n\n<p>\\[\\epsilon \\sim N(0,\\sigma^2)\\]<\/p>\n\n\n\n<p>\u3068\u8868\u3059\u3053\u3068\u304c\u53ef\u80fd\u3002\u9ad8\u6a4b\u5148\u751f\u306e\u6559\u79d1\u66f8\uff08Pg120~)\u306b\u8a73\u7d30\u306a\u8a18\u8f09\u304c\u3042\u308a\u307e\u3057\u305f\uff08\u7e70\u308a\u8fd4\u3057\u307e\u3059\u304c\u3001\u3081\u3063\u3061\u3083\u5206\u304b\u308a\u3084\u3059\u3044\u6559\u79d1\u66f8\u3067\u3059\u3002\uff09<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">R\u3067\u306e\u78ba\u8a8d\uff1a\u30c7\u30fc\u30bf\u751f\u6210<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u4eee\u5b9a\uff11\uff1a\u8aa4\u5dee\u9805\u306e\u671f\u5f85\u5024\u30bc\u30ed<\/li>\n\n\n\n<li>\u4eee\u5b9a\uff12\uff1a\u30d1\u30e9\u30e1\u30fc\u30bf\uff08\u6bcd\u6570\uff09\u306b\u304a\u3051\u308b\u7dda\u5f62\u6027<\/li>\n\n\n\n<li>\u4eee\u5b9a\uff13\uff1a\u8aa4\u5dee\u9805\u306e\u6761\u4ef6\u4ed8\u304d\u671f\u5f85\u5024\u30bc\u30ed<\/li>\n\n\n\n<li>\u4eee\u5b9a\uff14\uff1a\u5b8c\u5168\u306a\u591a\u91cd\u5171\u7dda\u6027\u304c\u306a\u3044\u3053\u3068<\/li>\n\n\n\n<li>\u4eee\u5b9a\uff15\uff1a\u8aa4\u5dee\u9805\u306e\u5206\u6563\u5747\u4e00\u6027<\/li>\n\n\n\n<li>\u4eee\u5b9a\uff16\uff1a\u8aa4\u5dee\u9805\u306e\u6b63\u898f\u6027<\/li>\n<\/ul>\n\n\n\n<p>\u4ee5\u4e0a\u3001\u91cd\u56de\u5e30\u5206\u6790\u306e\u4eee\u5b9a\u306b\u3064\u3044\u3066\u81ea\u5206\u306a\u308a\u306b\u307e\u3068\u3081\u305f\u3082\u306e\u3067\u3059\u3002\u3053\u3053\u304b\u3089\u306f\u3001\u9ad8\u6a4b\u5148\u751f\u306e\u6559\u79d1\u66f8\u3084Fox\u5148\u751f\u306e\u6559\u79d1\u66f8\u3092\u53c2\u8003\u306b\u3057\u306a\u304c\u3089\u30e2\u30c7\u30eb\u30c1\u30a7\u30c3\u30af\u3001\u7279\u306b\u30e2\u30c7\u30eb\u5f0f\u304c\u9069\u5207\u306b\u6307\u5b9a\u3067\u304d\u3066\u3044\u308b\u304b\u3092\u78ba\u8a8d\u3059\u308bDiagnostic Plot\u3092\u3044\u304f\u3064\u304b\u5b9f\u88c5\u3057\u3066\u307f\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u3053\u3053\u304b\u3089\u306fR\u3067\u30c7\u30fc\u30bf\u3092\u4f5c\u6210\u3057\u3066\u3001\u3042\u3048\u3066\u8aa4\u3063\u305f\u30e2\u30c7\u30eb\u3067\u30d5\u30a3\u30c3\u30c6\u30a3\u30f3\u30b0\u3057\u3066\u3001Diagnostic Plot\u304c\u3069\u306e\u3088\u3046\u306b\u306a\u308b\u306e\u304b\u3092\u78ba\u8a8d\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u30c7\u30fc\u30bf\u306f\u3001x1\u3068x2\u306e\u4e8c\u7a2e\u985e\u306e\u8aac\u660e\u5909\u6570\u304b\u3089\u3001\u76ee\u7684\u5909\u6570\u3092\u6b21\u306e5\u3064\u306e\u69cb\u9020\u3092\u3082\u3064y1\u304b\u3089y5\u307e\u3067\u4f5c\u6210\u3057\u307e\u3059\u3002\u3059\u3079\u3066\u3001\u8aa4\u5dee\u9805\u306f\u5e73\u57470\u3001\u5206\u6563\uff11\u3068\u3057\u3066\u3044\u307e\u3059\u3002Y5\u3060\u3051X2\u3092\u30e2\u30c7\u30eb\u306b\u542b\u307e\u306a\u3044\u3068\u3044\u3046\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n\n<p>\\[Y_1 = \\beta_0 + \\beta_1 X_1 + \\beta_2 X_2 + \\epsilon\\]<\/p>\n\n\n\n<p>\\[Y_2 = \\beta_0 + \\beta_1 log(X_1) + \\beta_2 X_2 + \\epsilon \\]<\/p>\n\n\n\n<p>\\[Y_3 = \\beta_0 + \\beta_1 \\sqrt{X_1} + \\beta_2 (X_2)^2 + \\epsilon\\]<\/p>\n\n\n\n<p>\\[Y_4 = \\exp(\\beta_0 + \\beta_1 X_1 + \\beta_2 X_2 + \\epsilon)\\]<\/p>\n\n\n\n<p>\\[Y_5 = \\beta_0 + \\beta_1 X_1 + \\beta_2 (X_1)^2 + \\epsilon \\]<\/p>\n\n\n\n<p>\u307e\u305f\u3001\u63a8\u5b9a\u3059\u308b$\\beta_k$\u306e\u5024\u306f\u3001\u305d\u308c\u305e\u308c\u3001<\/p>\n\n\n\n<p>\\[\\beta_0 = 0.5\\]<\/p>\n\n\n\n<p>\\[\\beta_1 = 0.9\\]<\/p>\n\n\n\n<p>\\[\\beta_2 = 0.6\\]<\/p>\n\n\n\n<p>\u3068\u7d71\u4e00\u3057\u3066\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>beta0 &lt;- 0.5\nbeta1 &lt;- 0.9\nbeta2 &lt;- 0.6\n\nset.seed(123456)\n\ndata2 &lt;- tibble(\n  id = 1:100,\n  x1 = runif(100,0,10),\n  x2 = runif(100,0,10),\n  y1 =     beta0 + beta1 *      x1  + beta2 * x2     + rnorm(100),\n  y2 =     beta0 + beta1 *  log(x1) + beta2 * x2     + rnorm(100),\n  y3 =     beta0 + beta1 * sqrt(x1) + beta2 * (x2^2)   + rnorm(100),\n  y4 = exp(beta0 + beta1 *      x1  + beta2 * x2     + rnorm(100)),\n  y5 =     beta0 + beta1 *      x1  + beta2 * x1^2   + rnorm(100)\n)<\/code><\/pre>\n\n\n\n<p>\u6ce8\uff1a$Y_4$\u306b\u3064\u3044\u3066\u306f\u3001<\/p>\n\n\n\n<p>\\[Y_4 = e^{\\beta_0 + \\beta_1 X_1 + \\beta_2 X_2 + \\epsilon} \\]<\/p>\n\n\n\n<p>\\[log(Y_4) = log \\left(e^{\\beta_0 + \\beta_1 X_1 + \\beta_2 X_2 + \\epsilon} \\right)\\]<\/p>\n\n\n\n<p>\\[= \\beta_0 + \\beta_1 X_1 + \\beta_2 X_2 + \\epsilon\\]<\/p>\n\n\n\n<p>\u3068\u306a\u308a\u3001\u300c\u76ee\u7684\u5909\u6570\u306e\u4f55\u3089\u304b\u306e\u95a2\u6570=&#8230;\u300d\u3068\u3044\u3046\u5f62\u3044\u306a\u3063\u3066\u3044\u308b\u306e\u3067\u7dda\u5f62\u6027\u306f\u4fdd\u305f\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u30e2\u30c7\u30eb\u30c1\u30a7\u30c3\u30af<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">\u300c\u30c7\u30fc\u30bf\u306e\u89b3\u5bdf\uff1a\u5358\u7d14\u306a\u6563\u5e03\u56f3\u306e\u78ba\u8a8d\u300d<\/h3>\n\n\n\n<p>\u5358\u7d14\u306a\u6563\u5e03\u56f3\u306e\u78ba\u8a8d\u3001\u30e2\u30c7\u30eb\u30c1\u30a7\u30c3\u30af\u306e\u6587\u8108\u3067\u306f\u3084\u3063\u3066\u306f\u3044\u3051\u306a\u3044\u3068\u79c1\u306f\u601d\u3046\u306e\u3067\u3059\u304c\u3001EDA\uff08Explaratory Data Analysis\uff09\u3092\u884c\u3046\u4e0a\u3067\u306f\u3001\u5fc5\u9808\u3060\u3068\u3082\u601d\u3046\u306e\u3067\u3001\u30e2\u30c7\u30eb\u30c1\u30a7\u30c3\u30af\u524d\u306b\u3001\u305d\u3082\u305d\u3082\u8aac\u660e\u5909\u6570\u3068\u76ee\u7684\u5909\u6570\u304c\u3069\u306e\u3088\u3046\u306b\u5206\u5e03\u3057\u3066\u3044\u308b\u304b\u3092\u78ba\u8a8d\u3059\u308b\u3053\u3068\u3092\u3084\u3063\u3066\u304a\u304d\u307e\u3059<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>plotgraph &lt;- function(d,tgty,ttl){\n  d |&gt; \n  select({{tgty}},x1,x2) |&gt; \n  pivot_longer(cols = !{{tgty}}, names_to = \"expvar\", values_to = \"x\") |&gt; \nggplot() +\n  geom_point(aes(x = x, y = {{tgty}}, color = expvar)) +\n  facet_wrap(~expvar, scales = \"free_x\") +\n    labs(title = ttl) +\n    theme(legend.position = \"none\")\n}\n\nplotgraph(data2, y1, \"\u76ee\u7684\u5909\u6570\uff1ay1\")<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/bunseki-data.com\/r-onlinecourse\/wp-content\/uploads\/2023\/11\/unnamed-chunk-6-1-15.png\" alt=\"\"\/><\/figure>\n\n\n\n<pre class=\"wp-block-code\"><code>plotgraph(data2, y2, \"\u76ee\u7684\u5909\u6570\uff1ay2\")<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/bunseki-data.com\/r-onlinecourse\/wp-content\/uploads\/2023\/11\/unnamed-chunk-6-2-1.png\" alt=\"\"\/><\/figure>\n\n\n\n<pre class=\"wp-block-code\"><code>plotgraph(data2, y3, \"\u76ee\u7684\u5909\u6570\uff1ay3\")<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/bunseki-data.com\/r-onlinecourse\/wp-content\/uploads\/2023\/11\/unnamed-chunk-6-3-1.png\" alt=\"\"\/><\/figure>\n\n\n\n<pre class=\"wp-block-code\"><code>plotgraph(data2, y4, \"\u76ee\u7684\u5909\u6570\uff1ay4\")<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/bunseki-data.com\/r-onlinecourse\/wp-content\/uploads\/2023\/11\/unnamed-chunk-6-4-1.png\" alt=\"\"\/><\/figure>\n\n\n\n<pre class=\"wp-block-code\"><code>plotgraph(data2, y5, \"\u76ee\u7684\u5909\u6570\uff1ay5\")<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/bunseki-data.com\/r-onlinecourse\/wp-content\/uploads\/2023\/11\/unnamed-chunk-6-5-1.png\" alt=\"\"\/><\/figure>\n\n\n\n<p>\u76f4\u7dda\u3067\u306a\u3055\u305d\u3046\u306a\u95a2\u4fc2\u3082\u898b\u3048\u307e\u3059\u304c\u3001\u3088\u304f\u308f\u304b\u3089\u306a\u3044\u3082\u306e\u3082\u3042\u308a\u3001\u5358\u4e00\u5909\u6570\u3068\u76ee\u7684\u5909\u6570\u3068\u306e\u9593\u306e\u95a2\u4fc2\u3092\u3001\u7279\u306b\u91cd\u56de\u5e30\u5206\u6790\u3092\u884c\u3046\u3068\u304d\u306f\u3001\u76ee\u8996\u3067\u8abf\u3079\u306b\u304b\u304b\u308b\u306e\u306f\u3001\u3042\u307e\u308a\u7b4b\u304c\u3088\u304f\u306a\u3044\u3088\u3046\u306a\u6c17\u304c\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u300c\u30e2\u30c7\u30eb\u30c1\u30a7\u30c3\u30af\uff1a\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u306e\u7dda\u5f62\u6027\u306e\u78ba\u8a8d\u300d<\/h3>\n\n\n\n<p>R\u3067\u4eee\u5b9a\u304c\u6e80\u305f\u3055\u308c\u3066\u3044\u308b\u304b\u3092\u78ba\u8a8d\u3059\u308b\u65b9\u6cd5\u306b\u3064\u3044\u3066\u3001Fox\u5148\u751f\u306eR Companion to&#8230; \u306e\uff18\u7ae0\u306b\u3001car\u30d1\u30c3\u30b1\u30fc\u30b8\u3092\u5229\u7528\u3057\u305f\u30c1\u30a7\u30c3\u30af\u65b9\u6cd5\u306b\u3064\u3044\u3066\u8a73\u7d30\u306b\u8aac\u660e\u304c\u3042\u308a\u307e\u3057\u305f\u3002\u9ad8\u6a4b\u5148\u751f\u306e\u6559\u79d1\u66f8\u3067\u3082\u7d39\u4ecb\u3055\u308c\u3066\u3044\u305f<code>car::crPlots<\/code>\u306a\u3069\u3092\u5229\u7528\u3057\u3066\u4eee\u5b9a\u3092\u30c1\u30a7\u30c3\u30af\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u307e\u305a\u306f\u30e2\u30c7\u30eb\u3092\u4f5c\u308a\u307e\u3059\u3002mod1\u4ee5\u5916\u306f\u3001\u3059\u3079\u3066\u8aa4\u3063\u305f\u30e2\u30c7\u30eb\u306b\u306a\u3063\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>mod1 &lt;- lm(y1 ~ x1 + x2, data = data2)\nmod2 &lt;- lm(y2 ~ x1 + x2, data = data2)\nmod3 &lt;- lm(y3 ~ x1 + x2, data = data2)\nmod4 &lt;- lm(y4 ~ x1 + x2, data = data2)\nmod5 &lt;- lm(y5 ~ x1 + x2, data = data2)<\/code><\/pre>\n\n\n\n<p>\u6a2a\u306b\u4e26\u3079\u3066\u8868\u306b\u3057\u3066\u307f\u308b\u3068\u3001\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u3001<\/p>\n\n\n\n<p>\\[\\beta_0 = 0.5\\]<\/p>\n\n\n\n<p>\\[\\beta_1 = 0.9\\]<\/p>\n\n\n\n<p>\\[\\beta_2 = 0.6\\]<\/p>\n\n\n\n<p>\u3092\u6b63\u3057\u304f\u63a8\u5b9a\u3067\u304d\u3066\u3044\u308b\u306e\u306f\u30e2\u30c7\u30eb1\u3060\u3051\u3067\u3059\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>compare_models(\n  list(mod1,mod2,mod3,mod4,mod5),\n  list(\"x1+x2\",\n       \"log(x1)+x2\",\n       \"sqrt(x1)+x2^2\",\n       \"exp(x1+x2)\",\n       \"x1+x1^2\"\n  )\n) |&gt; knitr::kable(caption = \"b0=0.5, b1=0.9, b2 = 0.6\")<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-table\"><table><thead><tr><th>term<\/th><th>x1+x2<\/th><th>log(x1)+x2<\/th><th>sqrt(x1)+x2^2<\/th><th>exp(x1+x2)<\/th><th>x1+x1^2<\/th><\/tr><\/thead><tbody><tr><td>(Intercept)<\/td><td>0.38(-0.12 &#8211; 0.88)<\/td><td>0.45(-0.13 &#8211; 1.02)<\/td><td>-8.89(-11.23 &#8211; -6.54)<\/td><td>-401 755.27(-682 288.31 &#8211; -121 222.23)<\/td><td>-8.29(-10.46 &#8211; -6.13)<\/td><\/tr><tr><td>x1<\/td><td>0.92(0.85 &#8211; 0.98)<\/td><td>0.25(0.18 &#8211; 0.33)<\/td><td>0.35(0.05 &#8211; 0.65)<\/td><td>52 828.15(16 680.81 &#8211; 88 975.49)<\/td><td>6.90(6.62 &#8211; 7.18)<\/td><\/tr><tr><td>x2<\/td><td>0.60(0.53 &#8211; 0.67)<\/td><td>0.61(0.53 &#8211; 0.69)<\/td><td>5.87(5.55 &#8211; 6.20)<\/td><td>53 743.08(14 606.08 &#8211; 92 880.08)<\/td><td>-0.08(-0.38 &#8211; 0.22)<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\"><code>car::residualPlots<\/code>\u3067\u6b8b\u5dee\u306e\u78ba\u8a8d<\/h4>\n\n\n\n<pre class=\"wp-block-code\"><code>car::residualPlots(mod2)<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/bunseki-data.com\/r-onlinecourse\/wp-content\/uploads\/2023\/11\/unnamed-chunk-9-1-7.png\" alt=\"\"\/><\/figure>\n\n\n\n<pre class=\"wp-block-code\"><code>##            Test stat Pr(&gt;|Test stat|)    \n## x1           -4.3686        3.162e-05 ***\n## x2           -1.3471           0.1811    \n## Tukey test   -1.1786           0.2385    \n## ---\n## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1<\/code><\/pre>\n\n\n\n<p>\u3053\u306eResidualPlots\u3067\u300c\u4e00\u3064\u3067\u3082\u771f\u3093\u4e2d\u3067\u76f4\u7dda\u3067\u306a\u3051\u308c\u3070\u300d\u3001\u30e2\u30c7\u30eb\u5f0f\u304c\u4eee\u5b9a\u3092\u6e80\u305f\u3057\u3066\u3044\u308b\u304b\u602a\u3057\u3044\u3068\u307f\u306a\u3057\u307e\u3057\u3087\u3046\u3068\u8a18\u8f09\u304c\u3042\u308a\u307e\u3057\u305f\u3002<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>one nonnull plot is enough to suggest that the specified model does not match the data.(Fox, Weisberg. An R Companion to Applied Regression. Third edition. Los Angeles: SAGE, 2019. pp535.<br>)<\/p>\n<\/blockquote>\n\n\n\n<p>\u4eca\u56de\u3001\u56e0\u5b50\u578b\u306e\u30c7\u30fc\u30bf\u306f\u3044\u308c\u3066\u3044\u307e\u305b\u3093\u304c\u3001\u56e0\u5b50\u578b\u306e\u5834\u5408\u306f\u7bb1\u3072\u3052\u56f3\u304c\u30d7\u30ed\u30c3\u30c8\u3055\u308c\u3001IQR\u304c\u540c\u3058\u304f\u3089\u3044\u306e\u5e45\u3067\u3042\u308b\u3053\u3068\u3092\u78ba\u8a8d\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n<p>\u3053\u306e\u30d7\u30ed\u30c3\u30c8\u3092\u8a66\u3057\u306bggplot\u3067\u518d\u73fe\u3057\u3066\u307f\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>ggresidPlots &lt;- function(model){\n  dat &lt;- as_tibble(model$model) |&gt; \n    mutate(resid = resid(model),\n           fit   = predict(model))\n\n  ggresidPlot &lt;- function(dat, tgt){\n    tgt &lt;- rlang::sym(tgt)\n    ggplot(dat,aes(x = !!tgt, y = resid)) +\n      geom_hline(yintercept = 0, linetype = \"dashed\", color = \"red\") +\n      geom_point() +\n      geom_smooth(method=\"lm\",\n                  formula = \"y ~ poly(x,2)\",\n                  se=FALSE) +\n      theme_bw()\n  }\n\n  tms &lt;- attr(model$terms,\"term.labels\")\n\n  map(c(tms,\"fit\"), ~{ggresidPlot(dat,.)}) %&gt;%\n    cowplot::plot_grid(plotlist = .)\n\n}\n\nggresidPlots(mod2)<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/bunseki-data.com\/r-onlinecourse\/wp-content\/uploads\/2023\/11\/unnamed-chunk-10-1-5.png\" alt=\"\"\/><\/figure>\n\n\n\n<p>car\u30d1\u30c3\u30b1\u30fc\u30b8\u306e\u57fa\u672c\u7684\u306a\u30d7\u30ed\u30c3\u30c8\u306f\u518d\u73fe\u3067\u304d\u307e\u3057\u305f\u3002\uff08\u3053\u306e\u95a2\u6570\u306f\u56e0\u5b50\u578b\u306f\u30d7\u30ed\u30c3\u30c8\u3067\u304d\u307e\u305b\u3093\u304c\u3001\u3082\u3046\u5c11\u3057\u6539\u9020\u3059\u308c\u3070\u56e0\u5b50\u578b\u3067\u3082\u3044\u3051\u308b\u306f\u305a\u3067\u3059\uff09\u3002<\/p>\n\n\n\n<p>\u6bd4\u8f03\u3057\u3066\u304a\u304f\u3068\u3001<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>compare_single_model &lt;- function(model, carfun, ownfun){\n    carfun(model)\n    tempplot &lt;- recordPlot()\n\n    tempgg   &lt;- ownfun(model)\n\n    return(\n      list(gcar = tempplot, gown = tempgg)\n    )\n}\n\ncompare_residual_plot &lt;- function(model){\n  compare_single_model(model, car::residualPlots, ggresidPlots)\n}<\/code><\/pre>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Model 1<\/li>\n<\/ul>\n\n\n\n<pre class=\"wp-block-code\"><code>compare_residual_plot(mod1)<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/bunseki-data.com\/r-onlinecourse\/wp-content\/uploads\/2023\/11\/unnamed-chunk-12-1-1.png\" alt=\"\"\/><\/figure>\n\n\n\n<pre class=\"wp-block-code\"><code>##            Test stat Pr(&gt;|Test stat|)\n## x1           -0.5117           0.6100\n## x2           -0.1163           0.9077\n## Tukey test    0.5267           0.5984<\/code><\/pre>\n\n\n\n<pre class=\"wp-block-code\"><code>## $gcar\n## \n## $gown<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/bunseki-data.com\/r-onlinecourse\/wp-content\/uploads\/2023\/11\/unnamed-chunk-12-2-1.png\" alt=\"\"\/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Model 2<\/li>\n<\/ul>\n\n\n\n<pre class=\"wp-block-code\"><code>compare_residual_plot(mod2)<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/bunseki-data.com\/r-onlinecourse\/wp-content\/uploads\/2023\/11\/unnamed-chunk-13-1-1.png\" alt=\"\"\/><\/figure>\n\n\n\n<pre class=\"wp-block-code\"><code>##            Test stat Pr(&gt;|Test stat|)    \n## x1           -4.3686        3.162e-05 ***\n## x2           -1.3471           0.1811    \n## Tukey test   -1.1786           0.2385    \n## ---\n## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1<\/code><\/pre>\n\n\n\n<pre class=\"wp-block-code\"><code>## $gcar\n## \n## $gown<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/bunseki-data.com\/r-onlinecourse\/wp-content\/uploads\/2023\/11\/unnamed-chunk-13-2-1.png\" alt=\"\"\/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Model 3<\/li>\n<\/ul>\n\n\n\n<pre class=\"wp-block-code\"><code>compare_residual_plot(mod3)<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/bunseki-data.com\/r-onlinecourse\/wp-content\/uploads\/2023\/11\/unnamed-chunk-14-1-6.png\" alt=\"\"\/><\/figure>\n\n\n\n<pre class=\"wp-block-code\"><code>##            Test stat Pr(&gt;|Test stat|)    \n## x1            0.5469           0.5857    \n## x2           40.4458           &lt;2e-16 ***\n## Tukey test   36.5250           &lt;2e-16 ***\n## ---\n## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1<\/code><\/pre>\n\n\n\n<pre class=\"wp-block-code\"><code>## $gcar\n## \n## $gown<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/bunseki-data.com\/r-onlinecourse\/wp-content\/uploads\/2023\/11\/unnamed-chunk-14-2-1.png\" alt=\"\"\/><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\">added-variable plots\/ partial-regression plots<\/h4>\n\n\n\n<p>\u3064\u304e\u306f\u3053\u306eDiagnostic\u30d7\u30ed\u30c3\u30c8\u3092\u898b\u3066\u3044\u304d\u307e\u3059\u3002Added Variable\u30d7\u30ed\u30c3\u30c8\u3042\u308b\u3044\u306fPartial-Regression\u30d7\u30ed\u30c3\u30c8\u306f\u6b21\u306e\u3088\u3046\u306a\u624b\u9806\u3067\u4f5c\u6210\u3055\u308c\u308b\u30d7\u30ed\u30c3\u30c8\u3067\u3059\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u76ee\u7684\u5909\u6570\u3092\u300c\u5bfe\u8c61\u3068\u3059\u308b\u8aac\u660e\u5909\u6570\u300d\uff08\u4f8b\u3048\u3070X1\u3068\u3059\u308b\uff09\u3092\u9664\u3044\u3066\u56de\u5e30\u5206\u6790\u3092\u884c\u3046\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u3053\u306e\u56de\u5e30\u5206\u6790\u306e\u7d50\u679c\u3067\u8a08\u7b97\u3067\u304d\u308b\u6b8b\u5dee\u306fx1\u3067\u300c\u8aac\u660e\u3055\u308c\u3066\u3044\u306a\u3044\u300d\u90e8\u5206\u3092\u542b\u3080\u6b8b\u5dee<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u300c\u5bfe\u8c61\u3068\u3059\u308b\u8aac\u660e\u5909\u6570\u300d\u306b\u5bfe\u3057\u3066\u3001\u4ed6\u306e\u8aac\u660e\u5909\u6570\u3067\u56de\u5e30\u5206\u6790\u3092\u884c\u3046\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u3053\u306e\u56de\u5e30\u5206\u6790\u3067\u5f97\u3089\u308c\u308b\u6b8b\u5dee\u306f\u3001\u300c\u5bfe\u8c61\u3068\u3059\u308b\u8aac\u660e\u5909\u6570\u300d\u304c\u4ed6\u306e\u8aac\u660e\u5909\u6570\u3067\u8aac\u660e\u3055\u308c\u3066\u3044\u306a\u3044\u90e8\u5206\u3092\u542b\u3080\u3002<\/p>\n\n\n\n<p>\u3042\u308b\u3044\u306f\u3001<\/p>\n\n\n\n<p>\u3053\u306e\u56de\u5e30\u5206\u6790\u3067\u5f97\u3089\u308c\u308b\u6b8b\u5dee\u306f\u3001\u300c\u5bfe\u8c61\u3068\u3059\u308b\u8aac\u660e\u5909\u6570\u300d\u306e\u7279\u5fb4\u304c\u4ed6\u306e\u5909\u6570\u3067\u6761\u4ef6\u3065\u3051\u3066\u3082\u6b8b\u308b\u90e8\u5206\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<p>\u3053\u306e\uff11\u3068\uff12\u306e\u624b\u9806\u306e\u6b8b\u5dee\u3092\uff59\u8ef8\u3068x\u8ef8\u306b\u8a2d\u5b9a\u3057\u305f\u6563\u5e03\u56f3\u304cAdded Variable\u30d7\u30ed\u30c3\u30c8\u3002<\/p>\n\n\n\n<p>\u30e2\u30c7\u30eb\u3067\u66f8\u304f\u3068\u3001X1\u306eAV\u30d7\u30ed\u30c3\u30c8\u3092\u66f8\u304f\u5834\u5408\u306f\u3001<\/p>\n\n\n\n<p>\\[Y \\sim X_2 + X_3 + \\cdots + X_k\\]<\/p>\n\n\n\n<p>\\[X_1 \\sim X_2 + X_3 + \\cdots + X_k\\]<br><br>\u306e\u4e8c\u3064\u306e\u30e2\u30c7\u30eb\u3092\u8003\u3048\u307e\u3059<\/p>\n\n\n\n<p><code>car<\/code>\u30d1\u30c3\u30b1\u30fc\u30b8\u3067\u30d7\u30ed\u30c3\u30c8\u3057\u3066\u307f\u308b\u3068<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>car::avPlots(mod2)<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/bunseki-data.com\/r-onlinecourse\/wp-content\/uploads\/2023\/11\/unnamed-chunk-15-1-6.png\" alt=\"\"\/><\/figure>\n\n\n\n<p>\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u4e00\u3064\u305a\u3064\u307f\u3066\u307f\u307e\u3059\u3002\u307e\u305a\u3001mod2\u306ex1\u304b\u3089\u3002<\/p>\n\n\n\n<p>\\[Y \\sim X_2 + X_3 + \\cdots + X_k\\]<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>avmod1 &lt;- lm(y2 ~ x2, data = data2)\n\ndata2 |&gt; \n  mutate(resid = avmod1$residuals) |&gt; \n  ggplot() +\n  geom_point(aes(x = x1, y = resid)) <\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/bunseki-data.com\/r-onlinecourse\/wp-content\/uploads\/2023\/11\/unnamed-chunk-16-1-1.png\" alt=\"\"\/><\/figure>\n\n\n\n<p>\u3053\u3093\u306a\u611f\u3058\u306e\u6b8b\u5dee\u3067\u3059\u3002<\/p>\n\n\n\n<p>\u6b21\u306b\u3001<\/p>\n\n\n\n<p>\\[X_1 \\sim X_2 + X_3 + \\cdots + X_k\\]<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>avmod2 &lt;- lm(x1 ~ x2, data = data2)\ndata2 |&gt; \n  mutate(resid = avmod2$residuals) |&gt; \n  ggplot() +\n  geom_point(aes(x = x1, y = resid)) <\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/bunseki-data.com\/r-onlinecourse\/wp-content\/uploads\/2023\/11\/unnamed-chunk-17-1-1.png\" alt=\"\"\/><\/figure>\n\n\n\n<p>\u3053\u3093\u306a\u611f\u3058\u306e\u6b8b\u5dee\u3067\u3059\u3002\u305d\u308c\u3067\u3001\u6b8b\u5dee\u540c\u58eb\u306e\u30d7\u30ed\u30c3\u30c8\u3092\u63cf\u304f\u3068\u3001\u6b21\u306e\u3088\u3046\u306a\u611f\u3058\u306b\u306a\u308a\u307e\u3059\uff08\u9752\u3044\u7dda\u306f\u6700\u5c11\u4e8c\u4e57\u6cd5\u306b\u3088\u308b\u56de\u5e30\u76f4\u7dda\u3067\u3059\u3002\uff09<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>tibble(\n  x = avmod2$residuals,\n  y = avmod1$residuals\n) |&gt; \nggplot(aes(x = x, y = y)) +\n  geom_point() +\n  geom_smooth(method = \"lm\", se=FALSE, formula = \"y~x\")<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/bunseki-data.com\/r-onlinecourse\/wp-content\/uploads\/2023\/11\/unnamed-chunk-18-1-1.png\" alt=\"\"\/><\/figure>\n\n\n\n<p>\u3053\u308c\u3092\u95a2\u6570\u5316\u3059\u308b\u3068<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>ggavPlots &lt;- function(model){\n  dat &lt;- as_tibble(model$model)\n  mokuteki &lt;- as.character(model$terms)&#91;2]\n  setumei &lt;- attr(model$terms,\"term.labels\")\n\n  ggavPlot &lt;- function(dat,mokuteki, setumei, tgt){\n\n    setumei_wo_tgt &lt;- setumei&#91;!(setumei %in% tgt)] |&gt; \n      str_c(collapse=\"+\")\n\n    fmla1 &lt;- str_glue(\"{mokuteki} ~ {setumei_wo_tgt}\")\n    fmla2 &lt;- str_glue(\"{tgt} ~ {setumei_wo_tgt}\")\n\n    avmod1 &lt;- lm(as.formula(fmla1), data = dat)\n    avmod2 &lt;- lm(as.formula(fmla2), data = dat)\n\n    tibble(\n      x = avmod2$residuals,\n      y = avmod1$residuals\n    ) |&gt; \n    ggplot(aes(x = x, y = y)) +\n      geom_point() +\n      geom_smooth(method = \"lm\", se=FALSE, formula = \"y~x\") +\n      labs(x = fmla2, y = fmla1)\n\n  }\n\n  map(setumei, ~{\n    ggavPlot(dat,mokuteki,setumei,.)\n  }) %&gt;%\n    cowplot::plot_grid(plotlist = .)\n\n}<\/code><\/pre>\n\n\n\n<p>\u3053\u3046\u306a\u308a\u307e\u3057\u305f\u3002\u3053\u306eAdded Variable\u30d7\u30ed\u30c3\u30c8\u3001\u3044\u304f\u3064\u304b\u7279\u5fb4\u304c\u3042\u308a(Fox, R companion to &#8230;, pg541)\u3001<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u9752\u3044\u7dda\u3067\u8868\u793a\u3055\u308c\u3066\u3044\u308b\u7dda\uff08OLS\u3067\u63a8\u5b9a\uff09\u306e\u50be\u304d\u304c\u3001\u5143\u3005\u306e\u30e2\u30c7\u30eb\u306e\u305d\u306e\u5909\u6570\u306e\u63a8\u5b9a\u5024\u3068\u540c\u3058\u3067\u3042\u308b\u3053\u3068<\/li>\n\n\n\n<li>Added Variable\u30d7\u30ed\u30c3\u30c8\u306e\u6b8b\u5dee\u304c\u5143\u3005\u306e\u30e2\u30c7\u30eb\u306e\u6b8b\u5dee\u3068\u540c\u3058\u3067\u3042\u308b\u3053\u3068<\/li>\n\n\n\n<li>x\u8ef8\u306e\u5024\u304c\u3001\u4ed6\u306e\u5909\u6570\u3067\u6761\u4ef6\u4ed8\u3051\u305f\u4e0a\u306e\u5909\u6570\u306e\u5024\u306e\u6b8b\u5dee\u3067\u3042\u308b\u305f\u3081\u3001x\u8ef8\u306e\u7aef\u306b\u3042\u308b\u30c7\u30fc\u30bf\u306f\u73cd\u3057\u3044\u30c7\u30fc\u30bf\u3068\u8003\u3048\u3089\u308c\u3001\u3053\u308c\u3089\u306e\u30c7\u30fc\u30bf\u304c\u63a8\u5b9a\u5024\u306b\u4e0e\u3048\u308b\u5f71\u97ff\u3092\u8996\u899a\u7684\u306b\u628a\u63e1\u3067\u304d\u308b\u3053\u3068<\/li>\n<\/ol>\n\n\n\n<p>\u3068\u306a\u308a\u307e\u3059\u3002\u305f\u3060\u3001\u5916\u308c\u5024\u3084\u30ec\u30d0\u30ec\u30c3\u30b8\u306e\u554f\u984c\u3092\u898b\u629c\u304f\u306b\u306f\u826f\u3044\u30d7\u30ed\u30c3\u30c8\u3067\u3059\u304c\u3001\u7dda\u5f62\u6027\u306e\u4eee\u5b9a\u3092\u898b\u308b\u306b\u306f\u30df\u30b9\u30ea\u30fc\u30c7\u30a3\u30f3\u30b0\u306a\u5834\u5408\u3082\u3042\u308b\u305f\u3081\u3001\u305d\u306e\u5834\u5408\u306f\u6b21\u306eComponent plus residual plot\u3082\u826f\u3044\u9078\u629e\u3089\u3057\u3044\u3067\u3059\u3002<\/p>\n\n\n\n<p>\u95a2\u6570\u304ccar\u306e\u7d50\u679c\u3068\u8996\u899a\u7684\u306b\u3082\u4e00\u81f4\u3059\u308b\u304b\u8abf\u3079\u3066\u304a\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>compare_av_plot &lt;- function(model){\n  compare_single_model(\n    model, \n    car::avPlots, \n    ggavPlots)\n}<\/code><\/pre>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Model 1<\/li>\n<\/ul>\n\n\n\n<pre class=\"wp-block-code\"><code>compare_av_plot(mod1)<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/bunseki-data.com\/r-onlinecourse\/wp-content\/uploads\/2023\/11\/unnamed-chunk-21-1-6.png\" alt=\"\"\/><\/figure>\n\n\n\n<pre class=\"wp-block-code\"><code>## $gcar\n## \n## $gown<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/bunseki-data.com\/r-onlinecourse\/wp-content\/uploads\/2023\/11\/unnamed-chunk-21-2-1.png\" alt=\"\"\/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Model 2<\/li>\n<\/ul>\n\n\n\n<pre class=\"wp-block-code\"><code>compare_av_plot(mod2)<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/bunseki-data.com\/r-onlinecourse\/wp-content\/uploads\/2023\/11\/unnamed-chunk-22-1-1.png\" alt=\"\"\/><\/figure>\n\n\n\n<pre class=\"wp-block-code\"><code>## $gcar\n## \n## $gown<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/bunseki-data.com\/r-onlinecourse\/wp-content\/uploads\/2023\/11\/unnamed-chunk-22-2-1.png\" alt=\"\"\/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Model 3<\/li>\n<\/ul>\n\n\n\n<pre class=\"wp-block-code\"><code>compare_av_plot(mod3)<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/bunseki-data.com\/r-onlinecourse\/wp-content\/uploads\/2023\/11\/unnamed-chunk-23-1-2.png\" alt=\"\"\/><\/figure>\n\n\n\n<pre class=\"wp-block-code\"><code>## $gcar\n## \n## $gown<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/bunseki-data.com\/r-onlinecourse\/wp-content\/uploads\/2023\/11\/unnamed-chunk-23-2-1.png\" alt=\"\"\/><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\">component plus residual plot \/ partial residual plots<\/h4>\n\n\n\n<p>\u3053\u3061\u3089\u3001\u9ad8\u6a4b\u5148\u751f\u306e\u6559\u79d1\u66f8\u3067\u3082\u7d39\u4ecb\u3055\u308c\u3066\u3044\u308bPlot\u3067\u3059\u304c\u3001Fox\u306e\u6559\u79d1\u66f8\u3067\u5177\u4f53\u7684\u306a\u63cf\u753b\u65b9\u6cd5\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u306f\u8aac\u660e\u3055\u308c\u3066\u3044\u306a\u304b\u3063\u305f\u306e\u3067\u3001Wikipedia\u3092\u53c2\u8003\u306b\u4f5c\u6210\u3057\u3066\u307f\u307e\u3057\u305f\u3002<\/p>\n\n\n\n<p><a href=\"https:\/\/en.wikipedia.org\/wiki\/Partial_residual_plot\">https:\/\/en.wikipedia.org\/wiki\/Partial_residual_plot<\/a><\/p>\n\n\n\n<p>\u3042\u3068\u3001Wikipedia\u304c\u53c2\u8003\u306b\u3057\u3066\u3044\u305f\u6587\u732e<\/p>\n\n\n\n<p>Velleman, Paul F, and Roy E Welsch. \u201cEfficient Computing of Regression Diagnostics,\u201d 2023.<\/p>\n\n\n\n<p>\u3092\u78ba\u8a8d\u3057\u305f\u3068\u3053\u308d Partial Residual Plot\u306f\u3001<\/p>\n\n\n\n<p>\\[y\u8ef8\uff1a\\beta_j X_j + \\epsilon\\]<\/p>\n\n\n\n<p>\\[x\u8ef8\uff1aX_j\\]<\/p>\n\n\n\n<p>\u3068\u3057\u305f\u6563\u5e03\u56f3\u3068\u306e\u3053\u3068\u306a\u306e\u3067\u3001\u3084\u3063\u3066\u307f\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>car::crPlots(mod5)<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/bunseki-data.com\/r-onlinecourse\/wp-content\/uploads\/2023\/11\/unnamed-chunk-24-1-5.png\" alt=\"\"\/><\/figure>\n\n\n\n<pre class=\"wp-block-code\"><code>ggcrPlots &lt;- function(model){\n\n  betas &lt;- enframe(model$coefficients) |&gt; \n    filter(name != \"(Intercept)\")\n\n  tempdata &lt;- model$model |&gt; \n    mutate(resid = model$residuals)\n\n  ggcrPlot &lt;- function(tempdata, tgt, betaval){\n    tempdata |&gt; \n      mutate(yaxis = betaval * !!rlang::sym(tgt)) |&gt; \n      mutate(yaxis = yaxis + resid) |&gt; \n      ggplot(aes(x = !!rlang::sym(tgt), y = yaxis)) +\n      geom_point() +\n      geom_smooth(method = \"lm\", formula = \"y ~ x\", se=FALSE, color = \"darkblue\", linetype = \"dashed\") +\n      geom_smooth(method = \"loess\", formula = \"y ~ x\", se=FALSE, color = \"deeppink\") +\n      theme_bw() +\n      labs(y = \"Component+Residual\")\n  }\n\n  res &lt;- map2(betas$name, betas$value, ~{\n    ggcrPlot(tempdata, .x, .y)\n  }) %&gt;%\n    cowplot::plot_grid(plotlist = .)\n\n  return(res)\n}\n\nggcrPlots(mod2)<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/bunseki-data.com\/r-onlinecourse\/wp-content\/uploads\/2023\/11\/unnamed-chunk-25-1-1.png\" alt=\"\"\/><\/figure>\n\n\n\n<p>\u8d64\u3044\u7dda\u306e\u5f15\u304d\u65b9\u3092ggplot\u306egeom_smooth\u3067\u5f15\u3044\u3066\u3044\u308b\u306e\u3067\u3001\u3061\u3087\u3063\u3068\u672c\u5bb6\u306e\u3082\u306e\u3068\u9055\u3046\u3088\u3046\u306b\u3082\u8a00\u3048\u307e\u3059\u304c\u3001\u6563\u5e03\u56f3\u305d\u306e\u3082\u306e\u306f\u4e00\u81f4\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u3053\u306eCoponent plus Residual\u30d7\u30ed\u30c3\u30c8\u3092\u307f\u308b\u3053\u3068\u3067\u3001$x_j$\u304c\u6982\u306d\u7dda\u5f62\u304b\u3001$x_j$\u306b\u4f55\u304b\u3057\u3089\u306e\u95a2\u6570\u3092\u9069\u5fdc\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u304b\u3092\u30c1\u30a7\u30c3\u30af\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3068\u89e3\u8aac\u304c\u3042\u308a\u307e\u3057\u305f\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u30e2\u30c7\u30eb<\/h2>\n\n\n\n<p>\u3053\u306eComponent plus Residual\u30d7\u30ed\u30c3\u30c8\u3092\u898b\u306a\u304c\u3089\u6b63\u3057\u3044\u30e2\u30c7\u30eb\u306e\u6307\u5b9a\u3092\u63a2\u3063\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Model2<\/h3>\n\n\n\n<p>\u307e\u305a\u306f\u30e2\u30c7\u30eb\uff12\u3067\u3059\u3002X1\u3092\u30ed\u30b0\u5909\u63db\u3059\u308c\u3070\u3046\u307e\u304f\u884c\u304f\u306f\u305a\u3067\u3059\u3002<\/p>\n\n\n\n<p>\\[Y_2 = \\beta_0 + \\beta_1 log(X_1) + \\beta_2 X_2 + \\epsilon\\]<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>ggcrPlots(mod2)<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/bunseki-data.com\/r-onlinecourse\/wp-content\/uploads\/2023\/11\/unnamed-chunk-26-1-4.png\" alt=\"\"\/><\/figure>\n\n\n\n<p>x2\u3082\u602a\u3057\u3044\u3067\u3059\u304c\u3001x1\u304c\u660e\u3089\u304b\u306b\u5916\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>mod2_1 &lt;- update(mod2, ~ x1^2 + x2)\nmod2_2 &lt;- update(mod2, ~ log(x1) + x2)\nmod2_3 &lt;- update(mod2, ~ sqrt(x1) + x2)<\/code><\/pre>\n\n\n\n<pre class=\"wp-block-code\"><code>ggcrPlots(mod2_1)<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/bunseki-data.com\/r-onlinecourse\/wp-content\/uploads\/2023\/11\/unnamed-chunk-28-1-1.png\" alt=\"\"\/><\/figure>\n\n\n\n<pre class=\"wp-block-code\"><code>car::residualPlots(mod2_1)<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/bunseki-data.com\/r-onlinecourse\/wp-content\/uploads\/2023\/11\/unnamed-chunk-29-1-3.png\" alt=\"\"\/><\/figure>\n\n\n\n<pre class=\"wp-block-code\"><code>##            Test stat Pr(&gt;|Test stat|)    \n## x1           -4.3686        3.162e-05 ***\n## x2           -1.3471           0.1811    \n## Tukey test   -1.1786           0.2385    \n## ---\n## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1<\/code><\/pre>\n\n\n\n<pre class=\"wp-block-code\"><code>ggcrPlots(mod2_2)<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/bunseki-data.com\/r-onlinecourse\/wp-content\/uploads\/2023\/11\/unnamed-chunk-30-1-3.png\" alt=\"\"\/><\/figure>\n\n\n\n<pre class=\"wp-block-code\"><code>car::residualPlots(mod2_2)<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/bunseki-data.com\/r-onlinecourse\/wp-content\/uploads\/2023\/11\/unnamed-chunk-31-1-1.png\" alt=\"\"\/><\/figure>\n\n\n\n<pre class=\"wp-block-code\"><code>##            Test stat Pr(&gt;|Test stat|)  \n## log(x1)       0.3818          0.70344  \n## x2           -1.7591          0.08174 .\n## Tukey test   -0.6579          0.51061  \n## ---\n## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1<\/code><\/pre>\n\n\n\n<pre class=\"wp-block-code\"><code>ggcrPlots(mod2_3)<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/bunseki-data.com\/r-onlinecourse\/wp-content\/uploads\/2023\/11\/unnamed-chunk-32-1-1.png\" alt=\"\"\/><\/figure>\n\n\n\n<pre class=\"wp-block-code\"><code>car::residualPlots(mod2_3)<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/bunseki-data.com\/r-onlinecourse\/wp-content\/uploads\/2023\/11\/unnamed-chunk-33-1-1.png\" alt=\"\"\/><\/figure>\n\n\n\n<pre class=\"wp-block-code\"><code>##            Test stat Pr(&gt;|Test stat|)    \n## sqrt(x1)     -4.1877        6.253e-05 ***\n## x2           -1.4953           0.1381    \n## Tukey test   -1.2589           0.2080    \n## ---\n## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1<\/code><\/pre>\n\n\n\n<p><code>mod2_2<\/code>\u3067\u30d5\u30a3\u30c3\u30c8\u3057\u3066\u3044\u308b\u3088\u3046\u306b\u898b\u3048\u307e\u3059\u306d\u3002Functional Form\u306e\u78ba\u8a8d\u306e\u5834\u5408car::residualPlots\u306e\u65b9\u304c\u5206\u304b\u308a\u3084\u3059\u3044\u3088\u3046\u306b\u3082\u601d\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u5c1a\u3001\u591a\u6570\u306e\u30e2\u30c7\u30eb\u691c\u8a3c\u3092\u884c\u3046\u5834\u5408\u306f\u3001<code>mfp<\/code>\u30d1\u30c3\u30b1\u30fc\u30b8\u3092\u5229\u7528\u3057\u3066\u3082\u826f\u3044\u304b\u3082\u3057\u308c\u307e\u305b\u3093\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>library(mfp)\nmodfp &lt;- mfp(y2 ~ fp(x1, scale=FALSE) + fp(x2, scale=FALSE), data = data2)\n\nmodfp &lt;- lm(modfp$formula, data = data2)<\/code><\/pre>\n\n\n\n<p>\u4f5c\u3063\u305f\u30e2\u30c7\u30eb\u3092\u4e26\u3079\u3066\u307f\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>list(mod2,mod2_1,mod2_2,mod2_3,modfp) |&gt; \n  map(~gtsummary::tbl_regression(.)) |&gt; \n  gtsummary::tbl_merge(tab_spanner = c(\"mod2\",\"mod2_1\",\"mod2_2\",\"mod2_3\",\"modfp\"))<\/code><\/pre>\n\n\n\n<p>&#8220;`{=html}<\/p>\n\n\n\n<div id=\"xuiibvmgop\" style=\"overflow-x: auto; overflow-y: auto; width: auto; height: auto; padding: 10px 0px 10px 0px;\"><style>#xuiibvmgop table {<br \/>\n  font-family: system-ui, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol', 'Noto Color Emoji';<br \/>\n  -webkit-font-smoothing: antialiased;<br \/>\n  -moz-osx-font-smoothing: grayscale;<br \/>\n}<\/p>\n<p>#xuiibvmgop thead, #xuiibvmgop tbody, #xuiibvmgop tfoot, #xuiibvmgop tr, #xuiibvmgop td, #xuiibvmgop th {<br \/>\n  border-style: none;<br \/>\n}<\/p>\n<p>#xuiibvmgop p {<br \/>\n  margin: 0;<br \/>\n  padding: 0;<br \/>\n}<\/p>\n<p>#xuiibvmgop .gt_table {<br \/>\n  display: table;<br \/>\n  border-collapse: collapse;<br \/>\n  line-height: normal;<br \/>\n  margin-left: auto;<br \/>\n  margin-right: auto;<br \/>\n  color: #333333;<br \/>\n  font-size: 16px;<br \/>\n  font-weight: normal;<br \/>\n  font-style: normal;<br \/>\n  background-color: #FFFFFF;<br \/>\n  width: auto;<br \/>\n  border-top-style: solid;<br \/>\n  border-top-width: 2px;<br \/>\n  border-top-color: #A8A8A8;<br \/>\n  border-right-style: none;<br \/>\n  border-right-width: 2px;<br \/>\n  border-right-color: #D3D3D3;<br \/>\n  border-bottom-style: solid;<br \/>\n  border-bottom-width: 2px;<br \/>\n  border-bottom-color: #A8A8A8;<br \/>\n  border-left-style: none;<br \/>\n  border-left-width: 2px;<br \/>\n  border-left-color: #D3D3D3;<br \/>\n}<\/p>\n<p>#xuiibvmgop .gt_caption {<br \/>\n  padding-top: 4px;<br \/>\n  padding-bottom: 4px;<br \/>\n}<\/p>\n<p>#xuiibvmgop .gt_title {<br \/>\n  color: #333333;<br \/>\n  font-size: 125%;<br \/>\n  font-weight: initial;<br \/>\n  padding-top: 4px;<br \/>\n  padding-bottom: 4px;<br \/>\n  padding-left: 5px;<br \/>\n  padding-right: 5px;<br \/>\n  border-bottom-color: #FFFFFF;<br \/>\n  border-bottom-width: 0;<br \/>\n}<\/p>\n<p>#xuiibvmgop .gt_subtitle {<br \/>\n  color: #333333;<br \/>\n  font-size: 85%;<br \/>\n  font-weight: initial;<br \/>\n  padding-top: 3px;<br \/>\n  padding-bottom: 5px;<br \/>\n  padding-left: 5px;<br \/>\n  padding-right: 5px;<br \/>\n  border-top-color: #FFFFFF;<br \/>\n  border-top-width: 0;<br \/>\n}<\/p>\n<p>#xuiibvmgop .gt_heading {<br \/>\n  background-color: #FFFFFF;<br \/>\n  text-align: center;<br \/>\n  border-bottom-color: #FFFFFF;<br \/>\n  border-left-style: none;<br \/>\n  border-left-width: 1px;<br \/>\n  border-left-color: #D3D3D3;<br \/>\n  border-right-style: none;<br \/>\n  border-right-width: 1px;<br \/>\n  border-right-color: #D3D3D3;<br \/>\n}<\/p>\n<p>#xuiibvmgop .gt_bottom_border {<br \/>\n  border-bottom-style: solid;<br \/>\n  border-bottom-width: 2px;<br \/>\n  border-bottom-color: #D3D3D3;<br \/>\n}<\/p>\n<p>#xuiibvmgop .gt_col_headings {<br \/>\n  border-top-style: solid;<br \/>\n  border-top-width: 2px;<br \/>\n  border-top-color: #D3D3D3;<br \/>\n  border-bottom-style: solid;<br \/>\n  border-bottom-width: 2px;<br \/>\n  border-bottom-color: #D3D3D3;<br \/>\n  border-left-style: none;<br \/>\n  border-left-width: 1px;<br \/>\n  border-left-color: #D3D3D3;<br \/>\n  border-right-style: none;<br \/>\n  border-right-width: 1px;<br \/>\n  border-right-color: #D3D3D3;<br \/>\n}<\/p>\n<p>#xuiibvmgop .gt_col_heading {<br \/>\n  color: #333333;<br \/>\n  background-color: #FFFFFF;<br \/>\n  font-size: 100%;<br \/>\n  font-weight: normal;<br \/>\n  text-transform: inherit;<br \/>\n  border-left-style: none;<br \/>\n  border-left-width: 1px;<br \/>\n  border-left-color: #D3D3D3;<br \/>\n  border-right-style: none;<br \/>\n  border-right-width: 1px;<br \/>\n  border-right-color: #D3D3D3;<br \/>\n  vertical-align: bottom;<br \/>\n  padding-top: 5px;<br \/>\n  padding-bottom: 6px;<br \/>\n  padding-left: 5px;<br \/>\n  padding-right: 5px;<br \/>\n  overflow-x: hidden;<br \/>\n}<\/p>\n<p>#xuiibvmgop .gt_column_spanner_outer {<br \/>\n  color: #333333;<br \/>\n  background-color: #FFFFFF;<br \/>\n  font-size: 100%;<br \/>\n  font-weight: normal;<br \/>\n  text-transform: inherit;<br \/>\n  padding-top: 0;<br \/>\n  padding-bottom: 0;<br \/>\n  padding-left: 4px;<br \/>\n  padding-right: 4px;<br \/>\n}<\/p>\n<p>#xuiibvmgop .gt_column_spanner_outer:first-child {<br \/>\n  padding-left: 0;<br \/>\n}<\/p>\n<p>#xuiibvmgop .gt_column_spanner_outer:last-child {<br \/>\n  padding-right: 0;<br \/>\n}<\/p>\n<p>#xuiibvmgop .gt_column_spanner {<br \/>\n  border-bottom-style: solid;<br \/>\n  border-bottom-width: 2px;<br \/>\n  border-bottom-color: #D3D3D3;<br \/>\n  vertical-align: bottom;<br \/>\n  padding-top: 5px;<br \/>\n  padding-bottom: 5px;<br \/>\n  overflow-x: hidden;<br \/>\n  display: inline-block;<br \/>\n  width: 100%;<br \/>\n}<\/p>\n<p>#xuiibvmgop .gt_spanner_row {<br \/>\n  border-bottom-style: hidden;<br \/>\n}<\/p>\n<p>#xuiibvmgop .gt_group_heading {<br \/>\n  padding-top: 8px;<br \/>\n  padding-bottom: 8px;<br \/>\n  padding-left: 5px;<br \/>\n  padding-right: 5px;<br \/>\n  color: #333333;<br \/>\n  background-color: #FFFFFF;<br \/>\n  font-size: 100%;<br \/>\n  font-weight: initial;<br \/>\n  text-transform: inherit;<br \/>\n  border-top-style: solid;<br \/>\n  border-top-width: 2px;<br \/>\n  border-top-color: #D3D3D3;<br \/>\n  border-bottom-style: solid;<br \/>\n  border-bottom-width: 2px;<br \/>\n  border-bottom-color: #D3D3D3;<br \/>\n  border-left-style: none;<br \/>\n  border-left-width: 1px;<br \/>\n  border-left-color: #D3D3D3;<br \/>\n  border-right-style: none;<br \/>\n  border-right-width: 1px;<br \/>\n  border-right-color: #D3D3D3;<br \/>\n  vertical-align: middle;<br \/>\n  text-align: left;<br \/>\n}<\/p>\n<p>#xuiibvmgop .gt_empty_group_heading {<br \/>\n  padding: 0.5px;<br \/>\n  color: #333333;<br \/>\n  background-color: #FFFFFF;<br \/>\n  font-size: 100%;<br \/>\n  font-weight: initial;<br \/>\n  border-top-style: solid;<br \/>\n  border-top-width: 2px;<br \/>\n  border-top-color: #D3D3D3;<br \/>\n  border-bottom-style: solid;<br \/>\n  border-bottom-width: 2px;<br \/>\n  border-bottom-color: #D3D3D3;<br \/>\n  vertical-align: middle;<br \/>\n}<\/p>\n<p>#xuiibvmgop .gt_from_md > :first-child {<br \/>\n  margin-top: 0;<br \/>\n}<\/p>\n<p>#xuiibvmgop .gt_from_md > :last-child {<br \/>\n  margin-bottom: 0;<br \/>\n}<\/p>\n<p>#xuiibvmgop .gt_row {<br \/>\n  padding-top: 8px;<br \/>\n  padding-bottom: 8px;<br \/>\n  padding-left: 5px;<br \/>\n  padding-right: 5px;<br \/>\n  margin: 10px;<br \/>\n  border-top-style: solid;<br \/>\n  border-top-width: 1px;<br \/>\n  border-top-color: #D3D3D3;<br \/>\n  border-left-style: none;<br \/>\n  border-left-width: 1px;<br \/>\n  border-left-color: #D3D3D3;<br \/>\n  border-right-style: none;<br \/>\n  border-right-width: 1px;<br \/>\n  border-right-color: #D3D3D3;<br \/>\n  vertical-align: middle;<br \/>\n  overflow-x: hidden;<br \/>\n}<\/p>\n<p>#xuiibvmgop .gt_stub {<br \/>\n  color: #333333;<br \/>\n  background-color: #FFFFFF;<br \/>\n  font-size: 100%;<br \/>\n  font-weight: initial;<br \/>\n  text-transform: inherit;<br \/>\n  border-right-style: solid;<br \/>\n  border-right-width: 2px;<br \/>\n  border-right-color: #D3D3D3;<br \/>\n  padding-left: 5px;<br \/>\n  padding-right: 5px;<br \/>\n}<\/p>\n<p>#xuiibvmgop .gt_stub_row_group {<br \/>\n  color: #333333;<br \/>\n  background-color: #FFFFFF;<br \/>\n  font-size: 100%;<br \/>\n  font-weight: initial;<br \/>\n  text-transform: inherit;<br \/>\n  border-right-style: solid;<br \/>\n  border-right-width: 2px;<br \/>\n  border-right-color: #D3D3D3;<br \/>\n  padding-left: 5px;<br \/>\n  padding-right: 5px;<br \/>\n  vertical-align: top;<br \/>\n}<\/p>\n<p>#xuiibvmgop .gt_row_group_first td {<br \/>\n  border-top-width: 2px;<br \/>\n}<\/p>\n<p>#xuiibvmgop .gt_row_group_first th {<br \/>\n  border-top-width: 2px;<br \/>\n}<\/p>\n<p>#xuiibvmgop .gt_summary_row {<br \/>\n  color: #333333;<br \/>\n  background-color: #FFFFFF;<br \/>\n  text-transform: inherit;<br \/>\n  padding-top: 8px;<br \/>\n  padding-bottom: 8px;<br \/>\n  padding-left: 5px;<br \/>\n  padding-right: 5px;<br \/>\n}<\/p>\n<p>#xuiibvmgop .gt_first_summary_row {<br \/>\n  border-top-style: solid;<br \/>\n  border-top-color: #D3D3D3;<br \/>\n}<\/p>\n<p>#xuiibvmgop .gt_first_summary_row.thick {<br \/>\n  border-top-width: 2px;<br \/>\n}<\/p>\n<p>#xuiibvmgop .gt_last_summary_row {<br \/>\n  padding-top: 8px;<br \/>\n  padding-bottom: 8px;<br \/>\n  padding-left: 5px;<br \/>\n  padding-right: 5px;<br \/>\n  border-bottom-style: solid;<br \/>\n  border-bottom-width: 2px;<br \/>\n  border-bottom-color: #D3D3D3;<br \/>\n}<\/p>\n<p>#xuiibvmgop .gt_grand_summary_row {<br \/>\n  color: #333333;<br \/>\n  background-color: #FFFFFF;<br \/>\n  text-transform: inherit;<br \/>\n  padding-top: 8px;<br \/>\n  padding-bottom: 8px;<br \/>\n  padding-left: 5px;<br \/>\n  padding-right: 5px;<br \/>\n}<\/p>\n<p>#xuiibvmgop .gt_first_grand_summary_row {<br \/>\n  padding-top: 8px;<br \/>\n  padding-bottom: 8px;<br \/>\n  padding-left: 5px;<br \/>\n  padding-right: 5px;<br \/>\n  border-top-style: double;<br \/>\n  border-top-width: 6px;<br \/>\n  border-top-color: #D3D3D3;<br \/>\n}<\/p>\n<p>#xuiibvmgop .gt_last_grand_summary_row_top {<br \/>\n  padding-top: 8px;<br \/>\n  padding-bottom: 8px;<br \/>\n  padding-left: 5px;<br \/>\n  padding-right: 5px;<br \/>\n  border-bottom-style: double;<br \/>\n  border-bottom-width: 6px;<br \/>\n  border-bottom-color: #D3D3D3;<br \/>\n}<\/p>\n<p>#xuiibvmgop .gt_striped {<br \/>\n  background-color: rgba(128, 128, 128, 0.05);<br \/>\n}<\/p>\n<p>#xuiibvmgop .gt_table_body {<br \/>\n  border-top-style: solid;<br \/>\n  border-top-width: 2px;<br \/>\n  border-top-color: #D3D3D3;<br \/>\n  border-bottom-style: solid;<br \/>\n  border-bottom-width: 2px;<br \/>\n  border-bottom-color: #D3D3D3;<br \/>\n}<\/p>\n<p>#xuiibvmgop .gt_footnotes {<br \/>\n  color: #333333;<br \/>\n  background-color: #FFFFFF;<br \/>\n  border-bottom-style: none;<br \/>\n  border-bottom-width: 2px;<br \/>\n  border-bottom-color: #D3D3D3;<br \/>\n  border-left-style: none;<br \/>\n  border-left-width: 2px;<br \/>\n  border-left-color: #D3D3D3;<br \/>\n  border-right-style: none;<br \/>\n  border-right-width: 2px;<br \/>\n  border-right-color: #D3D3D3;<br \/>\n}<\/p>\n<p>#xuiibvmgop .gt_footnote {<br \/>\n  margin: 0px;<br \/>\n  font-size: 90%;<br \/>\n  padding-top: 4px;<br \/>\n  padding-bottom: 4px;<br \/>\n  padding-left: 5px;<br \/>\n  padding-right: 5px;<br \/>\n}<\/p>\n<p>#xuiibvmgop .gt_sourcenotes {<br \/>\n  color: #333333;<br \/>\n  background-color: #FFFFFF;<br \/>\n  border-bottom-style: none;<br \/>\n  border-bottom-width: 2px;<br \/>\n  border-bottom-color: #D3D3D3;<br \/>\n  border-left-style: none;<br \/>\n  border-left-width: 2px;<br \/>\n  border-left-color: #D3D3D3;<br \/>\n  border-right-style: none;<br \/>\n  border-right-width: 2px;<br \/>\n  border-right-color: #D3D3D3;<br \/>\n}<\/p>\n<p>#xuiibvmgop .gt_sourcenote {<br \/>\n  font-size: 90%;<br \/>\n  padding-top: 4px;<br \/>\n  padding-bottom: 4px;<br \/>\n  padding-left: 5px;<br \/>\n  padding-right: 5px;<br \/>\n}<\/p>\n<p>#xuiibvmgop .gt_left {<br \/>\n  text-align: left;<br \/>\n}<\/p>\n<p>#xuiibvmgop .gt_center {<br \/>\n  text-align: center;<br \/>\n}<\/p>\n<p>#xuiibvmgop .gt_right {<br \/>\n  text-align: right;<br \/>\n  font-variant-numeric: tabular-nums;<br \/>\n}<\/p>\n<p>#xuiibvmgop .gt_font_normal {<br \/>\n  font-weight: normal;<br \/>\n}<\/p>\n<p>#xuiibvmgop .gt_font_bold {<br \/>\n  font-weight: bold;<br \/>\n}<\/p>\n<p>#xuiibvmgop .gt_font_italic {<br \/>\n  font-style: italic;<br \/>\n}<\/p>\n<p>#xuiibvmgop .gt_super {<br \/>\n  font-size: 65%;<br \/>\n}<\/p>\n<p>#xuiibvmgop .gt_footnote_marks {<br \/>\n  font-size: 75%;<br \/>\n  vertical-align: 0.4em;<br \/>\n  position: initial;<br \/>\n}<\/p>\n<p>#xuiibvmgop .gt_asterisk {<br \/>\n  font-size: 100%;<br \/>\n  vertical-align: 0;<br \/>\n}<\/p>\n<p>#xuiibvmgop .gt_indent_1 {<br \/>\n  text-indent: 5px;<br \/>\n}<\/p>\n<p>#xuiibvmgop .gt_indent_2 {<br \/>\n  text-indent: 10px;<br \/>\n}<\/p>\n<p>#xuiibvmgop .gt_indent_3 {<br \/>\n  text-indent: 15px;<br \/>\n}<\/p>\n<p>#xuiibvmgop .gt_indent_4 {<br \/>\n  text-indent: 20px;<br \/>\n}<\/p>\n<p>#xuiibvmgop .gt_indent_5 {<br \/>\n  text-indent: 25px;<br \/>\n}<br \/>\n<\/style>\n<table class=\"gt_table\" data-quarto-disable-processing=\"false\" data-quarto-bootstrap=\"false\">\n<thead>\n<tr class=\"gt_col_headings gt_spanner_row\">\n<th class=\"gt_col_heading gt_columns_bottom_border gt_left\" rowspan=\"2\" colspan=\"1\" scope=\"col\" id=\"<strong>Characteristic<\/strong>&#8220;><strong>Characteristic<\/strong><\/th>\n<th class=\"gt_center gt_columns_top_border gt_column_spanner_outer\" rowspan=\"1\" colspan=\"3\" scope=\"colgroup\" id=\"mod2\"><span class=\"gt_column_spanner\">mod2<\/span><\/th>\n<th class=\"gt_center gt_columns_top_border gt_column_spanner_outer\" rowspan=\"1\" colspan=\"3\" scope=\"colgroup\" id=\"mod2_1\"><span class=\"gt_column_spanner\">mod2_1<\/span><\/th>\n<th class=\"gt_center gt_columns_top_border gt_column_spanner_outer\" rowspan=\"1\" colspan=\"3\" scope=\"colgroup\" id=\"mod2_2\"><span class=\"gt_column_spanner\">mod2_2<\/span><\/th>\n<th class=\"gt_center gt_columns_top_border gt_column_spanner_outer\" rowspan=\"1\" colspan=\"3\" scope=\"colgroup\" id=\"mod2_3\"><span class=\"gt_column_spanner\">mod2_3<\/span><\/th>\n<th class=\"gt_center gt_columns_top_border gt_column_spanner_outer\" rowspan=\"1\" colspan=\"3\" scope=\"colgroup\" id=\"modfp\"><span class=\"gt_column_spanner\">modfp<\/span><\/th>\n<\/tr>\n<tr class=\"gt_col_headings\">\n<th class=\"gt_col_heading gt_columns_bottom_border gt_center\" rowspan=\"1\" colspan=\"1\" scope=\"col\" id=\"<strong>Beta<\/strong>&#8220;><strong>Beta<\/strong><\/th>\n<th class=\"gt_col_heading gt_columns_bottom_border gt_center\" rowspan=\"1\" colspan=\"1\" scope=\"col\" id=\"<strong>95% CI<\/strong><span class=&quot;gt_footnote_marks&quot; style=&quot;white-space:nowrap;font-style:italic;font-weight:normal;&quot;><sup>1<\/sup><\/span>&#8220;><strong>95% CI<\/strong><span class=\"gt_footnote_marks\" style=\"white-space: nowrap; font-style: italic; font-weight: normal;\"><sup>1<\/sup><\/span><\/th>\n<th class=\"gt_col_heading gt_columns_bottom_border gt_center\" rowspan=\"1\" colspan=\"1\" scope=\"col\" id=\"<strong>p-value<\/strong>&#8220;><strong>p-value<\/strong><\/th>\n<th class=\"gt_col_heading gt_columns_bottom_border gt_center\" rowspan=\"1\" colspan=\"1\" scope=\"col\" id=\"<strong>Beta<\/strong>&#8220;><strong>Beta<\/strong><\/th>\n<th class=\"gt_col_heading gt_columns_bottom_border gt_center\" rowspan=\"1\" colspan=\"1\" scope=\"col\" id=\"<strong>95% CI<\/strong><span class=&quot;gt_footnote_marks&quot; style=&quot;white-space:nowrap;font-style:italic;font-weight:normal;&quot;><sup>1<\/sup><\/span>&#8220;><strong>95% CI<\/strong><span class=\"gt_footnote_marks\" style=\"white-space: nowrap; font-style: italic; font-weight: normal;\"><sup>1<\/sup><\/span><\/th>\n<th class=\"gt_col_heading gt_columns_bottom_border gt_center\" rowspan=\"1\" colspan=\"1\" scope=\"col\" id=\"<strong>p-value<\/strong>&#8220;><strong>p-value<\/strong><\/th>\n<th class=\"gt_col_heading gt_columns_bottom_border gt_center\" rowspan=\"1\" colspan=\"1\" scope=\"col\" id=\"<strong>Beta<\/strong>&#8220;><strong>Beta<\/strong><\/th>\n<th class=\"gt_col_heading gt_columns_bottom_border gt_center\" rowspan=\"1\" colspan=\"1\" scope=\"col\" id=\"<strong>95% CI<\/strong><span class=&quot;gt_footnote_marks&quot; style=&quot;white-space:nowrap;font-style:italic;font-weight:normal;&quot;><sup>1<\/sup><\/span>&#8220;><strong>95% CI<\/strong><span class=\"gt_footnote_marks\" style=\"white-space: nowrap; font-style: italic; font-weight: normal;\"><sup>1<\/sup><\/span><\/th>\n<th class=\"gt_col_heading gt_columns_bottom_border gt_center\" rowspan=\"1\" colspan=\"1\" scope=\"col\" id=\"<strong>p-value<\/strong>&#8220;><strong>p-value<\/strong><\/th>\n<th class=\"gt_col_heading gt_columns_bottom_border gt_center\" rowspan=\"1\" colspan=\"1\" scope=\"col\" id=\"<strong>Beta<\/strong>&#8220;><strong>Beta<\/strong><\/th>\n<th class=\"gt_col_heading gt_columns_bottom_border gt_center\" rowspan=\"1\" colspan=\"1\" scope=\"col\" id=\"<strong>95% CI<\/strong><span class=&quot;gt_footnote_marks&quot; style=&quot;white-space:nowrap;font-style:italic;font-weight:normal;&quot;><sup>1<\/sup><\/span>&#8220;><strong>95% CI<\/strong><span class=\"gt_footnote_marks\" style=\"white-space: nowrap; font-style: italic; font-weight: normal;\"><sup>1<\/sup><\/span><\/th>\n<th class=\"gt_col_heading gt_columns_bottom_border gt_center\" rowspan=\"1\" colspan=\"1\" scope=\"col\" id=\"<strong>p-value<\/strong>&#8220;><strong>p-value<\/strong><\/th>\n<th class=\"gt_col_heading gt_columns_bottom_border gt_center\" rowspan=\"1\" colspan=\"1\" scope=\"col\" id=\"<strong>Beta<\/strong>&#8220;><strong>Beta<\/strong><\/th>\n<th class=\"gt_col_heading gt_columns_bottom_border gt_center\" rowspan=\"1\" colspan=\"1\" scope=\"col\" id=\"<strong>95% CI<\/strong><span class=&quot;gt_footnote_marks&quot; style=&quot;white-space:nowrap;font-style:italic;font-weight:normal;&quot;><sup>1<\/sup><\/span>&#8220;><strong>95% CI<\/strong><span class=\"gt_footnote_marks\" style=\"white-space: nowrap; font-style: italic; font-weight: normal;\"><sup>1<\/sup><\/span><\/th>\n<th class=\"gt_col_heading gt_columns_bottom_border gt_center\" rowspan=\"1\" colspan=\"1\" scope=\"col\" id=\"<strong>p-value<\/strong>&#8220;><strong>p-value<\/strong><\/th>\n<\/tr>\n<\/thead>\n<tbody class=\"gt_table_body\">\n<tr>\n<td headers=\"label\" class=\"gt_row gt_left\">x1<\/td>\n<td headers=\"estimate_1\" class=\"gt_row gt_center\">0.25<\/td>\n<td headers=\"ci_1\" class=\"gt_row gt_center\">0.18, 0.33<\/td>\n<td headers=\"p.value_1\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"estimate_2\" class=\"gt_row gt_center\">0.25<\/td>\n<td headers=\"ci_2\" class=\"gt_row gt_center\">0.18, 0.33<\/td>\n<td headers=\"p.value_2\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"estimate_3\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"ci_3\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"p.value_3\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"estimate_4\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"ci_4\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"p.value_4\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"estimate_5\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"ci_5\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"p.value_5\" class=\"gt_row gt_center\"><\/td>\n<\/tr>\n<tr>\n<td headers=\"label\" class=\"gt_row gt_left\">x2<\/td>\n<td headers=\"estimate_1\" class=\"gt_row gt_center\">0.61<\/td>\n<td headers=\"ci_1\" class=\"gt_row gt_center\">0.53, 0.69<\/td>\n<td headers=\"p.value_1\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"estimate_2\" class=\"gt_row gt_center\">0.61<\/td>\n<td headers=\"ci_2\" class=\"gt_row gt_center\">0.53, 0.69<\/td>\n<td headers=\"p.value_2\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"estimate_3\" class=\"gt_row gt_center\">0.61<\/td>\n<td headers=\"ci_3\" class=\"gt_row gt_center\">0.54, 0.68<\/td>\n<td headers=\"p.value_3\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"estimate_4\" class=\"gt_row gt_center\">0.60<\/td>\n<td headers=\"ci_4\" class=\"gt_row gt_center\">0.53, 0.68<\/td>\n<td headers=\"p.value_4\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"estimate_5\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"ci_5\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"p.value_5\" class=\"gt_row gt_center\"><\/td>\n<\/tr>\n<tr>\n<td headers=\"label\" class=\"gt_row gt_left\">log(x1)<\/td>\n<td headers=\"estimate_1\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"ci_1\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"p.value_1\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"estimate_2\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"ci_2\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"p.value_2\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"estimate_3\" class=\"gt_row gt_center\">0.83<\/td>\n<td headers=\"ci_3\" class=\"gt_row gt_center\">0.66, 1.0<\/td>\n<td headers=\"p.value_3\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"estimate_4\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"ci_4\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"p.value_4\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"estimate_5\" class=\"gt_row gt_center\">0.83<\/td>\n<td headers=\"ci_5\" class=\"gt_row gt_center\">0.66, 1.0<\/td>\n<td headers=\"p.value_5\" class=\"gt_row gt_center\"><\/td>\n<\/tr>\n<tr>\n<td headers=\"label\" class=\"gt_row gt_left\">sqrt(x1)<\/td>\n<td headers=\"estimate_1\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"ci_1\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"p.value_1\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"estimate_2\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"ci_2\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"p.value_2\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"estimate_3\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"ci_3\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"p.value_3\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"estimate_4\" class=\"gt_row gt_center\">1.1<\/td>\n<td headers=\"ci_4\" class=\"gt_row gt_center\">0.84, 1.4<\/td>\n<td headers=\"p.value_4\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"estimate_5\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"ci_5\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"p.value_5\" class=\"gt_row gt_center\"><\/td>\n<\/tr>\n<tr>\n<td headers=\"label\" class=\"gt_row gt_left\">I(x2^1)<\/td>\n<td headers=\"estimate_1\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"ci_1\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"p.value_1\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"estimate_2\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"ci_2\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"p.value_2\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"estimate_3\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"ci_3\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"p.value_3\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"estimate_4\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"ci_4\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"p.value_4\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"estimate_5\" class=\"gt_row gt_center\">0.61<\/td>\n<td headers=\"ci_5\" class=\"gt_row gt_center\">0.54, 0.68<\/td>\n<td headers=\"p.value_5\" class=\"gt_row gt_center\"><\/td>\n<\/tr>\n<\/tbody>\n<tfoot class=\"gt_footnotes\">\n<tr>\n<td class=\"gt_footnote\" colspan=\"16\"><span class=\"gt_footnote_marks\" style=\"white-space: nowrap; font-style: italic; font-weight: normal;\"><sup>1<\/sup><\/span> CI = Confidence Interval<\/td>\n<\/tr>\n<\/tfoot>\n<\/table>\n<\/div>\n\n\n\n<pre class=\"wp-block-code\"><code>\n### Model3\n\n\u3053\u3053\u304b\u3089\u306f\u6b8b\u308a\u306e\u30e2\u30c7\u30eb\u3082\u3055\u304f\u3055\u304f\u3068\u898b\u3066\u304a\u304d\u307e\u3057\u3087\u3046\u3002\n\n$\nY_3 = \\\\beta_0 + \\\\beta_1 \\\\sqrt{X_1} + \\\\beta_2 (X_2)^2 + \\\\epsilon\n$\n\n```r\nggcrPlots(mod3)<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/bunseki-data.com\/r-onlinecourse\/wp-content\/uploads\/2023\/11\/unnamed-chunk-36-1-1.png\" alt=\"\"\/><\/figure>\n\n\n\n<pre class=\"wp-block-code\"><code>car::residualPlots(mod3)<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/bunseki-data.com\/r-onlinecourse\/wp-content\/uploads\/2023\/11\/unnamed-chunk-37-1-1.png\" alt=\"\"\/><\/figure>\n\n\n\n<pre class=\"wp-block-code\"><code>##            Test stat Pr(&gt;|Test stat|)    \n## x1            0.5469           0.5857    \n## x2           40.4458           &lt;2e-16 ***\n## Tukey test   36.5250           &lt;2e-16 ***\n## ---\n## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1<\/code><\/pre>\n\n\n\n<p>\u660e\u3089\u304b\u306bx2\u304c\u304a\u304b\u3057\u3044\u3002x1\u306f\u3069\u3061\u3089\u306e\u30d7\u30ed\u30c3\u30c8\u3082\u3061\u3087\u3063\u3068\u8f9b\u3044\u304b\u3082\u3057\u308c\u307e\u305b\u3093\u3002<\/p>\n\n\n\n<p>mfp\u3067Transformation\u3092\u884c\u3046\u3068\u3001<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>modfp &lt;- mfp(y3 ~ fp(x1, scale=FALSE) + fp(x2, scale=FALSE), data = data2)\n\nmodfp &lt;- lm(modfp$formula, data = data2)\n\nsummary(modfp)<\/code><\/pre>\n\n\n\n<pre class=\"wp-block-code\"><code>## \n## Call:\n## lm(formula = modfp$formula, data = data2)\n## \n## Residuals:\n##     Min      1Q  Median      3Q     Max \n## -3.9323 -0.8209  0.1815  0.7583  2.3702 \n## \n## Coefficients:\n##             Estimate Std. Error t value Pr(&gt;|t|)    \n## (Intercept) 0.995572   0.237838   4.186 6.25e-05 ***\n## I(x2^2)     0.602832   0.003852 156.498  &lt; 2e-16 ***\n## I(x1^1)     0.272571   0.035917   7.589 1.98e-11 ***\n## ---\n## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n## \n## Residual standard error: 1.095 on 97 degrees of freedom\n## Multiple R-squared:  0.9961, Adjusted R-squared:  0.996 \n## F-statistic: 1.235e+04 on 2 and 97 DF,  p-value: &lt; 2.2e-16<\/code><\/pre>\n\n\n\n<p>\u3046\u307e\u304f\u63a8\u5b9a\u3067\u304d\u3066\u3044\u307e\u305b\u3093\u306d\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>mod3_1 &lt;- update(mod3, ~ x1 + I(x2^2))\nggcrPlots(mod3_1)<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/bunseki-data.com\/r-onlinecourse\/wp-content\/uploads\/2023\/11\/unnamed-chunk-39-1-1.png\" alt=\"\"\/><\/figure>\n\n\n\n<pre class=\"wp-block-code\"><code>car::residualPlots(mod3_1)<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/bunseki-data.com\/r-onlinecourse\/wp-content\/uploads\/2023\/11\/unnamed-chunk-40-1-1.png\" alt=\"\"\/><\/figure>\n\n\n\n<pre class=\"wp-block-code\"><code>##            Test stat Pr(&gt;|Test stat|)\n## x1            1.4724           0.1442\n## I(x2^2)      -0.0769           0.9389\n## Tukey test    0.0524           0.9582<\/code><\/pre>\n\n\n\n<p>\u5fae\u5999\u306bx1\u304c\u66f2\u304c\u3063\u3066\u3044\u308b\u3088\u3046\u306b\u898b\u3048\u306a\u304f\u3082\u306a\u3044<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>mod3_2 &lt;- update(mod3, ~ sqrt(x1) + I(x2^2))\nggcrPlots(mod3_2)<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/bunseki-data.com\/r-onlinecourse\/wp-content\/uploads\/2023\/11\/unnamed-chunk-41-1-1.png\" alt=\"\"\/><\/figure>\n\n\n\n<pre class=\"wp-block-code\"><code>car::residualPlots(mod3_2)<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/bunseki-data.com\/r-onlinecourse\/wp-content\/uploads\/2023\/11\/unnamed-chunk-42-1-1.png\" alt=\"\"\/><\/figure>\n\n\n\n<pre class=\"wp-block-code\"><code>##            Test stat Pr(&gt;|Test stat|)   \n## sqrt(x1)      3.1279         0.002331 **\n## I(x2^2)      -0.1066         0.915337   \n## Tukey test    0.0191         0.984800   \n## ---\n## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1<\/code><\/pre>\n\n\n\n<p>residualPlots\u3067\u3059\u308b\u3068\u6b63\u3057\u3044\u5f62\u306b\u3059\u308b\u3068x1\u306f\u3088\u308a\u66f2\u304c\u3063\u3066\u3044\u308b\u3088\u3046\u306b\u3082\u898b\u3048\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>list(mod3, mod3_1, mod3_2, modfp) |&gt; \n  map(~gtsummary::tbl_regression(.)) |&gt; \n  gtsummary::tbl_merge(tab_spanner = c(\"mod3\",\"mod3_1\",\"mod3_2\",\"modfp\"))<\/code><\/pre>\n\n\n\n<p>&#8220;`{=html}<\/p>\n\n\n\n<div id=\"vquivrtgsb\" style=\"overflow-x: auto; overflow-y: auto; width: auto; height: auto; padding: 10px 0px 10px 0px;\"><style>#vquivrtgsb table {<br \/>\n  font-family: system-ui, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji', 'Segoe UI Symbol', 'Noto Color Emoji';<br \/>\n  -webkit-font-smoothing: antialiased;<br \/>\n  -moz-osx-font-smoothing: grayscale;<br \/>\n}<\/p>\n<p>#vquivrtgsb thead, #vquivrtgsb tbody, #vquivrtgsb tfoot, #vquivrtgsb tr, #vquivrtgsb td, #vquivrtgsb th {<br \/>\n  border-style: none;<br \/>\n}<\/p>\n<p>#vquivrtgsb p {<br \/>\n  margin: 0;<br \/>\n  padding: 0;<br \/>\n}<\/p>\n<p>#vquivrtgsb .gt_table {<br \/>\n  display: table;<br \/>\n  border-collapse: collapse;<br \/>\n  line-height: normal;<br \/>\n  margin-left: auto;<br \/>\n  margin-right: auto;<br \/>\n  color: #333333;<br \/>\n  font-size: 16px;<br \/>\n  font-weight: normal;<br \/>\n  font-style: normal;<br \/>\n  background-color: #FFFFFF;<br \/>\n  width: auto;<br \/>\n  border-top-style: solid;<br \/>\n  border-top-width: 2px;<br \/>\n  border-top-color: #A8A8A8;<br \/>\n  border-right-style: none;<br \/>\n  border-right-width: 2px;<br \/>\n  border-right-color: #D3D3D3;<br \/>\n  border-bottom-style: solid;<br \/>\n  border-bottom-width: 2px;<br \/>\n  border-bottom-color: #A8A8A8;<br \/>\n  border-left-style: none;<br \/>\n  border-left-width: 2px;<br \/>\n  border-left-color: #D3D3D3;<br \/>\n}<\/p>\n<p>#vquivrtgsb .gt_caption {<br \/>\n  padding-top: 4px;<br \/>\n  padding-bottom: 4px;<br \/>\n}<\/p>\n<p>#vquivrtgsb .gt_title {<br \/>\n  color: #333333;<br \/>\n  font-size: 125%;<br \/>\n  font-weight: initial;<br \/>\n  padding-top: 4px;<br \/>\n  padding-bottom: 4px;<br \/>\n  padding-left: 5px;<br \/>\n  padding-right: 5px;<br \/>\n  border-bottom-color: #FFFFFF;<br \/>\n  border-bottom-width: 0;<br \/>\n}<\/p>\n<p>#vquivrtgsb .gt_subtitle {<br \/>\n  color: #333333;<br \/>\n  font-size: 85%;<br \/>\n  font-weight: initial;<br \/>\n  padding-top: 3px;<br \/>\n  padding-bottom: 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1px;<br \/>\n  border-left-color: #D3D3D3;<br \/>\n  border-right-style: none;<br \/>\n  border-right-width: 1px;<br \/>\n  border-right-color: #D3D3D3;<br \/>\n}<\/p>\n<p>#vquivrtgsb .gt_col_heading {<br \/>\n  color: #333333;<br \/>\n  background-color: #FFFFFF;<br \/>\n  font-size: 100%;<br \/>\n  font-weight: normal;<br \/>\n  text-transform: inherit;<br \/>\n  border-left-style: none;<br \/>\n  border-left-width: 1px;<br \/>\n  border-left-color: #D3D3D3;<br \/>\n  border-right-style: none;<br \/>\n  border-right-width: 1px;<br \/>\n  border-right-color: #D3D3D3;<br \/>\n  vertical-align: bottom;<br \/>\n  padding-top: 5px;<br \/>\n  padding-bottom: 6px;<br \/>\n  padding-left: 5px;<br \/>\n  padding-right: 5px;<br \/>\n  overflow-x: hidden;<br \/>\n}<\/p>\n<p>#vquivrtgsb .gt_column_spanner_outer {<br \/>\n  color: #333333;<br \/>\n  background-color: #FFFFFF;<br \/>\n  font-size: 100%;<br \/>\n  font-weight: normal;<br \/>\n  text-transform: inherit;<br \/>\n  padding-top: 0;<br \/>\n  padding-bottom: 0;<br \/>\n  padding-left: 4px;<br \/>\n  padding-right: 4px;<br \/>\n}<\/p>\n<p>#vquivrtgsb .gt_column_spanner_outer:first-child {<br \/>\n  padding-left: 0;<br \/>\n}<\/p>\n<p>#vquivrtgsb .gt_column_spanner_outer:last-child {<br \/>\n  padding-right: 0;<br \/>\n}<\/p>\n<p>#vquivrtgsb .gt_column_spanner {<br \/>\n  border-bottom-style: solid;<br \/>\n  border-bottom-width: 2px;<br \/>\n  border-bottom-color: #D3D3D3;<br \/>\n  vertical-align: bottom;<br \/>\n  padding-top: 5px;<br \/>\n  padding-bottom: 5px;<br \/>\n  overflow-x: hidden;<br \/>\n  display: inline-block;<br \/>\n  width: 100%;<br \/>\n}<\/p>\n<p>#vquivrtgsb .gt_spanner_row {<br \/>\n  border-bottom-style: hidden;<br \/>\n}<\/p>\n<p>#vquivrtgsb .gt_group_heading {<br \/>\n  padding-top: 8px;<br \/>\n  padding-bottom: 8px;<br \/>\n  padding-left: 5px;<br \/>\n  padding-right: 5px;<br \/>\n  color: #333333;<br \/>\n  background-color: #FFFFFF;<br \/>\n  font-size: 100%;<br \/>\n  font-weight: initial;<br \/>\n  text-transform: inherit;<br \/>\n  border-top-style: solid;<br \/>\n  border-top-width: 2px;<br \/>\n  border-top-color: #D3D3D3;<br \/>\n  border-bottom-style: solid;<br \/>\n  border-bottom-width: 2px;<br \/>\n  border-bottom-color: #D3D3D3;<br \/>\n  border-left-style: none;<br \/>\n  border-left-width: 1px;<br \/>\n  border-left-color: #D3D3D3;<br \/>\n  border-right-style: none;<br \/>\n  border-right-width: 1px;<br \/>\n  border-right-color: #D3D3D3;<br \/>\n  vertical-align: middle;<br \/>\n  text-align: left;<br \/>\n}<\/p>\n<p>#vquivrtgsb .gt_empty_group_heading {<br \/>\n  padding: 0.5px;<br \/>\n  color: #333333;<br \/>\n  background-color: #FFFFFF;<br \/>\n  font-size: 100%;<br \/>\n  font-weight: initial;<br \/>\n  border-top-style: solid;<br \/>\n  border-top-width: 2px;<br \/>\n  border-top-color: #D3D3D3;<br \/>\n  border-bottom-style: solid;<br \/>\n  border-bottom-width: 2px;<br \/>\n  border-bottom-color: #D3D3D3;<br \/>\n  vertical-align: middle;<br \/>\n}<\/p>\n<p>#vquivrtgsb .gt_from_md > :first-child {<br \/>\n  margin-top: 0;<br \/>\n}<\/p>\n<p>#vquivrtgsb .gt_from_md > :last-child {<br \/>\n  margin-bottom: 0;<br \/>\n}<\/p>\n<p>#vquivrtgsb .gt_row {<br \/>\n  padding-top: 8px;<br \/>\n  padding-bottom: 8px;<br \/>\n  padding-left: 5px;<br \/>\n  padding-right: 5px;<br \/>\n  margin: 10px;<br \/>\n  border-top-style: solid;<br \/>\n  border-top-width: 1px;<br \/>\n  border-top-color: #D3D3D3;<br \/>\n  border-left-style: none;<br \/>\n  border-left-width: 1px;<br \/>\n  border-left-color: #D3D3D3;<br \/>\n  border-right-style: none;<br \/>\n  border-right-width: 1px;<br \/>\n  border-right-color: #D3D3D3;<br \/>\n  vertical-align: middle;<br \/>\n  overflow-x: hidden;<br \/>\n}<\/p>\n<p>#vquivrtgsb .gt_stub {<br \/>\n  color: #333333;<br \/>\n  background-color: #FFFFFF;<br \/>\n  font-size: 100%;<br \/>\n  font-weight: initial;<br \/>\n  text-transform: inherit;<br \/>\n  border-right-style: solid;<br \/>\n  border-right-width: 2px;<br \/>\n  border-right-color: #D3D3D3;<br \/>\n  padding-left: 5px;<br \/>\n  padding-right: 5px;<br \/>\n}<\/p>\n<p>#vquivrtgsb .gt_stub_row_group {<br \/>\n  color: #333333;<br \/>\n  background-color: #FFFFFF;<br \/>\n  font-size: 100%;<br \/>\n  font-weight: initial;<br \/>\n  text-transform: inherit;<br \/>\n  border-right-style: solid;<br \/>\n  border-right-width: 2px;<br \/>\n  border-right-color: #D3D3D3;<br \/>\n  padding-left: 5px;<br \/>\n  padding-right: 5px;<br \/>\n  vertical-align: top;<br \/>\n}<\/p>\n<p>#vquivrtgsb .gt_row_group_first td {<br \/>\n  border-top-width: 2px;<br \/>\n}<\/p>\n<p>#vquivrtgsb .gt_row_group_first th {<br \/>\n  border-top-width: 2px;<br \/>\n}<\/p>\n<p>#vquivrtgsb .gt_summary_row {<br \/>\n  color: #333333;<br \/>\n  background-color: #FFFFFF;<br \/>\n  text-transform: inherit;<br \/>\n  padding-top: 8px;<br \/>\n  padding-bottom: 8px;<br \/>\n  padding-left: 5px;<br \/>\n  padding-right: 5px;<br \/>\n}<\/p>\n<p>#vquivrtgsb .gt_first_summary_row {<br \/>\n  border-top-style: solid;<br \/>\n  border-top-color: #D3D3D3;<br \/>\n}<\/p>\n<p>#vquivrtgsb .gt_first_summary_row.thick {<br \/>\n  border-top-width: 2px;<br \/>\n}<\/p>\n<p>#vquivrtgsb .gt_last_summary_row {<br \/>\n  padding-top: 8px;<br \/>\n  padding-bottom: 8px;<br \/>\n  padding-left: 5px;<br \/>\n  padding-right: 5px;<br \/>\n  border-bottom-style: solid;<br \/>\n  border-bottom-width: 2px;<br \/>\n  border-bottom-color: #D3D3D3;<br \/>\n}<\/p>\n<p>#vquivrtgsb .gt_grand_summary_row {<br \/>\n  color: #333333;<br \/>\n  background-color: #FFFFFF;<br \/>\n  text-transform: inherit;<br \/>\n  padding-top: 8px;<br \/>\n  padding-bottom: 8px;<br \/>\n  padding-left: 5px;<br \/>\n  padding-right: 5px;<br \/>\n}<\/p>\n<p>#vquivrtgsb .gt_first_grand_summary_row {<br \/>\n  padding-top: 8px;<br \/>\n  padding-bottom: 8px;<br \/>\n  padding-left: 5px;<br \/>\n  padding-right: 5px;<br \/>\n  border-top-style: double;<br \/>\n  border-top-width: 6px;<br \/>\n  border-top-color: #D3D3D3;<br \/>\n}<\/p>\n<p>#vquivrtgsb .gt_last_grand_summary_row_top {<br \/>\n  padding-top: 8px;<br \/>\n  padding-bottom: 8px;<br \/>\n  padding-left: 5px;<br \/>\n  padding-right: 5px;<br \/>\n  border-bottom-style: double;<br \/>\n  border-bottom-width: 6px;<br \/>\n  border-bottom-color: #D3D3D3;<br \/>\n}<\/p>\n<p>#vquivrtgsb .gt_striped {<br \/>\n  background-color: rgba(128, 128, 128, 0.05);<br \/>\n}<\/p>\n<p>#vquivrtgsb .gt_table_body {<br \/>\n  border-top-style: solid;<br \/>\n  border-top-width: 2px;<br \/>\n  border-top-color: #D3D3D3;<br \/>\n  border-bottom-style: solid;<br \/>\n  border-bottom-width: 2px;<br \/>\n  border-bottom-color: #D3D3D3;<br \/>\n}<\/p>\n<p>#vquivrtgsb .gt_footnotes {<br \/>\n  color: #333333;<br \/>\n  background-color: #FFFFFF;<br \/>\n  border-bottom-style: none;<br \/>\n  border-bottom-width: 2px;<br \/>\n  border-bottom-color: #D3D3D3;<br \/>\n  border-left-style: none;<br \/>\n  border-left-width: 2px;<br \/>\n  border-left-color: #D3D3D3;<br \/>\n  border-right-style: none;<br \/>\n  border-right-width: 2px;<br \/>\n  border-right-color: #D3D3D3;<br \/>\n}<\/p>\n<p>#vquivrtgsb .gt_footnote {<br \/>\n  margin: 0px;<br \/>\n  font-size: 90%;<br \/>\n  padding-top: 4px;<br \/>\n  padding-bottom: 4px;<br \/>\n  padding-left: 5px;<br \/>\n  padding-right: 5px;<br \/>\n}<\/p>\n<p>#vquivrtgsb .gt_sourcenotes {<br \/>\n  color: #333333;<br \/>\n  background-color: #FFFFFF;<br \/>\n  border-bottom-style: none;<br \/>\n  border-bottom-width: 2px;<br \/>\n  border-bottom-color: #D3D3D3;<br \/>\n  border-left-style: none;<br \/>\n  border-left-width: 2px;<br \/>\n  border-left-color: #D3D3D3;<br \/>\n  border-right-style: none;<br \/>\n  border-right-width: 2px;<br \/>\n  border-right-color: #D3D3D3;<br \/>\n}<\/p>\n<p>#vquivrtgsb .gt_sourcenote {<br \/>\n  font-size: 90%;<br \/>\n  padding-top: 4px;<br \/>\n  padding-bottom: 4px;<br \/>\n  padding-left: 5px;<br \/>\n  padding-right: 5px;<br \/>\n}<\/p>\n<p>#vquivrtgsb .gt_left {<br \/>\n  text-align: left;<br \/>\n}<\/p>\n<p>#vquivrtgsb .gt_center {<br \/>\n  text-align: center;<br \/>\n}<\/p>\n<p>#vquivrtgsb .gt_right {<br \/>\n  text-align: right;<br \/>\n  font-variant-numeric: tabular-nums;<br \/>\n}<\/p>\n<p>#vquivrtgsb .gt_font_normal {<br \/>\n  font-weight: normal;<br \/>\n}<\/p>\n<p>#vquivrtgsb .gt_font_bold {<br \/>\n  font-weight: bold;<br \/>\n}<\/p>\n<p>#vquivrtgsb .gt_font_italic {<br \/>\n  font-style: italic;<br \/>\n}<\/p>\n<p>#vquivrtgsb .gt_super {<br \/>\n  font-size: 65%;<br \/>\n}<\/p>\n<p>#vquivrtgsb .gt_footnote_marks {<br \/>\n  font-size: 75%;<br \/>\n  vertical-align: 0.4em;<br \/>\n  position: initial;<br \/>\n}<\/p>\n<p>#vquivrtgsb .gt_asterisk {<br \/>\n  font-size: 100%;<br \/>\n  vertical-align: 0;<br \/>\n}<\/p>\n<p>#vquivrtgsb .gt_indent_1 {<br \/>\n  text-indent: 5px;<br \/>\n}<\/p>\n<p>#vquivrtgsb .gt_indent_2 {<br \/>\n  text-indent: 10px;<br \/>\n}<\/p>\n<p>#vquivrtgsb .gt_indent_3 {<br \/>\n  text-indent: 15px;<br \/>\n}<\/p>\n<p>#vquivrtgsb .gt_indent_4 {<br \/>\n  text-indent: 20px;<br \/>\n}<\/p>\n<p>#vquivrtgsb .gt_indent_5 {<br \/>\n  text-indent: 25px;<br \/>\n}<br \/>\n<\/style>\n<table class=\"gt_table\" data-quarto-disable-processing=\"false\" data-quarto-bootstrap=\"false\">\n<thead>\n<tr class=\"gt_col_headings gt_spanner_row\">\n<th class=\"gt_col_heading gt_columns_bottom_border gt_left\" rowspan=\"2\" colspan=\"1\" scope=\"col\" id=\"<strong>Characteristic<\/strong>&#8220;><strong>Characteristic<\/strong><\/th>\n<th class=\"gt_center gt_columns_top_border gt_column_spanner_outer\" rowspan=\"1\" colspan=\"3\" scope=\"colgroup\" id=\"mod3\"><span class=\"gt_column_spanner\">mod3<\/span><\/th>\n<th class=\"gt_center gt_columns_top_border gt_column_spanner_outer\" rowspan=\"1\" colspan=\"3\" scope=\"colgroup\" id=\"mod3_1\"><span class=\"gt_column_spanner\">mod3_1<\/span><\/th>\n<th class=\"gt_center gt_columns_top_border gt_column_spanner_outer\" rowspan=\"1\" colspan=\"3\" scope=\"colgroup\" id=\"mod3_2\"><span class=\"gt_column_spanner\">mod3_2<\/span><\/th>\n<th class=\"gt_center gt_columns_top_border gt_column_spanner_outer\" rowspan=\"1\" colspan=\"3\" scope=\"colgroup\" id=\"modfp\"><span class=\"gt_column_spanner\">modfp<\/span><\/th>\n<\/tr>\n<tr class=\"gt_col_headings\">\n<th class=\"gt_col_heading gt_columns_bottom_border gt_center\" rowspan=\"1\" colspan=\"1\" scope=\"col\" id=\"<strong>Beta<\/strong>&#8220;><strong>Beta<\/strong><\/th>\n<th class=\"gt_col_heading gt_columns_bottom_border gt_center\" rowspan=\"1\" colspan=\"1\" scope=\"col\" id=\"<strong>95% CI<\/strong><span class=&quot;gt_footnote_marks&quot; style=&quot;white-space:nowrap;font-style:italic;font-weight:normal;&quot;><sup>1<\/sup><\/span>&#8220;><strong>95% CI<\/strong><span class=\"gt_footnote_marks\" style=\"white-space: nowrap; font-style: italic; font-weight: normal;\"><sup>1<\/sup><\/span><\/th>\n<th class=\"gt_col_heading gt_columns_bottom_border gt_center\" rowspan=\"1\" colspan=\"1\" scope=\"col\" id=\"<strong>p-value<\/strong>&#8220;><strong>p-value<\/strong><\/th>\n<th class=\"gt_col_heading gt_columns_bottom_border gt_center\" rowspan=\"1\" colspan=\"1\" scope=\"col\" id=\"<strong>Beta<\/strong>&#8220;><strong>Beta<\/strong><\/th>\n<th class=\"gt_col_heading gt_columns_bottom_border gt_center\" rowspan=\"1\" colspan=\"1\" scope=\"col\" id=\"<strong>95% CI<\/strong><span class=&quot;gt_footnote_marks&quot; style=&quot;white-space:nowrap;font-style:italic;font-weight:normal;&quot;><sup>1<\/sup><\/span>&#8220;><strong>95% CI<\/strong><span class=\"gt_footnote_marks\" style=\"white-space: nowrap; font-style: italic; font-weight: normal;\"><sup>1<\/sup><\/span><\/th>\n<th class=\"gt_col_heading gt_columns_bottom_border gt_center\" rowspan=\"1\" colspan=\"1\" scope=\"col\" id=\"<strong>p-value<\/strong>&#8220;><strong>p-value<\/strong><\/th>\n<th class=\"gt_col_heading gt_columns_bottom_border gt_center\" rowspan=\"1\" colspan=\"1\" scope=\"col\" id=\"<strong>Beta<\/strong>&#8220;><strong>Beta<\/strong><\/th>\n<th class=\"gt_col_heading gt_columns_bottom_border gt_center\" rowspan=\"1\" colspan=\"1\" scope=\"col\" id=\"<strong>95% CI<\/strong><span class=&quot;gt_footnote_marks&quot; style=&quot;white-space:nowrap;font-style:italic;font-weight:normal;&quot;><sup>1<\/sup><\/span>&#8220;><strong>95% CI<\/strong><span class=\"gt_footnote_marks\" style=\"white-space: nowrap; font-style: italic; font-weight: normal;\"><sup>1<\/sup><\/span><\/th>\n<th class=\"gt_col_heading gt_columns_bottom_border gt_center\" rowspan=\"1\" colspan=\"1\" scope=\"col\" id=\"<strong>p-value<\/strong>&#8220;><strong>p-value<\/strong><\/th>\n<th class=\"gt_col_heading gt_columns_bottom_border gt_center\" rowspan=\"1\" colspan=\"1\" scope=\"col\" id=\"<strong>Beta<\/strong>&#8220;><strong>Beta<\/strong><\/th>\n<th class=\"gt_col_heading gt_columns_bottom_border gt_center\" rowspan=\"1\" colspan=\"1\" scope=\"col\" id=\"<strong>95% CI<\/strong><span class=&quot;gt_footnote_marks&quot; style=&quot;white-space:nowrap;font-style:italic;font-weight:normal;&quot;><sup>1<\/sup><\/span>&#8220;><strong>95% CI<\/strong><span class=\"gt_footnote_marks\" style=\"white-space: nowrap; font-style: italic; font-weight: normal;\"><sup>1<\/sup><\/span><\/th>\n<th class=\"gt_col_heading gt_columns_bottom_border gt_center\" rowspan=\"1\" colspan=\"1\" scope=\"col\" id=\"<strong>p-value<\/strong>&#8220;><strong>p-value<\/strong><\/th>\n<\/tr>\n<\/thead>\n<tbody class=\"gt_table_body\">\n<tr>\n<td headers=\"label\" class=\"gt_row gt_left\">x1<\/td>\n<td headers=\"estimate_1\" class=\"gt_row gt_center\">0.35<\/td>\n<td headers=\"ci_1\" class=\"gt_row gt_center\">0.05, 0.65<\/td>\n<td headers=\"p.value_1\" class=\"gt_row gt_center\">0.025<\/td>\n<td headers=\"estimate_2\" class=\"gt_row gt_center\">0.27<\/td>\n<td headers=\"ci_2\" class=\"gt_row gt_center\">0.20, 0.34<\/td>\n<td headers=\"p.value_2\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"estimate_3\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"ci_3\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"p.value_3\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"estimate_4\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"ci_4\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"p.value_4\" class=\"gt_row gt_center\"><\/td>\n<\/tr>\n<tr>\n<td headers=\"label\" class=\"gt_row gt_left\">x2<\/td>\n<td headers=\"estimate_1\" class=\"gt_row gt_center\">5.9<\/td>\n<td headers=\"ci_1\" class=\"gt_row gt_center\">5.5, 6.2<\/td>\n<td headers=\"p.value_1\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"estimate_2\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"ci_2\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"p.value_2\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"estimate_3\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"ci_3\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"p.value_3\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"estimate_4\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"ci_4\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"p.value_4\" class=\"gt_row gt_center\"><\/td>\n<\/tr>\n<tr>\n<td headers=\"label\" class=\"gt_row gt_left\">I(x2^2)<\/td>\n<td headers=\"estimate_1\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"ci_1\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"p.value_1\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"estimate_2\" class=\"gt_row gt_center\">0.60<\/td>\n<td headers=\"ci_2\" class=\"gt_row gt_center\">0.60, 0.61<\/td>\n<td headers=\"p.value_2\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"estimate_3\" class=\"gt_row gt_center\">0.60<\/td>\n<td headers=\"ci_3\" class=\"gt_row gt_center\">0.59, 0.61<\/td>\n<td headers=\"p.value_3\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"estimate_4\" class=\"gt_row gt_center\">0.60<\/td>\n<td headers=\"ci_4\" class=\"gt_row gt_center\">0.60, 0.61<\/td>\n<td headers=\"p.value_4\" class=\"gt_row gt_center\"><\/td>\n<\/tr>\n<tr>\n<td headers=\"label\" class=\"gt_row gt_left\">sqrt(x1)<\/td>\n<td headers=\"estimate_1\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"ci_1\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"p.value_1\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"estimate_2\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"ci_2\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"p.value_2\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"estimate_3\" class=\"gt_row gt_center\">0.99<\/td>\n<td headers=\"ci_3\" class=\"gt_row gt_center\">0.70, 1.3<\/td>\n<td headers=\"p.value_3\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"estimate_4\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"ci_4\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"p.value_4\" class=\"gt_row gt_center\"><\/td>\n<\/tr>\n<tr>\n<td headers=\"label\" class=\"gt_row gt_left\">I(x1^1)<\/td>\n<td headers=\"estimate_1\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"ci_1\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"p.value_1\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"estimate_2\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"ci_2\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"p.value_2\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"estimate_3\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"ci_3\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"p.value_3\" class=\"gt_row gt_center\"><\/td>\n<td headers=\"estimate_4\" class=\"gt_row gt_center\">0.27<\/td>\n<td headers=\"ci_4\" class=\"gt_row gt_center\">0.20, 0.34<\/td>\n<td headers=\"p.value_4\" class=\"gt_row gt_center\"><\/td>\n<\/tr>\n<\/tbody>\n<tfoot class=\"gt_footnotes\">\n<tr>\n<td class=\"gt_footnote\" colspan=\"13\"><span class=\"gt_footnote_marks\" style=\"white-space: nowrap; font-style: italic; font-weight: normal;\"><sup>1<\/sup><\/span> CI = Confidence Interval<\/td>\n<\/tr>\n<\/tfoot>\n<\/table>\n<\/div>\n\n\n\n<p><br>\u3042\u307e\u308a\u30d7\u30ed\u30c3\u30c8\u304c\u3042\u3063\u3066\u3044\u308b\u3068\u601d\u3048\u306a\u3044\u3067\u3059\u304c\u3001\u63a8\u5b9a\u5024\u30010.9\u30680.6\u306b\u4e00\u756a\u8fd1\u3044\u5024\u304c\u6b63\u3057\u3044\u30e2\u30c7\u30eb\u5f0f\u3092\u6307\u5b9a\u3057\u305f\u3068\u304d\u3067\u3059\u306d\u3002<br><br><\/p>\n\n\n\n\n\n\n\n\n\n\n\n<h3 class=\"wp-block-heading\">Model4<\/h3>\n\n\n\n<p>\\[Y_4 = \\\\exp(\\\\beta_0 + \\\\beta_1 X_1 + \\\\beta_2 X_2 + \\\\epsilon)\\]<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>ggcrPlots(mod4)<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/bunseki-data.com\/r-onlinecourse\/wp-content\/uploads\/2023\/11\/unnamed-chunk-44-1-1.png\" alt=\"\"\/><\/figure>\n\n\n\n<pre class=\"wp-block-code\"><code>car::residualPlots(mod4)<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/bunseki-data.com\/r-onlinecourse\/wp-content\/uploads\/2023\/11\/unnamed-chunk-45-1-1.png\" alt=\"\"\/><\/figure>\n\n\n\n<pre class=\"wp-block-code\"><code>##            Test stat Pr(&gt;|Test stat|)    \n## x1            2.8065         0.006065 ** \n## x2            2.2309         0.028013 *  \n## Tukey test    5.6966        1.222e-08 ***\n## ---\n## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1<\/code><\/pre>\n\n\n\n<p>\u304a\u304b\u3057\u3044\u3067\u3059\u306d\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>mod4_1 &lt;- update(mod4, log(y4) ~ x1 + x2)\nggcrPlots(mod4_1)<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/bunseki-data.com\/r-onlinecourse\/wp-content\/uploads\/2023\/11\/unnamed-chunk-46-1-1.png\" alt=\"\"\/><\/figure>\n\n\n\n<pre class=\"wp-block-code\"><code>car::residualPlots(mod4_1)<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/bunseki-data.com\/r-onlinecourse\/wp-content\/uploads\/2023\/11\/unnamed-chunk-47-1-1.png\" alt=\"\"\/><\/figure>\n\n\n\n<pre class=\"wp-block-code\"><code>##            Test stat Pr(&gt;|Test stat|)\n## x1            0.2725           0.7858\n## x2            0.5365           0.5928\n## Tukey test    0.2862           0.7747<\/code><\/pre>\n\n\n\n<p>\u307e\u3063\u3059\u3050\u306b\u306a\u308a\u307e\u3057\u305f\u306d\u3002\u3053\u306e\u624b\u306e\u5909\u63db\u306fMFP\u3067\u306f\u591a\u5206\u96e3\u3057\u3044\u306e\u3067\u5272\u611b\u3057\u307e\u3059\u3002\u3053\u3053\u307e\u3067\u307f\u3066\u3082\u3001residualPlots\u306e\u65b9\u304c\u5f62\u3092\u3046\u307e\u304f\u3068\u3089\u3048\u305f\u3068\u304d\u306b\u307e\u3063\u3059\u3050\u306b\u306a\u3063\u3066\u3044\u308b\u306e\u3067\u5206\u304b\u308a\u3084\u3059\u3044\u304b\u3082\u3068\u601d\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>list(mod4, mod4_1) 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\/>\n  color: #333333;<br \/>\n  background-color: #FFFFFF;<br \/>\n  border-bottom-style: none;<br \/>\n  border-bottom-width: 2px;<br \/>\n  border-bottom-color: #D3D3D3;<br \/>\n  border-left-style: none;<br \/>\n  border-left-width: 2px;<br \/>\n  border-left-color: #D3D3D3;<br \/>\n  border-right-style: none;<br \/>\n  border-right-width: 2px;<br \/>\n  border-right-color: #D3D3D3;<br \/>\n}<\/p>\n<p>#itcguvzdvq .gt_footnote {<br \/>\n  margin: 0px;<br \/>\n  font-size: 90%;<br \/>\n  padding-top: 4px;<br \/>\n  padding-bottom: 4px;<br \/>\n  padding-left: 5px;<br \/>\n  padding-right: 5px;<br \/>\n}<\/p>\n<p>#itcguvzdvq .gt_sourcenotes {<br \/>\n  color: #333333;<br \/>\n  background-color: #FFFFFF;<br \/>\n  border-bottom-style: none;<br \/>\n  border-bottom-width: 2px;<br \/>\n  border-bottom-color: #D3D3D3;<br \/>\n  border-left-style: none;<br \/>\n  border-left-width: 2px;<br \/>\n  border-left-color: #D3D3D3;<br \/>\n  border-right-style: none;<br \/>\n  border-right-width: 2px;<br \/>\n  border-right-color: #D3D3D3;<br \/>\n}<\/p>\n<p>#itcguvzdvq .gt_sourcenote {<br \/>\n  font-size: 90%;<br \/>\n  padding-top: 4px;<br \/>\n  padding-bottom: 4px;<br \/>\n  padding-left: 5px;<br \/>\n  padding-right: 5px;<br \/>\n}<\/p>\n<p>#itcguvzdvq .gt_left {<br \/>\n  text-align: left;<br \/>\n}<\/p>\n<p>#itcguvzdvq .gt_center {<br \/>\n  text-align: center;<br \/>\n}<\/p>\n<p>#itcguvzdvq .gt_right {<br \/>\n  text-align: right;<br \/>\n  font-variant-numeric: tabular-nums;<br \/>\n}<\/p>\n<p>#itcguvzdvq .gt_font_normal {<br \/>\n  font-weight: normal;<br \/>\n}<\/p>\n<p>#itcguvzdvq .gt_font_bold {<br \/>\n  font-weight: bold;<br \/>\n}<\/p>\n<p>#itcguvzdvq .gt_font_italic {<br \/>\n  font-style: italic;<br \/>\n}<\/p>\n<p>#itcguvzdvq .gt_super {<br \/>\n  font-size: 65%;<br \/>\n}<\/p>\n<p>#itcguvzdvq .gt_footnote_marks {<br \/>\n  font-size: 75%;<br \/>\n  vertical-align: 0.4em;<br \/>\n  position: initial;<br \/>\n}<\/p>\n<p>#itcguvzdvq .gt_asterisk {<br \/>\n  font-size: 100%;<br \/>\n  vertical-align: 0;<br \/>\n}<\/p>\n<p>#itcguvzdvq .gt_indent_1 {<br \/>\n  text-indent: 5px;<br \/>\n}<\/p>\n<p>#itcguvzdvq .gt_indent_2 {<br \/>\n  text-indent: 10px;<br \/>\n}<\/p>\n<p>#itcguvzdvq .gt_indent_3 {<br \/>\n  text-indent: 15px;<br \/>\n}<\/p>\n<p>#itcguvzdvq .gt_indent_4 {<br \/>\n  text-indent: 20px;<br \/>\n}<\/p>\n<p>#itcguvzdvq .gt_indent_5 {<br \/>\n  text-indent: 25px;<br \/>\n}<br \/>\n<\/style>\n<table class=\"gt_table\" data-quarto-disable-processing=\"false\" data-quarto-bootstrap=\"false\">\n<thead>\n<tr class=\"gt_col_headings gt_spanner_row\">\n<th class=\"gt_col_heading gt_columns_bottom_border gt_left\" rowspan=\"2\" colspan=\"1\" scope=\"col\" id=\"<strong>Characteristic<\/strong>&#8220;><strong>Characteristic<\/strong><\/th>\n<th class=\"gt_center gt_columns_top_border gt_column_spanner_outer\" rowspan=\"1\" colspan=\"3\" scope=\"colgroup\" id=\"mod4\"><span class=\"gt_column_spanner\">mod4<\/span><\/th>\n<th class=\"gt_center gt_columns_top_border gt_column_spanner_outer\" rowspan=\"1\" colspan=\"3\" scope=\"colgroup\" id=\"mod4_1\"><span class=\"gt_column_spanner\">mod4_1<\/span><\/th>\n<\/tr>\n<tr class=\"gt_col_headings\">\n<th class=\"gt_col_heading gt_columns_bottom_border gt_center\" rowspan=\"1\" colspan=\"1\" scope=\"col\" id=\"<strong>Beta<\/strong>&#8220;><strong>Beta<\/strong><\/th>\n<th class=\"gt_col_heading gt_columns_bottom_border gt_center\" rowspan=\"1\" colspan=\"1\" scope=\"col\" id=\"<strong>95% CI<\/strong><span class=&quot;gt_footnote_marks&quot; style=&quot;white-space:nowrap;font-style:italic;font-weight:normal;&quot;><sup>1<\/sup><\/span>&#8220;><strong>95% CI<\/strong><span class=\"gt_footnote_marks\" style=\"white-space: nowrap; font-style: italic; font-weight: normal;\"><sup>1<\/sup><\/span><\/th>\n<th class=\"gt_col_heading gt_columns_bottom_border gt_center\" rowspan=\"1\" colspan=\"1\" scope=\"col\" id=\"<strong>p-value<\/strong>&#8220;><strong>p-value<\/strong><\/th>\n<th class=\"gt_col_heading gt_columns_bottom_border gt_center\" rowspan=\"1\" colspan=\"1\" scope=\"col\" id=\"<strong>Beta<\/strong>&#8220;><strong>Beta<\/strong><\/th>\n<th class=\"gt_col_heading gt_columns_bottom_border gt_center\" rowspan=\"1\" colspan=\"1\" scope=\"col\" id=\"<strong>95% CI<\/strong><span class=&quot;gt_footnote_marks&quot; style=&quot;white-space:nowrap;font-style:italic;font-weight:normal;&quot;><sup>1<\/sup><\/span>&#8220;><strong>95% CI<\/strong><span class=\"gt_footnote_marks\" style=\"white-space: nowrap; font-style: italic; font-weight: normal;\"><sup>1<\/sup><\/span><\/th>\n<th class=\"gt_col_heading gt_columns_bottom_border gt_center\" rowspan=\"1\" colspan=\"1\" scope=\"col\" id=\"<strong>p-value<\/strong>&#8220;><strong>p-value<\/strong><\/th>\n<\/tr>\n<\/thead>\n<tbody class=\"gt_table_body\">\n<tr>\n<td headers=\"label\" class=\"gt_row gt_left\">x1<\/td>\n<td headers=\"estimate_1\" class=\"gt_row gt_center\">52,828<\/td>\n<td headers=\"ci_1\" class=\"gt_row gt_center\">16,681, 88,975<\/td>\n<td headers=\"p.value_1\" class=\"gt_row gt_center\">0.005<\/td>\n<td headers=\"estimate_2\" class=\"gt_row gt_center\">0.88<\/td>\n<td headers=\"ci_2\" class=\"gt_row gt_center\">0.82, 0.94<\/td>\n<td headers=\"p.value_2\" class=\"gt_row gt_center\"><\/td>\n<\/tr>\n<tr>\n<td headers=\"label\" class=\"gt_row gt_left\">x2<\/td>\n<td headers=\"estimate_1\" class=\"gt_row gt_center\">53,743<\/td>\n<td headers=\"ci_1\" class=\"gt_row gt_center\">14,606, 92,880<\/td>\n<td headers=\"p.value_1\" class=\"gt_row gt_center\">0.008<\/td>\n<td headers=\"estimate_2\" class=\"gt_row gt_center\">0.62<\/td>\n<td headers=\"ci_2\" class=\"gt_row gt_center\">0.56, 0.68<\/td>\n<td headers=\"p.value_2\" class=\"gt_row gt_center\"><\/td>\n<\/tr>\n<\/tbody>\n<tfoot class=\"gt_footnotes\">\n<tr>\n<td class=\"gt_footnote\" colspan=\"7\"><span class=\"gt_footnote_marks\" style=\"white-space: nowrap; font-style: italic; font-weight: normal;\"><sup>1<\/sup><\/span> CI = Confidence Interval<\/td>\n<\/tr>\n<\/tfoot>\n<\/table>\n<\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Model 5<\/h3>\n\n\n\n<p>\u3053\u308c\u306f\u552f\u4e00x2\u3092\u30e2\u30c7\u30eb\u306b\u5229\u7528\u3057\u3066\u3044\u306a\u3044\u3082\u306e\u3067\u3059\u3002<\/p>\n\n\n\n\n\n\n\n<p>\\[Y_5 = \\\\beta_0 + \\\\beta_1 X_1 + \\\\beta_2 (X_1)^2 + \\\\epsilon \\]<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>ggcrPlots(mod5)<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/bunseki-data.com\/r-onlinecourse\/wp-content\/uploads\/2023\/11\/unnamed-chunk-49-1-1.png\" alt=\"\"\/><\/figure>\n\n\n\n<pre class=\"wp-block-code\"><code>car::residualPlots(mod5)<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/bunseki-data.com\/r-onlinecourse\/wp-content\/uploads\/2023\/11\/unnamed-chunk-50-1-1.png\" alt=\"\"\/><\/figure>\n\n\n\n<pre class=\"wp-block-code\"><code>##            Test stat Pr(&gt;|Test stat|)    \n## x1           41.6982           &lt;2e-16 ***\n## x2           -0.2333            0.816    \n## Tukey test   40.9928           &lt;2e-16 ***\n## ---\n## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1<\/code><\/pre>\n\n\n\n<p>x2\u306f\u95a2\u4fc2\u306a\u3055\u305d\u3046\u3001x1\u306f\u4e8c\u4e57\u3063\u307d\u3044\u3067\u3059\u306d<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>mod5_1 &lt;- update(mod5, y5 ~ I(x1^2) + x2 )\nggcrPlots(mod5_1)<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/bunseki-data.com\/r-onlinecourse\/wp-content\/uploads\/2023\/11\/unnamed-chunk-51-1-1.png\" alt=\"\"\/><\/figure>\n\n\n\n<pre class=\"wp-block-code\"><code>car::residualPlots(mod5_1)<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/bunseki-data.com\/r-onlinecourse\/wp-content\/uploads\/2023\/11\/unnamed-chunk-52-1-1.png\" alt=\"\"\/><\/figure>\n\n\n\n<pre class=\"wp-block-code\"><code>##            Test stat Pr(&gt;|Test stat|)    \n## I(x1^2)      -4.7813        6.277e-06 ***\n## x2           -1.6786          0.09648 .  \n## Tukey test   -4.7824        1.732e-06 ***\n## ---\n## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1<\/code><\/pre>\n\n\n\n<p>residualPlots\u3067\u307f\u308b\u3068\u3001x1\u304c\u307e\u3060\u4f55\u304b\u304a\u304b\u3057\u3044\u306e\u304c\u660e\u78ba\u306b\u308f\u304b\u308a\u307e\u3059\u3002\u5ff5\u306e\u305f\u3081\u3001car\u306e\u65b9\u3067\u3082CR\u30d7\u30ed\u30c3\u30c8\u898b\u3066\u307f\u3066\u3082\u81ea\u4f5c\u95a2\u6570\u3068\u7d50\u679c\u5909\u308f\u3089\u306a\u3044\u306e\u3067\u3001\u3084\u3063\u3071\u308a\u6b8b\u5dee\u3092\u76f4\u63a5\u898b\u3066\u3042\u3052\u308b\u65b9\u304c\u826f\u3044\u306e\u304b\u3082\u3057\u308c\u307e\u305b\u3093\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>car::crPlots(mod5_1)<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/bunseki-data.com\/r-onlinecourse\/wp-content\/uploads\/2023\/11\/unnamed-chunk-53-1-1.png\" alt=\"\"\/><\/figure>\n\n\n\n<p>mfp\u3067\u5909\u63db\u3092\u63a2\u3057\u3066\u3042\u3052\u308b\u3068\u3001<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>modfp &lt;- mfp(y5 ~ fp(x1, scale=FALSE) + fp(x2, scale=FALSE), data = data2)\n\nmodfp &lt;- lm(modfp$formula, data = data2)\n\nsummary(modfp)<\/code><\/pre>\n\n\n\n<pre class=\"wp-block-code\"><code>## \n## Call:\n## lm(formula = modfp$formula, data = data2)\n## \n## Residuals:\n##     Min      1Q  Median      3Q     Max \n## -3.4188 -0.7926 -0.0557  0.9019  2.4042 \n## \n## Coefficients:\n##              Estimate Std. Error t value Pr(&gt;|t|)    \n## (Intercept)  2.433054   0.265804   9.154 9.02e-15 ***\n## I(x1^2)      0.684542   0.003756 182.271  &lt; 2e-16 ***\n## I(x2^1)     -0.031012   0.041714  -0.743    0.459    \n## ---\n## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n## \n## Residual standard error: 1.176 on 97 degrees of freedom\n## Multiple R-squared:  0.9971, Adjusted R-squared:  0.997 \n## F-statistic: 1.662e+04 on 2 and 97 DF,  p-value: &lt; 2.2e-16<\/code><\/pre>\n\n\n\n<p>\u3046\u307e\u304f\u63a8\u5b9a\u306f\u3057\u3066\u304f\u308c\u3066\u3044\u306a\u3044\u3067\u3059\u3002\u6b63\u3057\u3044\u30e2\u30c7\u30eb\u3092\u3064\u304f\u308b\u3068\u3001<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>mod5_2 &lt;- update(mod5, y5 ~ I(x1^2) + I(x1) )\nggcrPlots(mod5_2)<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/bunseki-data.com\/r-onlinecourse\/wp-content\/uploads\/2023\/11\/unnamed-chunk-55-1-1.png\" alt=\"\"\/><\/figure>\n\n\n\n<pre class=\"wp-block-code\"><code>car::residualPlots(mod5_2)<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"http:\/\/bunseki-data.com\/r-onlinecourse\/wp-content\/uploads\/2023\/11\/unnamed-chunk-56-1-1.png\" alt=\"\"\/><\/figure>\n\n\n\n<pre class=\"wp-block-code\"><code>##            Test stat Pr(&gt;|Test stat|)\n## I(x1^2)       0.7338           0.4648\n## I(x1)        -0.9784           0.3304\n## Tukey test    0.7458           0.4558<\/code><\/pre>\n\n\n\n<p>\u3084\u306f\u308a\u3001Residual Plot\u3067\u307f\u308b\u3068\u5206\u304b\u308a\u3084\u3059\u3044\u3067\u3059\u306d\u3002<br>\uff08\u3082\u3061\u308d\u3093\u3001\u5b9f\u969b\u306e\u30c7\u30fc\u30bf\u304c\u3053\u3093\u306a\u304d\u308c\u3044\u306b\u306a\u308b\u3053\u3068\u306f\u306a\u3044\u3053\u3068\u306f\u627f\u77e5\u306e\u4e0a\u3067\u3059\u304c\u3001\u307e\u3063\u3059\u3050\u306b\u306a\u308b\u3068\u3044\u3046\u898b\u65b9\u3092\u3059\u308b\u65b9\u304c\u5206\u304b\u308a\u3084\u3059\u3044\u306e\u304b\u3082\u3057\u308c\u307e\u305b\u3093\uff09<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>compare_models(\n  list(mod5, modfp, mod5_1, mod5_2),\n  list(\"mod5\",\"modfp\",\"mod5_1\",\"mod5_2\")\n)<\/code><\/pre>\n\n\n\n<pre class=\"wp-block-code\"><code>## # A tibble: 6 \u00d7 5\n##   term        mod5                  modfp            mod5_1 mod5_2\n##   &lt;chr&gt;       &lt;glue&gt;                &lt;glue&gt;           &lt;glue&gt; &lt;glue&gt;\n## 1 (Intercept) -8.29(-10.46 - -6.13) 2.43(1.91 - 2.9\u2026 2.43(\u2026 0.65(\u2026\n## 2 x1          6.90(6.62 - 7.18)     &lt;NA&gt;             &lt;NA&gt;   &lt;NA&gt;  \n## 3 x2          -0.08(-0.38 - 0.22)   &lt;NA&gt;             -0.03\u2026 &lt;NA&gt;  \n## 4 I(x1^2)     &lt;NA&gt;                  0.68(0.68 - 0.6\u2026 0.68(\u2026 0.60(\u2026\n## 5 I(x2^1)     &lt;NA&gt;                  -0.03(-0.11 - 0\u2026 &lt;NA&gt;   &lt;NA&gt;  \n## 6 I(x1)       &lt;NA&gt;                  &lt;NA&gt;             &lt;NA&gt;   0.94(\u2026<\/code><\/pre>\n\n\n\n<h2 class=\"wp-block-heading\">\u304a\u308f\u308a\u306b\uff08\u500b\u4eba\u306e\u611f\u60f3\uff09<\/h2>\n\n\n\n<p>\u6700\u5f8c\u307e\u3067\u8aad\u3093\u3067\u3044\u305f\u3060\u3044\u3066\u3044\u308b\u65b9\u304c\u3044\u3089\u3063\u3057\u3083\u3044\u307e\u3057\u305f\u3089\u3042\u308a\u304c\u3068\u3046\u3054\u3056\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u8272\u3005\u306a\u624b\u6cd5\u304c\u6559\u79d1\u66f8\u3067\u7d39\u4ecb\u3055\u308c\u3066\u3044\u307e\u3057\u305f\u304c\u3001\u518d\u73fe\u3059\u308b\u3053\u3068\u3067\u5c11\u3057\u7406\u89e3\u304c\u6df1\u307e\u3063\u305f\u6c17\u304c\u3057\u307e\u3059\u3002\u3067\u3082\u3001\u3059\u304f\u306a\u304f\u3068\u3082\u4eca\u56de\u306e\u4f8b\u3067\u306f\u3001\u4e00\u756a\u3088\u304f\u3044\u308f\u308c\u308b\u6b8b\u5dee\u306e\u78ba\u8a8d\u304c\u3001\u30e2\u30c7\u30eb\u306e\u5f62\u3092\u8abf\u3079\u308b\u306e\u306b\u6709\u7528\u305d\u3046\u306a\u306e\u3067\u3001\u4eca\u5f8c\u306f\u6b8b\u5dee\u3092\u76f4\u63a5\u898b\u308b+\u4ed6\u306e\u30d7\u30ed\u30c3\u30c8\u3092\u53c2\u8003\u7a0b\u5ea6\u306b\u898b\u308b\u3068\u3044\u3046\u3088\u3046\u306a\u4f7f\u3044\u65b9\u3092\u3057\u3088\u3046\u3068\u601d\u3044\u307e\u3057\u305f\u3002<\/p>\n\n\n\n<p>\u3082\u3057\u9593\u9055\u3044\u3084\u8a8d\u8b58\u9055\u3044\u3092\u767a\u898b\u3055\u308c\u305f\u65b9\u304c\u3044\u3089\u3063\u3057\u3083\u3044\u307e\u3057\u305f\u3089\u3001\u304a\u6559\u3048\u3044\u305f\u3060\u3051\u308b\u3068\u5b09\u3057\u304f\u601d\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<p>Have a happy R life!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u306f\u3058\u3081\u306b \u4ed5\u4e8b\u95a2\u4fc2\u3067\u3001\u91cd\u56de\u5e30\u5206\u6790\u3092\u7523\u696d\u4fdd\u5065\u8077\u3084\u4eba\u4e8b\u90e8\u306e\u8208\u5473\u304c\u3042\u308b\u4eba\u306b\u6559\u3048\u305f\u3044\u3068\u601d\u3044\u7acb\u3061\uff08\u672c\u696d\u306f\u5b9f\u306f\uff01\uff1f\u7523\u696d\u533b\u3067\u3059\uff09\u3001\u6539\u3081\u3066\u91cd\u56de\u5e30\u5206\u6790\u3092\u3061\u3083\u3093\u3068\u3084\u308b\u65b9\u6cd5\u3092\u52c9\u5f37\u3057\u305f\u306a\u304b\u3067\u3001\u30e2\u30c7\u30eb\u30c1\u30a7\u30c3\u30af\u306e\u65b9\u6cd5\u306b\u3064\u3044\u3066\u5b9f\u306f\u305d\u3093\u306a\u306b\u6df1\u304f\u7406\u89e3\u3067\u304d\u3066\u3044\u306a\u3044\u3068\u3044\u3046\u3053\u3068\u306b\u6c17\u3065\u304d\u3001\u52c9\u5f37\u3057\u305f\u3053\u3068\u3092\u307e\u3068\u3081\u3066\u307f\u307e\u3057\u305f\u3002\u3053\u306e\u8a18\u4e8b\u3001\u304b\u306a\u308a\u52c9\u5f37\u30ce\u30fc\u30c8\u3068\u304b\u30e1\u30e2\u306b\u8fd1\u3044\u5f62\u306a\u306e\u3092\u3054\u7559\u610f\u304f\u3060\u3055\u3044\u3002 \u5168\u4f53\u50cf\u3068\u3057\u3066\u306f\u3001 \u3068\u3044\u3046\u6d41\u308c\u3067\u3059\u3002 \u8b1d\u8f9e \u3053\u306e\u8a18\u4e8b\u306f\u3001\u79c1\u304cTwiter\u306b\u3064\u3076\u3084\u3044\u305f\u7591\u554f\u306b\u591a\u304f\u306e\u65b9\u304c\u304a\u8fd4\u4e8b\u3044\u305f\u3060\u3044\u305f\u3053\u3068\u304b\u3089\u3001\u4f5c\u6210\u3057\u3088\u3046\u3068\u8003\u3048\u307e\u3057\u305f\u3002\u30b3\u30e1\u30f3\u30c8\u3092\u3044\u305f\u3060\u3044\u305f\u5168\u3066\u306e\u65b9\u306b\u6df1\u3044\u611f\u8b1d\u3092\u7533\u3057\u4e0a\u3052\u307e\u3059\u3002 \u53c2\u8003\u56f3\u66f8 \u3053\u306e\u8a18\u4e8b\u3092\u66f8\u304f\u306b\u3042\u305f\u308a\u3001\u6b21\u306e\u6559\u79d1\u66f8\u3092\u53c2\u8003\u306b\u3057\u3066\u3044\u307e\u3059\u3002 \u9ad8\u6a4b \u5c06\u5b9c(2022)\u300e\u7d71\u8a08\u7684\u56e0\u679c\u63a8\u8ad6\u306e\u7406\u8ad6\u3068\u5b9f\u88c5\u2015\u6f5c\u5728\u7684\u7d50\u679c\u5909\u6570\u3068\u6b20\u6e2c\u30c7\u30fc\u30bf\u2015\u300f\u5171\u7acb\u51fa\u7248 Fox, John, Sanford Weisberg. An R Companion to Applied Regression. Third edition. Los Angeles: SAGE, 2019 Jeffrey M Wooldridge. Introductory EconomEtrIcs A modern Approach 7e Fox, John, Regression Diagnostics An Introduction Second Edition. \u3068\u304f\u306b\u3001\u9ad8\u6a4b\u5148\u751f\u306e\u672c\u3001\u5165\u624b\u3057\u3066\u3044\u305f\u306e\u306b\u3001\u6700\u521d\u306e\u90e8\u5206\u3092\u8aad\u307f\u98db\u3070\u3057\u3066\u3044\u3066\u3001\u53cd\u7701\u3057\u3066\u3044\u307e\u3059\u3002\u3082\u306e\u3059\u3054\u304f\u5206\u304b\u308a\u3084\u3059\u3044\u672c\u306a\u306e\u3067\u3001R User\u3067\u306a\u304f\u3066\u3082\u30aa\u30b9\u30b9\u30e1\u3067\u3059\u3002 \u30e2\u30c7\u30eb\u30c1\u30a7\u30c3\u30af \u91cd\u56de\u5e30\u5206\u6790\u3092\u884c\u3046\u969b\u306b\u3001\u9069\u5207\u306a\u5206\u6790\u304c\u884c\u3048\u3066\u3044\u308b\u304b\u3092\u8abf\u3079\u308b\u305f\u3081\u306e\u300c\u30e2\u30c7\u30eb\u30c1\u30a7\u30c3\u30af\u300d\u3092\u884c\u3046\u3053\u3068\u306f\u91cd\u8981\u3067\u3059\u3002\u3053\u306e\u8a18\u4e8b\u3067\u306f\u3001\u91cd\u56de\u5e30\u5206\u6790\u304c\u9069\u5fdc\u3057\u3066\u3044\u308b\u30c7\u30fc\u30bf\u306b\u5bfe\u3057\u3066\u3001\u9069\u5207\u306b\u7528\u3044\u308b\u3053\u3068\u304c\u3067\u304d\u3066\u3044\u308b\u304b\u3001\u7279\u306b\u7dda\u5f62\u6027\u306e\u78ba\u8a8d\u306b\u3064\u3044\u3066\u3092\uff32\u3067\u8abf\u3079\u308b\u65b9\u6cd5\u3092\u89e3\u8aac\u3057\u3066\u3044\u304d\u307e\u3059\u3002 \u8868\u8a18 \u6b21\u306e\u3088\u3046\u306a\u30c7\u30fc\u30bf$n$\u500b\uff08\u884c\uff09\u306e\u30b5\u30f3\u30d7\u30eb\u3092\u542b\u3080\u30c7\u30fc\u30bf\u304c\u3042\u308b\u3068\u3057\u3066\u3001$i$\u756a\uff08\u884c\uff09\u76ee\u306e\u76ee\u7684\u5909\u6570\u3092$yi$\u3068\u8868\u8a18\u3057\u307e\u3059\u3002$k$\u500b\u306e\u8aac\u660e\u5909\u6570\u304c\u3042\u308b\u3068\u3057\u3066\u3001$i$\u884c\u76ee\u306e\u8aac\u660e\u5909\u6570\u3092\u3001$x{i1}, x{i2}, \\cdots x{ik}$\u306e\u3088\u3046\u306b\u8868\u8a18\u3057\u307e\u3059\u3002 $Y$ $X_1$ $X_2$ $\\cdots$ $X_k$ $y_1$ $x_{11}$ $x_{12}$ $\\cdots$ $x_{1k}$ $y_1$ $x_{21}$ $x_{22}$ $\\cdots$ $x_{2k}$ $\\vdots$ $\\vdots$ $\\vdots$ $\\ddots$ $\\vdots$ $y_i$ $x_{i1}$ $x_{i2}$ $\\cdots$ $x_{ik}$ $\\vdots$ $\\vdots$ $\\vdots$ $\\ddots$ $\\vdots$ $y_n$ $x_{n1}$ $x_{n2}$ $\\cdots$ $x_{nk}$ \u91cd\u56de\u5e30\u5206\u6790\u306eAssumption\uff08\u4eee\u5b9a\uff09 \u91cd\u56de\u5e30\u5206\u6790\u306e\u30e2\u30c7\u30eb\uff1a \\[y_i = \\beta_0 + \\beta_1_x{i1} + \\cdots + \\beta_k_x{ik} + \\epsilon_i\\] \u306b\u304a\u3044\u3066\u3001\u8272\u3005\u306a\u4eee\u5b9a\u304c\u304a\u304b\u308c\u3066\u3044\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u4eee\u5b9a\u306f\u7d50\u69cb\u5f37\u3044\u4eee\u5b9a\u306a\u306e\u3067\u3001\u30e2\u30c7\u30eb\u3092\u4f5c\u6210\u3057\u305f\u3068\u304d\u306b\u3001\u305d\u308c\u3092\u691c\u8a3c\u3059\u308b\u5fc5\u8981\u304c\u3067\u3066\u304d\u307e\u3059\u3002\u4eee\u5b9a\u306f\u3001\u9ad8\u6a4b\u5148\u751f\u306e\u6559\u79d1\u66f8\u3068Wooldridge\u5148\u751f\u306e\u6559\u79d1\u66f8\u304b\u3089\u629c\u7c8b\u3057\u3066\u3044\u307e\u3059\u3002 \u5c1a\u3001Wooldridge\u306e\u6559\u79d1\u66f8\u3067\u306f\u3001\u63a8\u5b9a\u5024$\\beta_j$\u304c\u3001\u4eee\u5b9a\uff12\uff0d\uff15\u3067\u304c\u30d0\u30a4\u30a2\u30b9\u306a\u304f\u63a8\u5b9a\u3067\u304d\u308b\u3053\u3068\u3001\u4eee\u5b9a\uff16\u3067\u5206\u6563\u304c\u63a8\u5b9a\u3067\u304d\u308b\u3068\u306e\u8a18\u8f09\u304c\u3042\u308a\u307e\u3059\u3002 \u4eee\u5b9a\uff11\uff1a\u8aa4\u5dee\u9805\u306e\u671f\u5f85\u5024\u30bc\u30ed \u8aa4\u5dee\u9805\u306e\u671f\u5f85\u5024\u30bc\u30ed(\u4eee\u5b9a1)\u306f\u3001\u6e80\u305f\u3057\u3066\u3044\u306a\u3044\u5834\u5408\u306f\u3001\u5207\u7247\u9805($\\beta_0$) \u306b\u5f71\u97ff\u3092\u4e0e\u3048\u308b\u3002\u305f\u3060\u3001\u305d\u308c\u4ee5\u5916\u306e$\\beta_1 \\cdots \\beta_k$\u306b\u306f\u5f71\u97ff\u3092\u4e0e\u3048\u306a\u3044\u3002 \u4f5c\u6210\u3057\u305f\u30c7\u30fc\u30bf\u306fy1\u5909\u6570\u304c\u8aa4\u5dee\u9805\u304c\u5e73\u57470\u3001SD1\u306e\u6b63\u898f\u5206\u5e03\u306b\u3057\u305f\u304c\u3044\u3001y2\u306f\u5e73\u574710\u8aa4\u5dee\u98051\u306e\u6b63\u898f\u5206\u5e03\u306b\u5f93\u3046\u3002\u3069\u3061\u3089\u306e\u76ee\u7684\u5909\u6570\u3082\u3001\u03b2\u306e\u5024\u306f\u540c\u3058\u3067\u3042\u308a\u3001$\\beta_0=10$,$\\beta_1 = 3$\u3068\u8a2d\u5b9a\u3057\u3066\u3044\u307e\u3059\u3002 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"swell_btn_cv_data":"","footnotes":""},"categories":[8,33],"tags":[],"class_list":["post-616","post","type-post","status-publish","format-standard","hentry","category-8","category-33"],"_links":{"self":[{"href":"https:\/\/bunseki-data.com\/r-onlinecourse\/wp-json\/wp\/v2\/posts\/616","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/bunseki-data.com\/r-onlinecourse\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bunseki-data.com\/r-onlinecourse\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bunseki-data.com\/r-onlinecourse\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/bunseki-data.com\/r-onlinecourse\/wp-json\/wp\/v2\/comments?post=616"}],"version-history":[{"count":5,"href":"https:\/\/bunseki-data.com\/r-onlinecourse\/wp-json\/wp\/v2\/posts\/616\/revisions"}],"predecessor-version":[{"id":624,"href":"https:\/\/bunseki-data.com\/r-onlinecourse\/wp-json\/wp\/v2\/posts\/616\/revisions\/624"}],"wp:attachment":[{"href":"https:\/\/bunseki-data.com\/r-onlinecourse\/wp-json\/wp\/v2\/media?parent=616"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bunseki-data.com\/r-onlinecourse\/wp-json\/wp\/v2\/categories?post=616"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bunseki-data.com\/r-onlinecourse\/wp-json\/wp\/v2\/tags?post=616"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}