{"id":1095,"date":"2023-07-27T16:32:06","date_gmt":"2023-07-27T16:32:06","guid":{"rendered":"https:\/\/statorials.org\/ar\/%d8%aa%d8%ad%d9%88%d9%8a%d9%84-%d9%85%d8%b1%d8%a8%d8%b9-%d9%83%d9%88%d9%83%d8%b3-%d8%a7%d9%95%d9%84%d9%89-%d8%b5\/"},"modified":"2023-07-27T16:32:06","modified_gmt":"2023-07-27T16:32:06","slug":"%d8%aa%d8%ad%d9%88%d9%8a%d9%84-%d9%85%d8%b1%d8%a8%d8%b9-%d9%83%d9%88%d9%83%d8%b3-%d8%a7%d9%95%d9%84%d9%89-%d8%b5","status":"publish","type":"post","link":"https:\/\/statorials.org\/ar\/%d8%aa%d8%ad%d9%88%d9%8a%d9%84-%d9%85%d8%b1%d8%a8%d8%b9-%d9%83%d9%88%d9%83%d8%b3-%d8%a7%d9%95%d9%84%d9%89-%d8%b5\/","title":{"rendered":"\u0643\u064a\u0641\u064a\u0629 \u0625\u062c\u0631\u0627\u0621 \u062a\u062d\u0648\u064a\u0644 box-cox \u0641\u064a \u0644\u063a\u0629 r (\u0645\u0639 \u0623\u0645\u062b\u0644\u0629)"},"content":{"rendered":"<p><\/p>\n<hr>\n<p style=\";text-align:right;direction:rtl\"><span style=\"color: #000000;\">\u064a\u0639\u062f <strong>\u062a\u062d\u0648\u064a\u0644 box-cox<\/strong> \u0637\u0631\u064a\u0642\u0629 \u0634\u0627\u0626\u0639\u0629 \u0627\u0644\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0644\u062a\u062d\u0648\u064a\u0644 \u0645\u062c\u0645\u0648\u0639\u0629 \u0628\u064a\u0627\u0646\u0627\u062a \u063a\u064a\u0631 \u0645\u0648\u0632\u0639\u0629 \u0628\u0634\u0643\u0644 \u0637\u0628\u064a\u0639\u064a \u0625\u0644\u0649 \u0645\u062c\u0645\u0648\u0639\u0629 \u0645\u0648\u0632\u0639\u0629 \u0628\u0634\u0643\u0644 \u0637\u0628\u064a\u0639\u064a .<\/span><\/p>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">\u0627\u0644\u0641\u0643\u0631\u0629 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0648\u0631\u0627\u0621 \u0647\u0630\u0647 \u0627\u0644\u0637\u0631\u064a\u0642\u0629 \u0647\u064a \u0625\u064a\u062c\u0627\u062f \u0642\u064a\u0645\u0629 \u0644\u0640 lect \u0628\u062d\u064a\u062b \u062a\u0643\u0648\u0646 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0627\u0644\u0645\u062d\u0648\u0644\u0629 \u0642\u0631\u064a\u0628\u0629 \u0642\u062f\u0631 \u0627\u0644\u0625\u0645\u0643\u0627\u0646 \u0645\u0646 \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u0637\u0628\u064a\u0639\u064a\u060c \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0635\u064a\u063a\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629:<\/span><\/p>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">y(\uf06c) = (y <sup>\uf06c<\/sup> \u2013 1) \/ \uf06c \u0625\u0630\u0627 y \u2260 0<\/span><\/li>\n<li style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">y(lect) = log(y) \u0625\u0630\u0627 \u0643\u0627\u0646\u062a y = 0<\/span><\/li>\n<\/ul>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">\u064a\u0645\u0643\u0646\u0646\u0627 \u0625\u062c\u0631\u0627\u0621 \u062a\u062d\u0648\u064a\u0644 box-cox \u0641\u064a R \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u062f\u0627\u0644\u0629 <strong>boxcox()<\/strong> \u0645\u0646 \u0645\u0643\u062a\u0628\u0629 <strong>MASS()<\/strong> .<\/span> <span style=\"color: #000000;\">\u064a\u0648\u0636\u062d \u0627\u0644\u0645\u062b\u0627\u0644 \u0627\u0644\u062a\u0627\u0644\u064a \u0643\u064a\u0641\u064a\u0629 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0647\u0630\u0647 \u0627\u0644\u0648\u0638\u064a\u0641\u0629 \u0639\u0645\u0644\u064a\u064b\u0627.<\/span><\/p>\n<p style=\";text-align:right;direction:rtl\"> <em><span style=\"color: #000000;\">\u0627\u0631\u062c\u0639 \u0625\u0644\u0649 <a href=\"https:\/\/www.ime.usp.br\/~abe\/lista\/pdfm9cJKUmFZp.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">\u0647\u0630\u0647 \u0627\u0644\u0645\u0642\u0627\u0644\u0629<\/a> \u0645\u0646 \u062c\u0627\u0645\u0639\u0629 \u0643\u0648\u0646\u064a\u062a\u064a\u0643\u062a \u0644\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u0649 \u0645\u0644\u062e\u0635 \u0644\u0637\u064a\u0641 \u0644\u062a\u0637\u0648\u0631 \u062a\u062d\u0648\u0644 Box-Cox.<\/span><\/em><\/p>\n<h3 style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\"><strong>\u0645\u062b\u0627\u0644: \u062a\u062d\u0648\u064a\u0644 Box-Cox \u0641\u064a R<\/strong><\/span><\/h3>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">\u064a\u0648\u0636\u062d \u0627\u0644\u062a\u0639\u0644\u064a\u0645\u0629 \u0627\u0644\u0628\u0631\u0645\u062c\u064a\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629 \u0643\u064a\u0641\u064a\u0629 \u0645\u0644\u0627\u0621\u0645\u0629 \u0646\u0645\u0648\u0630\u062c \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u062e\u0637\u064a \u0644\u0645\u062c\u0645\u0648\u0639\u0629 \u0628\u064a\u0627\u0646\u0627\u062a\u060c \u062b\u0645 \u0627\u0633\u062a\u062e\u062f\u0645 \u0627\u0644\u062f\u0627\u0644\u0629 <strong>boxcox()<\/strong> \u0644\u0644\u0639\u062b\u0648\u0631 \u0639\u0644\u0649 lambda \u0627\u0644\u0623\u0645\u062b\u0644 \u0644\u062a\u062d\u0648\u064a\u0644 <a href=\"https:\/\/statorials.org\/ar\/\u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a-\u0627\u0644\u0627\u0633\u062a\u062c\u0627\u0628\u0627\u062a-\u0627\u0644\u062a\u0641\u0633\u064a\u0631\u064a\u0629\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u0645\u062a\u063a\u064a\u0631 \u0627\u0644\u0627\u0633\u062a\u062c\u0627\u0628\u0629<\/a> \u0648\u0645\u0644\u0627\u0621\u0645\u0629 \u0646\u0645\u0648\u0630\u062c \u062c\u062f\u064a\u062f.<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #993300;\">library<\/span> (MASS)\n\n<span style=\"color: #008080;\">#create data<\/span>\ny=c(1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 6, 7, 8)\nx=c(7, 7, 8, 3, 2, 4, 4, 6, 6, 7, 5, 3, 3, 5, 8)\n\n<span style=\"color: #008080;\">#fit linear regression model<\/span>\nmodel &lt;- lm(y~x)\n\n<span style=\"color: #008080;\">#find optimal lambda for Box-Cox transformation<\/span> \nbc &lt;- boxcox(y ~ x)\n(lambda &lt;- bc$x[which.max(bc$y)])\n\n[1] -0.4242424\n\n<span style=\"color: #008080;\">#fit new linear regression model using the Box-Cox transformation<\/span>\nnew_model &lt;- lm(((y^lambda-1)\/lambda) ~ x)\n<\/strong><\/pre>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">\u0648\u062a\u0628\u064a\u0646 \u0623\u0646 \u0644\u0627\u0645\u062f\u0627 \u0627\u0644\u0623\u0645\u062b\u0644 \u0647\u0648 <strong>-0.4242424<\/strong> . \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a\u060c \u0642\u0627\u0645 \u0646\u0645\u0648\u0630\u062c \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u062c\u062f\u064a\u062f \u0628\u0627\u0633\u062a\u0628\u062f\u0627\u0644 \u0645\u062a\u063a\u064a\u0631 \u0627\u0644\u0627\u0633\u062a\u062c\u0627\u0628\u0629 \u0627\u0644\u0623\u0635\u0644\u064a y \u0628\u0627\u0644\u0645\u062a\u063a\u064a\u0631 y = (y <sup>-0.4242424<\/sup> \u2013 1) \/ -0.4242424.<\/span><\/p>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">\u064a\u0648\u0636\u062d \u0627\u0644\u062a\u0639\u0644\u064a\u0645\u0629 \u0627\u0644\u0628\u0631\u0645\u062c\u064a\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629 \u0643\u064a\u0641\u064a\u0629 \u0625\u0646\u0634\u0627\u0621 <a href=\"https:\/\/statorials.org\/ar\/\u0634\u062e\u0635-\u0645\u0627-\u0627\u0644\u0645\u0648\u0654\u0627\u0645\u0631\u0627\u062a-\u0635\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u0645\u062e\u0637\u0637\u064a QQ<\/a> \u0641\u064a R \u0644\u062a\u0635\u0648\u0631 \u0627\u0644\u0627\u062e\u062a\u0644\u0627\u0641\u0627\u062a \u0641\u064a \u0627\u0644\u0642\u064a\u0645 \u0627\u0644\u0645\u062a\u0628\u0642\u064a\u0629 \u0628\u064a\u0646 \u0646\u0645\u0648\u0630\u062c\u064a \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631:<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#define plotting area<\/span>\nop &lt;- par(pty = \"s\", mfrow = c(1, 2))\n\n<span style=\"color: #008080;\">#QQ plot for original model<\/span>\nqqnorm(model$residuals)\nqqline(model$residuals)\n\n<span style=\"color: #008080;\">#QQ plot for Box-Cox transformed model<\/span>\nqqnorm(new_model$residuals)\nqqline(new_model$residuals)\n\n<span style=\"color: #008080;\">#display both QQ plots<\/span>\nby(op)\n<\/strong><\/pre>\n<p style=\";text-align:right;direction:rtl\"><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-11193 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/boitecoxr1.png\" alt=\"\u062a\u0645 \u062a\u062d\u0648\u064a\u0644 \u062a\u0636\u0627\u0631\u064a\u0633 QQ \u0628\u0648\u0627\u0633\u0637\u0629 Box-Cox \u0641\u064a R\" width=\"501\" height=\"301\" srcset=\"\" sizes=\"\"><\/p>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">\u0628\u0634\u0643\u0644 \u0639\u0627\u0645\u060c \u0625\u0630\u0627 \u0643\u0627\u0646\u062a \u0646\u0642\u0627\u0637 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u062a\u0642\u0639 \u0639\u0644\u0649 \u0637\u0648\u0644 \u062e\u0637 \u0642\u0637\u0631\u064a \u0645\u0633\u062a\u0642\u064a\u0645 \u0641\u064a \u0645\u062e\u0637\u0637 QQ\u060c \u0641\u0645\u0646 \u0627\u0644\u0645\u0631\u062c\u062d \u0623\u0646 \u062a\u062a\u0628\u0639 \u0645\u062c\u0645\u0648\u0639\u0629 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u0637\u0628\u064a\u0639\u064a.<\/span><\/p>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">\u0644\u0627\u062d\u0638 \u0643\u064a\u0641 \u064a\u0646\u062a\u062c \u0646\u0645\u0648\u0630\u062c Box-cox \u0627\u0644\u0645\u062a\u062d\u0648\u0644 \u0645\u062e\u0637\u0637 QQ \u0628\u062e\u0637 \u0623\u0643\u062b\u0631 \u0627\u0633\u062a\u0642\u0627\u0645\u0629 \u0645\u0646 \u0646\u0645\u0648\u0630\u062c \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u0623\u0635\u0644\u064a.<\/span><\/p>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">\u064a\u0634\u064a\u0631 \u0647\u0630\u0627 \u0625\u0644\u0649 \u0623\u0646 \u0628\u0642\u0627\u064a\u0627 \u0646\u0645\u0648\u0630\u062c \u0628\u0648\u0643\u0633 \u0643\u0648\u0643\u0633 \u0627\u0644\u0645\u062a\u062d\u0648\u0644 \u064a\u062a\u0645 \u062a\u0648\u0632\u064a\u0639\u0647\u0627 \u0628\u0634\u0643\u0644 \u0637\u0628\u064a\u0639\u064a \u0623\u0643\u062b\u0631\u060c \u0645\u0645\u0627 \u064a\u0644\u0628\u064a \u0623\u062d\u062f <a href=\"https:\/\/statorials.org\/ar\/\u0627\u0641\u062a\u0631\u0627\u0636\u0627\u062a-\u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631-\u0627\u0644\u062e\u0637\u064a\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u0627\u0641\u062a\u0631\u0627\u0636\u0627\u062a \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u062e\u0637\u064a<\/a> .<\/span><\/p>\n<h3 style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\"><strong>\u0645\u0635\u0627\u062f\u0631 \u0625\u0636\u0627\u0641\u064a\u0629<\/strong><\/span><\/h3>\n<p style=\";text-align:right;direction:rtl\"> <a href=\"https:\/\/statorials.org\/ar\/\u062a\u062d\u0648\u064a\u0644-\u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a-\u0627\u0655\u0644\u0649-\u0635\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u0643\u064a\u0641\u064a\u0629 \u062a\u062d\u0648\u064a\u0644 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0625\u0644\u0649 \u0644\u063a\u0629 R (\u0627\u0644\u0633\u062c\u0644\u060c \u0627\u0644\u062c\u0630\u0631 \u0627\u0644\u062a\u0631\u0628\u064a\u0639\u064a\u060c \u0627\u0644\u062c\u0630\u0631 \u0627\u0644\u062a\u0643\u0639\u064a\u0628\u064a)<\/a><br \/> <a href=\"https:\/\/statorials.org\/ar\/\u0634\u062e\u0635-\u0645\u0627-\u0627\u0644\u0645\u0648\u0654\u0627\u0645\u0631\u0627\u062a-\u0635\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u0643\u064a\u0641\u064a\u0629 \u0625\u0646\u0634\u0627\u0621 \u0648\u062a\u0641\u0633\u064a\u0631 \u0645\u0624\u0627\u0645\u0631\u0629 QQ \u0641\u064a R<\/a><br \/> <a href=\"https:\/\/statorials.org\/ar\/\u0627\u062e\u062a\u0628\u0627\u0631-\u0634\u0627\u0628\u064a\u0631\u0648-\u0648\u064a\u0644\u0643-\u0635\/\">\u0643\u064a\u0641\u064a\u0629 \u0625\u062c\u0631\u0627\u0621 \u0627\u062e\u062a\u0628\u0627\u0631 \u0634\u0627\u0628\u064a\u0631\u0648 \u0648\u064a\u0644\u0643 \u0644\u0644\u062d\u064a\u0627\u0629 \u0627\u0644\u0637\u0628\u064a\u0639\u064a\u0629 \u0641\u064a R<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u064a\u0639\u062f \u062a\u062d\u0648\u064a\u0644 box-cox \u0637\u0631\u064a\u0642\u0629 \u0634\u0627\u0626\u0639\u0629 \u0627\u0644\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0644\u062a\u062d\u0648\u064a\u0644 \u0645\u062c\u0645\u0648\u0639\u0629 \u0628\u064a\u0627\u0646\u0627\u062a \u063a\u064a\u0631 \u0645\u0648\u0632\u0639\u0629 \u0628\u0634\u0643\u0644 \u0637\u0628\u064a\u0639\u064a \u0625\u0644\u0649 \u0645\u062c\u0645\u0648\u0639\u0629 \u0645\u0648\u0632\u0639\u0629 \u0628\u0634\u0643\u0644 \u0637\u0628\u064a\u0639\u064a . \u0627\u0644\u0641\u0643\u0631\u0629 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0648\u0631\u0627\u0621 \u0647\u0630\u0647 \u0627\u0644\u0637\u0631\u064a\u0642\u0629 \u0647\u064a \u0625\u064a\u062c\u0627\u062f \u0642\u064a\u0645\u0629 \u0644\u0640 lect \u0628\u062d\u064a\u062b \u062a\u0643\u0648\u0646 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0627\u0644\u0645\u062d\u0648\u0644\u0629 \u0642\u0631\u064a\u0628\u0629 \u0642\u062f\u0631 \u0627\u0644\u0625\u0645\u0643\u0627\u0646 \u0645\u0646 \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u0637\u0628\u064a\u0639\u064a\u060c \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0635\u064a\u063a\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629: y(\uf06c) = (y \uf06c \u2013 1) \/ \uf06c \u0625\u0630\u0627 y \u2260 0 y(lect) 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