{"id":4338,"date":"2025-07-27T19:56:08","date_gmt":"2025-07-27T10:56:08","guid":{"rendered":"https:\/\/best-biostatistics.com\/toukei-er\/?p=4338"},"modified":"2025-07-27T19:56:10","modified_gmt":"2025-07-27T10:56:10","slug":"weighted-least-squares-in-multiple-regression-listening-to-the-datas-hidden-voice","status":"publish","type":"post","link":"https:\/\/best-biostatistics.com\/toukei-er\/entry\/weighted-least-squares-in-multiple-regression-listening-to-the-datas-hidden-voice\/","title":{"rendered":"\u91cd\u56de\u5e30\u5206\u6790\u306b\u304a\u3051\u308b\u91cd\u307f\u4ed8\u304d\u6700\u5c0f\u4e8c\u4e57\u6cd5\uff1a\u30c7\u30fc\u30bf\u306e\u6f5c\u5728\u7684\u306a\u58f0\u3092\u8074\u304f"},"content":{"rendered":"\n<p>\u91cd\u56de\u5e30\u5206\u6790\u306f\u3001\u8907\u6570\u306e\u8aac\u660e\u5909\u6570\u3092\u7528\u3044\u3066\u76ee\u7684\u5909\u6570\u3092\u4e88\u6e2c\u3059\u308b\u5f37\u529b\u306a\u7d71\u8a08\u624b\u6cd5\u3067\u3042\u308b\u3002\u3057\u304b\u3057\u3001OLS\uff08Ordinary Least Squares\uff1a\u901a\u5e38\u306e\u6700\u5c0f\u4e8c\u4e57\u6cd5\uff09\u3092\u9069\u7528\u3059\u308b\u969b\u306b\u3001\u3042\u308b\u91cd\u8981\u306a\u4eee\u5b9a\u304c\u6e80\u305f\u3055\u308c\u306a\u3044\u5834\u5408\u3001\u305d\u306e\u30e2\u30c7\u30eb\u306e\u4fe1\u983c\u6027\u304c\u640d\u306a\u308f\u308c\u308b\u3053\u3068\u304c\u3042\u308b\u3002\u305d\u308c\u304c\u300c<strong>\u7b49\u5206\u6563\u6027<\/strong>\u300d\u306e\u4eee\u5b9a\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<p>\u672c\u8a18\u4e8b\u3067\u306f\u3001\u3053\u306e\u7b49\u5206\u6563\u6027\u306e\u4eee\u5b9a\u304c\u6e80\u305f\u3055\u308c\u306a\u3044\u5834\u5408\u306b\u6709\u52b9\u306a\u300c<strong>\u91cd\u307f\u4ed8\u304d\u6700\u5c0f\u4e8c\u4e57\u6cd5\uff08Weighted Least Squares: WLS\uff09<\/strong>\u300d\u306b\u3064\u3044\u3066\u3001\u305d\u306e\u6982\u8981\u3001\u610f\u7fa9\u3001\u5177\u4f53\u7684\u306a\u9069\u7528\u4f8b\u3001\u305d\u3057\u3066\u7d71\u8a08\u30bd\u30d5\u30c8\u30a6\u30a7\u30a2R\u3092\u7528\u3044\u305f\u8a08\u7b97\u4f8b\u3068\u7d50\u679c\u306e\u89e3\u91c8\u307e\u3067\u3092\u8a73\u3057\u304f\u89e3\u8aac\u3059\u308b\u3002<\/p>\n\n\n\n<!--more-->\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\u91cd\u307f\u4ed8\u304d\u6700\u5c0f\u4e8c\u4e57\u6cd5\uff08WLS\uff09\u3068\u306f\uff1f<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">\u6982\u8981<\/h3>\n\n\n\n<p>\u91cd\u307f\u4ed8\u304d\u6700\u5c0f\u4e8c\u4e57\u6cd5\u306f\u3001OLS\u306e\u62e1\u5f35\u3067\u3042\u308a\u3001\u5404\u89b3\u6e2c\u5024\u306b\u7570\u306a\u308b\u300c<strong>\u91cd\u307f<\/strong>\u300d\u3092\u5272\u308a\u5f53\u3066\u308b\u3053\u3068\u3067\u3001\u7570\u306a\u3063\u305f\u5206\u6563\u3092\u6301\u3064\u30c7\u30fc\u30bf\uff08<strong>\u4e0d\u5747\u4e00\u5206\u6563\uff1aHeteroscedasticity<\/strong>\uff09\u306b\u5bfe\u51e6\u3059\u308b\u56de\u5e30\u5206\u6790\u624b\u6cd5\u3067\u3042\u308b\u3002OLS\u3067\u306f\u3001\u3059\u3079\u3066\u306e\u89b3\u6e2c\u5024\u304c\u7b49\u3057\u3044\u5206\u6563\u3092\u6301\u3064\u3068\u4eee\u5b9a\u3059\u308b\u304c\u3001WLS\u3067\u306f\u3053\u306e\u4eee\u5b9a\u3092\u7de9\u548c\u3057\u3001\u5206\u6563\u306e\u5c0f\u3055\u3044\u89b3\u6e2c\u5024\u306b\u306f\u5927\u304d\u306a\u91cd\u307f\u3092\u3001\u5206\u6563\u306e\u5927\u304d\u3044\u89b3\u6e2c\u5024\u306b\u306f\u5c0f\u3055\u306a\u91cd\u307f\u3092\u5272\u308a\u5f53\u3066\u308b\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u3088\u308a\u3070\u3089\u3064\u304d\u306e\u5c11\u306a\u3044\u3001\u4fe1\u983c\u6027\u306e\u9ad8\u3044\u89b3\u6e2c\u5024\u304c\u30e2\u30c7\u30eb\u63a8\u5b9a\u306b\u3088\u308a\u5927\u304d\u304f\u8ca2\u732e\u3059\u308b\u3088\u3046\u306b\u306a\u308b\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u610f\u7fa9<\/h3>\n\n\n\n<p>WLS\u3092\u7528\u3044\u308b\u610f\u7fa9\u306f\u4ee5\u4e0b\u306e\u70b9\u306b\u3042\u308b\u3002<\/p>\n\n\n\n<ol start=\"1\" class=\"wp-block-list\">\n<li><strong>\u52b9\u7387\u7684\u306a\u63a8\u5b9a\u91cf\u306e\u7372\u5f97<\/strong>: \u4e0d\u5747\u4e00\u5206\u6563\u304c\u5b58\u5728\u3059\u308bOLS\u3067\u306f\u3001\u63a8\u5b9a\u91cf\u306e\u5206\u6563\u304c\u6700\u5c0f\u3067\u306f\u306a\u304f\u306a\u308a\u3001\u52b9\u7387\u7684\u306a\u63a8\u5b9a\u304c\u884c\u3048\u306a\u3044\u3002WLS\u3092\u7528\u3044\u308b\u3053\u3068\u3067\u3001\u6700\u5c0f\u5206\u6563\u4e0d\u504f\u63a8\u5b9a\u91cf\uff08BLUE: Best Linear Unbiased Estimator\uff09\u306b\u8fd1\u3044\u3001\u3088\u308a\u52b9\u7387\u7684\u306a\u63a8\u5b9a\u91cf\u3092\u7372\u5f97\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002<\/li>\n\n\n\n<li><strong>\u4fe1\u983c\u6027\u306e\u9ad8\u3044\u63a8\u8ad6<\/strong>: \u6b63\u3057\u3044\u6a19\u6e96\u8aa4\u5dee\u3092\u63a8\u5b9a\u3067\u304d\u308b\u305f\u3081\u3001\u4fc2\u6570\u306e\u6709\u610f\u6027\u691c\u5b9a\u3084\u4fe1\u983c\u533a\u9593\u306e\u63a8\u5b9a\u304c\u3088\u308a\u6b63\u78ba\u306b\u306a\u308b\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u30e2\u30c7\u30eb\u306e\u89e3\u91c8\u3084\u4e88\u6e2c\u306e\u4fe1\u983c\u6027\u304c\u5411\u4e0a\u3059\u308b\u3002<\/li>\n\n\n\n<li><strong>\u30e2\u30c7\u30eb\u306e\u9069\u5408\u6027\u5411\u4e0a<\/strong>: \u4e0d\u5747\u4e00\u5206\u6563\u3092\u8003\u616e\u3059\u308b\u3053\u3068\u3067\u3001\u30c7\u30fc\u30bf\u69cb\u9020\u306b\u3088\u308a\u9069\u5408\u3057\u305f\u30e2\u30c7\u30eb\u3092\u69cb\u7bc9\u3067\u304d\u308b\u3002<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\u5177\u4f53\u4f8b\uff1a\u6240\u5f97\u3068\u6559\u80b2\u5e74\u6570\u3068\u8caf\u84c4\u984d<\/h2>\n\n\n\n<p>\u3042\u308b\u5730\u57df\u306e\u4f4f\u6c11\u306e\u6240\u5f97\u3001\u6559\u80b2\u5e74\u6570\u3001\u8caf\u84c4\u984d\u306b\u95a2\u3059\u308b\u30c7\u30fc\u30bf\u3092\u53ce\u96c6\u3057\u305f\u3068\u4eee\u5b9a\u3059\u308b\u3002\u6240\u5f97\u3068\u6559\u80b2\u5e74\u6570\u3092\u8aac\u660e\u5909\u6570\u3001\u8caf\u84c4\u984d\u3092\u76ee\u7684\u5909\u6570\u3068\u3057\u3066\u91cd\u56de\u5e30\u5206\u6790\u3092\u884c\u3046\u3053\u3068\u3092\u8003\u3048\u308b\u3002<\/p>\n\n\n\n<p>\u3053\u306e\u30c7\u30fc\u30bf\u3067\u306f\u3001\u6240\u5f97\u304c\u9ad8\u3044\u4eba\u307b\u3069\u8caf\u84c4\u984d\u306e\u3070\u3089\u3064\u304d\u304c\u5927\u304d\u3044\uff08\u3064\u307e\u308a\u3001\u9ad8\u6240\u5f97\u8005\u306e\u4e2d\u306b\u306f\u8caf\u84c4\u3092\u305f\u304f\u3055\u3093\u3059\u308b\u4eba\u3082\u3044\u308c\u3070\u3001\u3042\u307e\u308a\u3057\u306a\u3044\u4eba\u3082\u3044\u308b\uff09\u3068\u3044\u3046\u50be\u5411\u304c\u898b\u3089\u308c\u308b\u304b\u3082\u3057\u308c\u306a\u3044\u3002\u3053\u308c\u306f\u4e0d\u5747\u4e00\u5206\u6563\u306e\u4e00\u4f8b\u3067\u3042\u308b\u3002\u3053\u306e\u3088\u3046\u306a\u5834\u5408\u3001\u6240\u5f97\u304c\u4f4e\u3044\u4eba\u3005\u306e\u8caf\u84c4\u984d\u306e\u4e88\u6e2c\u306f\u6bd4\u8f03\u7684\u6b63\u78ba\u3067\u3042\u308b\u4e00\u65b9\u3001\u6240\u5f97\u304c\u9ad8\u3044\u4eba\u3005\u306e\u8caf\u84c4\u984d\u306e\u4e88\u6e2c\u306f\u3070\u3089\u3064\u304d\u304c\u5927\u304d\u304f\u306a\u308b\u305f\u3081\u3001OLS\u3067\u306f\u9ad8\u6240\u5f97\u8005\u306e\u30c7\u30fc\u30bf\u304c\u30e2\u30c7\u30eb\u63a8\u5b9a\u306b\u904e\u5ea6\u306b\u5f71\u97ff\u3092\u4e0e\u3048\u3066\u3057\u307e\u3046\u53ef\u80fd\u6027\u304c\u3042\u308b\u3002<\/p>\n\n\n\n<p>\u305d\u3053\u3067\u3001WLS\u3092\u9069\u7528\u3057\u3001\u8caf\u84c4\u984d\u306e\u3070\u3089\u3064\u304d\u304c\u5c0f\u3055\u3044\uff08\u5206\u6563\u304c\u5c0f\u3055\u3044\uff09\u89b3\u6e2c\u5024\uff08\u4f8b\u3048\u3070\u6240\u5f97\u306e\u4f4e\u3044\u4eba\u3005\u306e\u30c7\u30fc\u30bf\uff09\u306b\u306f\u5927\u304d\u306a\u91cd\u307f\u3092\u3001\u8caf\u84c4\u984d\u306e\u3070\u3089\u3064\u304d\u304c\u5927\u304d\u3044\uff08\u5206\u6563\u304c\u5927\u304d\u3044\uff09\u89b3\u6e2c\u5024\uff08\u6240\u5f97\u306e\u9ad8\u3044\u4eba\u3005\u306e\u30c7\u30fc\u30bf\uff09\u306b\u306f\u5c0f\u3055\u306a\u91cd\u307f\u3092\u5272\u308a\u5f53\u3066\u308b\u3053\u3068\u3067\u3001\u3088\u308a\u9069\u5207\u306a\u56de\u5e30\u30e2\u30c7\u30eb\u3092\u69cb\u7bc9\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">R\u3067\u306e\u8a08\u7b97\u4f8b\u3068\u7d50\u679c\u89e3\u91c8<\/h3>\n\n\n\n<p>\u3053\u3053\u3067\u306f\u3001R\u3092\u7528\u3044\u3066WLS\u306e\u8a08\u7b97\u4f8b\u3092\u793a\u3059\u3002\u67b6\u7a7a\u306e\u30c7\u30fc\u30bf\u3092\u4f5c\u6210\u3057\u3066\u8aac\u660e\u3059\u308b\u3002<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code># \u5fc5\u8981\u306a\u30e9\u30a4\u30d6\u30e9\u30ea\u3092\u30ed\u30fc\u30c9\nlibrary(lmtest) # \u5171\u5206\u6563\u884c\u5217\u3092\u63a8\u5b9a\u3059\u308b\u305f\u3081\u306b\u5fc5\u8981\n\n# \u67b6\u7a7a\u306e\u30c7\u30fc\u30bf\u3092\u751f\u6210\nset.seed(123)\nn &lt;- 100\nincome &lt;- round(runif(n, 300, 1000)) # \u6240\u5f97 (\u5358\u4f4d: \u4e07\u5186)\neducation &lt;- round(sample(8:18, n, replace = TRUE)) # \u6559\u80b2\u5e74\u6570\n# \u8caf\u84c4\u984d\u306b\u4e0d\u5747\u4e00\u5206\u6563\u3092\u5c0e\u5165\nsaving &lt;- round(50 + 0.1 * income + 5 * education + rnorm(n, 0, income * 0.05))\n\n# \u30c7\u30fc\u30bf\u30d5\u30ec\u30fc\u30e0\u3092\u4f5c\u6210\ndata &lt;- data.frame(income, education, saving)\n\n# \u4e0d\u5747\u4e00\u5206\u6563\u306e\u78ba\u8a8d (\u6b8b\u5dee\u30d7\u30ed\u30c3\u30c8)\n# \u307e\u305a\u306f\u901a\u5e38\u306eOLS\u3092\u5b9f\u884c\nols_model &lt;- lm(saving ~ income + education, data = data)\npar(mfrow = c(2, 1), mar = c(4, 5, 2, 2), oma = c(0, 0, 2, 0), cex.main = 1.5, cex.lab = 1.5, cex.axis = 1.5)\nplot(ols_model$fitted.values, ols_model$residuals,\n     xlab = \"\u4e88\u6e2c\u5024\", ylab = \"\u6b8b\u5dee\",\n     main = \"OLS\u56de\u5e30\u306e\u6b8b\u5dee\u30d7\u30ed\u30c3\u30c8\")\nabline(h = 0, col = \"red\", lty = 2)\n\n# \u6b8b\u5dee\u304c\u4e88\u6e2c\u5024\u306e\u5897\u52a0\u3068\u3068\u3082\u306b\u5e83\u304c\u308b\u50be\u5411\u304c\u898b\u3089\u308c\u308b\u5834\u5408\u3001\u4e0d\u5747\u4e00\u5206\u6563\u304c\u7591\u308f\u308c\u308b\n\n# \u91cd\u307f\u3092\u6c7a\u5b9a\uff08\u5206\u6563\u306e\u9006\u6570\u3092\u91cd\u307f\u3068\u3059\u308b\uff09\n# \u3053\u3053\u3067\u306f\u7c21\u7565\u5316\u306e\u305f\u3081\u3001income\u304c\u5927\u304d\u3044\u307b\u3069\u5206\u6563\u304c\u5927\u304d\u3044\u3068\u4eee\u5b9a\u3057\u3001income\u306e\u9006\u6570\u3092\u91cd\u307f\u3068\u3059\u308b\n# \u3088\u308a\u53b3\u5bc6\u306b\u306f\u3001\u5206\u6563\u95a2\u6570\u3092\u30e2\u30c7\u30eb\u5316\u3057\u3066\u91cd\u307f\u3092\u6c7a\u5b9a\u3059\u308b\u304c\u3001\u3053\u3053\u3067\u306f\u7c21\u7565\u5316\nweights &lt;- 1 \/ income\n\n# \u91cd\u307f\u4ed8\u304d\u6700\u5c0f\u4e8c\u4e57\u6cd5 (WLS) \u3092\u5b9f\u884c\nwls_model &lt;- lm(saving ~ income + education, data = data, weights = weights)\n\n# \u7d50\u679c\u306e\u30b5\u30de\u30ea\u30fc\nsummary(ols_model)\nsummary(wls_model)\n\n# \u7d50\u679c\u306e\u6bd4\u8f03 (\u4fc2\u6570\u3068\u6a19\u6e96\u8aa4\u5dee)\n# OLS\u306e\u4fc2\u6570\u3068\u6a19\u6e96\u8aa4\u5dee\nols_coef &lt;- coef(summary(ols_model))\nols_coef_df &lt;- as.data.frame(ols_coef)\ncolnames(ols_coef_df) &lt;- c(\"OLS Estimate\", \"OLS Std. Error\", \"OLS t value\", \"OLS Pr(>|t|)\")\n\n# WLS\u306e\u4fc2\u6570\u3068\u6a19\u6e96\u8aa4\u5dee\nwls_coef &lt;- coef(summary(wls_model))\nwls_coef_df &lt;- as.data.frame(wls_coef)\ncolnames(wls_coef_df) &lt;- c(\"WLS Estimate\", \"WLS Std. Error\", \"WLS t value\", \"WLS Pr(>|t|)\")\n\n# \u6bd4\u8f03\u306e\u305f\u3081\u306b\u30c7\u30fc\u30bf\u30d5\u30ec\u30fc\u30e0\u3092\u7d50\u5408\nresults_comparison &lt;- merge(ols_coef_df, wls_coef_df, by = 0)\nrownames(results_comparison) &lt;- results_comparison$Row.names\nresults_comparison &lt;- results_comparison&#91;, -1]\nprint(results_comparison)\n<\/code><\/pre>\n\n\n\n<p>\u5b9f\u884c\u7d50\u679c\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"663\" height=\"513\" src=\"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2025\/07\/Screenshot-from-2025-07-27-19-46-13.png\" alt=\"\" class=\"wp-image-4339\" srcset=\"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2025\/07\/Screenshot-from-2025-07-27-19-46-13.png 663w, https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2025\/07\/Screenshot-from-2025-07-27-19-46-13-300x232.png 300w\" sizes=\"(max-width: 663px) 100vw, 663px\" \/><\/figure>\n\n\n\n<p>\u4e0d\u5747\u4e00\u5206\u6563\u306e\u78ba\u8a8d (\u6b8b\u5dee\u30d7\u30ed\u30c3\u30c8)\u3067\u3001\u6b8b\u5dee\u304c\u4e88\u6e2c\u5024\u306e\u5897\u52a0\u3068\u3068\u3082\u306b\u5e83\u304c\u308b\u50be\u5411\u304c\u898b\u3089\u308c\u308b\u5834\u5408\u3001\u4e0d\u5747\u4e00\u5206\u6563\u304c\u7591\u308f\u308c\u308b\uff08\u4eca\u56de\u306e\u5834\u5408\u306f\u305d\u308c\u307b\u3069\u3067\u3082\u306a\u3044\u304c\u3001\u4e0d\u5747\u4e00\u5206\u6563\u304c\u7591\u308f\u308c\u305f\u3053\u3068\u3068\u4eee\u5b9a\u3057\u3066\u9032\u3081\u308b\uff09<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>> # \u7d50\u679c\u306e\u30b5\u30de\u30ea\u30fc\n> summary(ols_model)\n\nCall:\nlm(formula = saving ~ income + education, data = data)\n\nResiduals:\n    Min      1Q  Median      3Q     Max \n-84.853 -19.630  -1.528  22.628  91.078 \n\nCoefficients:\n            Estimate Std. Error t value Pr(>|t|)    \n(Intercept) 44.31370   21.86490   2.027   0.0454 *  \nincome       0.08845    0.01837   4.815 5.42e-06 ***\neducation    5.80067    1.28243   4.523 1.73e-05 ***\n---\nSignif. codes:  0 \u2018***\u2019 0.001 \u2018**\u2019 0.01 \u2018*\u2019 0.05 \u2018.\u2019 0.1 \u2018 \u2019 1\n\nResidual standard error: 36.41 on 97 degrees of freedom\nMultiple R-squared:  0.298,     Adjusted R-squared:  0.2835 \nF-statistic: 20.59 on 2 and 97 DF,  p-value: 3.533e-08\n\n> summary(wls_model)\n\nCall:\nlm(formula = saving ~ income + education, data = data, weights = weights)\n\nWeighted Residuals:\n     Min       1Q   Median       3Q      Max \n-3.06394 -0.87100 -0.03169  0.84237  3.00088 \n\nCoefficients:\n            Estimate Std. Error t value Pr(>|t|)    \n(Intercept) 60.74260   19.67855   3.087  0.00264 ** \nincome       0.08086    0.01700   4.757 6.85e-06 ***\neducation    4.94611    1.15245   4.292 4.20e-05 ***\n---\nSignif. codes:  0 \u2018***\u2019 0.001 \u2018**\u2019 0.01 \u2018*\u2019 0.05 \u2018.\u2019 0.1 \u2018 \u2019 1\n\nResidual standard error: 1.366 on 97 degrees of freedom\nMultiple R-squared:  0.2765,    Adjusted R-squared:  0.2615 \nF-statistic: 18.53 on 2 and 97 DF,  p-value: 1.528e-07\n\n> \n\n> print(results_comparison)\n            OLS Estimate OLS Std. Error OLS t value OLS Pr(>|t|) WLS Estimate\n(Intercept)  44.31369826    21.86489811    2.026705 4.543732e-02  60.74260273\neducation     5.80067082     1.28242638    4.523200 1.725943e-05   4.94611068\nincome        0.08844673     0.01837012    4.814707 5.424308e-06   0.08085543\n            WLS Std. Error WLS t value WLS Pr(>|t|)\n(Intercept)    19.67854732    3.086742 2.638157e-03\neducation       1.15245335    4.291810 4.198862e-05\nincome          0.01699848    4.756626 6.853118e-06\n> <\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">\u7d50\u679c\u306e\u89e3\u91c8<\/h3>\n\n\n\n<p>\u4e0a\u8a18\u306eR\u30b3\u30fc\u30c9\u3092\u5b9f\u884c\u3059\u308b\u3068\u3001OLS\u3068WLS\u305d\u308c\u305e\u308c\u306e\u56de\u5e30\u7d50\u679c\u306e\u30b5\u30de\u30ea\u30fc\u304c\u8868\u793a\u3055\u308c\u3001\u3055\u3089\u306b\u4e21\u8005\u306e\u4fc2\u6570\u3068\u6a19\u6e96\u8aa4\u5dee\u304c\u6bd4\u8f03\u3057\u3066\u898b\u3089\u308c\u308b\u3088\u3046\u306a\u4e00\u89a7\u304c\u51fa\u529b\u3055\u308c\u308b\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u6b8b\u5dee\u30d7\u30ed\u30c3\u30c8<\/strong>: OLS\u30e2\u30c7\u30eb\u306e\u6b8b\u5dee\u30d7\u30ed\u30c3\u30c8\u3092\u898b\u308b\u3068\u3001\u4e0d\u5747\u4e00\u6587\u3055\u304c\u5b58\u5728\u3059\u308b\u5834\u5408\u3001\u4e88\u6e2c\u5024\u306e\u5897\u52a0\u3068\u3068\u3082\u306b\u6b8b\u5dee\u306e\u3070\u3089\u3064\u304d\u304c\u5927\u304d\u304f\u306a\u3063\u3066\u3044\u308b\u3053\u3068\u304c\u8996\u899a\u7684\u306b\u78ba\u8a8d\u3067\u304d\u308b\u3002<\/li>\n\n\n\n<li><strong>\u4fc2\u6570\u306e\u6bd4\u8f03<\/strong>: OLS\u3068WLS\u3067\u63a8\u5b9a\u3055\u308c\u308b\u4fc2\u6570\u306e\u5024\u306f\u3001\u5fc5\u305a\u3057\u3082\u5927\u304d\u304f\u5909\u308f\u3089\u306a\u3044\u304b\u3082\u3057\u308c\u306a\u3044\u304c\u3001\u91cd\u8981\u306a\u306e\u306f\u6a19\u6e96\u8aa4\u5dee\u3067\u3042\u308b\u3002<\/li>\n\n\n\n<li><strong>\u6a19\u6e96\u8aa4\u5dee\u306e\u6bd4\u8f03<\/strong>: WLS\u30e2\u30c7\u30eb\u3067\u306f\u3001OLS\u30e2\u30c7\u30eb\u3068\u6bd4\u8f03\u3057\u3066\u3001\u5404\u4fc2\u6570\u306e\u6a19\u6e96\u8aa4\u5dee\u304c\u5c0f\u3055\u304f\u306a\u3063\u3066\u3044\u308b\u3053\u3068\u304c\u671f\u5f85\u3055\u308c\u308b\u3002\u7279\u306b\u3001\u4e0d\u5747\u4e00\u5206\u6563\u306e\u5f71\u97ff\u3092\u5f37\u304f\u53d7\u3051\u308b\u5909\u6570\uff08\u4e0a\u8a18\u306e\u4f8b\u3067\u306f\u6240\u5f97\uff09\u306e\u4fc2\u6570\u306b\u304a\u3044\u3066\u3001\u305d\u306e\u52b9\u679c\u304c\u9855\u8457\u306b\u73fe\u308c\u308b\u3053\u3068\u306b\u306a\u308b\u3002\u6a19\u6e96\u8aa4\u5dee\u304c\u5c0f\u3055\u3044\u3068\u3044\u3046\u3053\u3068\u306f\u3001\u63a8\u5b9a\u3055\u308c\u305f\u4fc2\u6570\u306e\u4fe1\u983c\u6027\u304c\u9ad8\u3044\u3053\u3068\u3092\u610f\u5473\u3059\u308b\uff08\u4eca\u56de\u306e\u4f8b\u3067\u306f\u305d\u308c\u307b\u3069\u5927\u304d\u306a\u5909\u5316\u306f\u306a\u304b\u3063\u305f\u304c\u30010.0184 \u304b\u30890.0170 \u3068\u82e5\u5e72\u5c0f\u3055\u304f\u306a\u3063\u305f\uff09<\/li>\n\n\n\n<li><strong>t\u5024\u3068p\u5024<\/strong>: \u6a19\u6e96\u8aa4\u5dee\u304c\u5c0f\u3055\u304f\u306a\u308b\u3053\u3068\u3067\u3001t\u5024\u304c\u5927\u304d\u304f\u306a\u308a\u3001p\u5024\u304c\u5c0f\u3055\u304f\u306a\u308b\u50be\u5411\u304c\u898b\u3089\u308c\u308b\uff08\u4e0a\u8a18\u306e\u4f8b\u306f\u5f53\u3066\u306f\u307e\u3089\u306a\u3044\u304c\uff09\u3002\u3053\u308c\u306b\u3088\u308a\u3001OLS\u3067\u306f\u7d71\u8a08\u7684\u306b\u6709\u610f\u3067\u306a\u304b\u3063\u305f\u4fc2\u6570\u304c\u3001WLS\u3067\u306f\u6709\u610f\u306b\u306a\u308b\u53ef\u80fd\u6027\u304c\u3042\u308b\u3002\u3053\u308c\u306f\u3001WLS\u304c\u3088\u308a\u52b9\u7387\u7684\u306a\u63a8\u5b9a\u3092\u53ef\u80fd\u306b\u3057\u3001\u3088\u308a\u6b63\u78ba\u306a\u7d71\u8a08\u7684\u63a8\u8ad6\u3092\u5c0e\u304f\u3053\u3068\u3092\u793a\u3057\u3066\u3044\u308b\u3002<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<div id=\"biost-1380871274\" class=\"biost- biost-entity-placement\"><p style=\"text-align: center;\"><span style=\"font-size: 20px;\"><strong><a href=\"https:\/\/best-biostatistics.com\/kmhl\">\uff1e\uff1e\u3082\u3046\u7d71\u8a08\u3067\u60a9\u3080\u306e\u306f\u7d42\u308f\u308a\u306b\u3057\u307e\u305b\u3093\u304b\uff1f\u00a0<\/a><\/strong><\/span><\/p>\r\n<a href=\"https:\/\/best-biostatistics.com\/kmhl\"><img class=\"aligncenter wp-image-2794 size-full\" src=\"https:\/\/best-biostatistics.com\/wp\/wp-content\/uploads\/2023\/11\/bn_r_03.png\" alt=\"\" width=\"500\" height=\"327\" \/><\/a>\r\n<p style=\"text-align: center;\"><span style=\"color: #ff0000; font-size: 20px;\"><strong><span class=\"marker2\">\u21911\u4e07\u4eba\u4ee5\u4e0a\u306e\u533b\u7642\u5f93\u4e8b\u8005\u304c\u8cfc\u8aad\u4e2d<\/span><\/strong><\/span><\/p><\/div><h2 class=\"wp-block-heading\">\u307e\u3068\u3081<\/h2>\n\n\n\n<p>\u91cd\u307f\u4ed8\u304d\u6700\u5c0f\u4e8c\u4e57\u6cd5\u306f\u3001\u30c7\u30fc\u30bf\u306b\u4e0d\u5747\u4e00\u5206\u6563\u304c\u5b58\u5728\u3059\u308b\u5834\u5408\u306b\u3001\u901a\u5e38\u306e\u6700\u5c0f\u4e8c\u4e57\u6cd5\u3088\u308a\u3082\u4fe1\u983c\u6027\u306e\u9ad8\u3044\u56de\u5e30\u30e2\u30c7\u30eb\u3092\u69cb\u7bc9\u3059\u308b\u305f\u3081\u306e\u5f37\u529b\u306a\u30c4\u30fc\u30eb\u3067\u3042\u308b\u3002\u5404\u89b3\u6e2c\u5024\u306e\u3070\u3089\u3064\u304d\u306e\u5927\u304d\u3055\u306b\u5fdc\u3058\u3066\u9069\u5207\u306a\u91cd\u307f\u3092\u5272\u308a\u5f53\u3066\u308b\u3053\u3068\u3067\u3001\u3088\u308a\u52b9\u7387\u7684\u306a\u4fc2\u6570\u63a8\u5b9a\u3068\u3001\u3088\u308a\u6b63\u78ba\u306a\u7d71\u8a08\u7684\u63a8\u8ad6\u3092\u53ef\u80fd\u306b\u3059\u308b\u3002<\/p>\n\n\n\n<p>WLS\u3092\u9069\u7528\u3059\u308b\u969b\u306b\u306f\u3001\u9069\u5207\u306a\u91cd\u307f\u306e\u9078\u629e\u304c\u91cd\u8981\u3068\u306a\u308b\u3002\u91cd\u307f\u306f\u3001\u5206\u6563\u306e\u9006\u6570\u3068\u3057\u3066\u5b9a\u7fa9\u3055\u308c\u308b\u3053\u3068\u304c\u591a\u3044\u304c\u3001\u305d\u306e\u5206\u6563\u95a2\u6570\u3092\u3069\u306e\u3088\u3046\u306b\u63a8\u5b9a\u3059\u308b\u304b\u306f\u3001\u30c7\u30fc\u30bf\u306e\u7279\u6027\u3084\u5206\u6790\u306e\u76ee\u7684\u306b\u5fdc\u3058\u3066\u614e\u91cd\u306b\u691c\u8a0e\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u3002\u672c\u8a18\u4e8b\u304c\u3001\u91cd\u56de\u5e30\u5206\u6790\u306b\u304a\u3051\u308bWLS\u306e\u7406\u89e3\u3092\u6df1\u3081\u308b\u4e00\u52a9\u3068\u306a\u308c\u3070\u5e78\u3044\u3067\u3042\u308b\u3002<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n","protected":false},"excerpt":{"rendered":"<p>\u91cd\u56de\u5e30\u5206\u6790\u306f\u3001\u8907\u6570\u306e\u8aac\u660e\u5909\u6570\u3092\u7528\u3044\u3066\u76ee\u7684\u5909\u6570\u3092\u4e88\u6e2c\u3059\u308b\u5f37\u529b\u306a\u7d71\u8a08\u624b\u6cd5\u3067\u3042\u308b\u3002\u3057\u304b\u3057\u3001OLS\uff08Ordinary Least Squares\uff1a\u901a\u5e38\u306e\u6700\u5c0f\u4e8c\u4e57\u6cd5\uff09\u3092\u9069\u7528\u3059\u308b\u969b\u306b\u3001\u3042\u308b\u91cd\u8981\u306a\u4eee\u5b9a\u304c\u6e80\u305f\u3055\u308c\u306a\u3044\u5834\u5408\u3001\u305d\u306e\u30e2\u30c7\u30eb\u306e\u4fe1 [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":4339,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"swell_btn_cv_data":"","_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[23],"tags":[],"class_list":["post-4338","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-23"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"https:\/\/best-biostatistics.com\/toukei-er\/wp-content\/uploads\/2025\/07\/Screenshot-from-2025-07-27-19-46-13.png","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/4338","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/comments?post=4338"}],"version-history":[{"count":2,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/4338\/revisions"}],"predecessor-version":[{"id":4341,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/posts\/4338\/revisions\/4341"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/media\/4339"}],"wp:attachment":[{"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/media?parent=4338"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/categories?post=4338"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/best-biostatistics.com\/toukei-er\/wp-json\/wp\/v2\/tags?post=4338"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}