{"id":915,"date":"2023-07-28T07:59:26","date_gmt":"2023-07-28T07:59:26","guid":{"rendered":"https:\/\/statorials.org\/ar\/%d9%85%d8%b3%d8%a7%d9%81%d8%a9-%d9%85%d8%a7%d9%87%d8%a7%d9%84%d8%a7%d9%86%d9%88%d8%a8%d9%8a%d8%b3-%d8%b5\/"},"modified":"2023-07-28T07:59:26","modified_gmt":"2023-07-28T07:59:26","slug":"%d9%85%d8%b3%d8%a7%d9%81%d8%a9-%d9%85%d8%a7%d9%87%d8%a7%d9%84%d8%a7%d9%86%d9%88%d8%a8%d9%8a%d8%b3-%d8%b5","status":"publish","type":"post","link":"https:\/\/statorials.org\/ar\/%d9%85%d8%b3%d8%a7%d9%81%d8%a9-%d9%85%d8%a7%d9%87%d8%a7%d9%84%d8%a7%d9%86%d9%88%d8%a8%d9%8a%d8%b3-%d8%b5\/","title":{"rendered":"\u0643\u064a\u0641\u064a\u0629 \u062d\u0633\u0627\u0628 \u0645\u0633\u0627\u0641\u0629 mahalanobis \u0641\u064a r"},"content":{"rendered":"<p><\/p>\n<hr>\n<p style=\";text-align:right;direction:rtl\"><span style=\"color: #000000;\"><strong>\u0645\u0633\u0627\u0641\u0629 Mahalanobis<\/strong> \u0647\u064a \u0627\u0644\u0645\u0633\u0627\u0641\u0629 \u0628\u064a\u0646 \u0646\u0642\u0637\u062a\u064a\u0646 \u0641\u064a \u0645\u0633\u0627\u062d\u0629 \u0645\u062a\u0639\u062f\u062f\u0629 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a.<\/span><\/p>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">\u0648\u063a\u0627\u0644\u0628\u0627 \u0645\u0627 \u064a\u0633\u062a\u062e\u062f\u0645 \u0644\u0644\u0643\u0634\u0641 \u0639\u0646 \u0627\u0644\u0642\u064a\u0645 \u0627\u0644\u0645\u062a\u0637\u0631\u0641\u0629 \u0641\u064a \u0627\u0644\u062a\u062d\u0644\u064a\u0644\u0627\u062a \u0627\u0644\u0625\u062d\u0635\u0627\u0626\u064a\u0629 \u0627\u0644\u062a\u064a \u062a\u0646\u0637\u0648\u064a \u0639\u0644\u0649 \u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0645\u062a\u0639\u062f\u062f\u0629.<\/span><\/p>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">\u064a\u0634\u0631\u062d \u0647\u0630\u0627 \u0627\u0644\u0628\u0631\u0646\u0627\u0645\u062c \u0627\u0644\u062a\u0639\u0644\u064a\u0645\u064a \u0643\u064a\u0641\u064a\u0629 \u062d\u0633\u0627\u0628 \u0645\u0633\u0627\u0641\u0629 Mahalanobis \u0641\u064a R.<\/span><\/p>\n<h2 style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\"><strong>\u0645\u062b\u0627\u0644: \u0645\u0633\u0627\u0641\u0629 \u0645\u0627\u0647\u0627\u0644\u0627\u0646\u0648\u0628\u064a\u0633 \u0641\u064a R<\/strong><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">\u0627\u0633\u062a\u062e\u062f\u0645 \u0627\u0644\u062e\u0637\u0648\u0627\u062a \u0627\u0644\u062a\u0627\u0644\u064a\u0629 \u0644\u062d\u0633\u0627\u0628 \u0645\u0633\u0627\u0641\u0629 Mahalanobis \u0644\u0643\u0644 <a href=\"https:\/\/statorials.org\/ar\/\u0627\u0644\u0645\u0644\u0627\u062d\u0638\u0629-\u0641\u064a-\u0627\u0644\u0627\u0655\u062d\u0635\u0627\u0621\/\" target=\"_blank\" rel=\"noopener\">\u0645\u0644\u0627\u062d\u0638\u0629<\/a> \u0641\u064a \u0645\u062c\u0645\u0648\u0639\u0629 \u0628\u064a\u0627\u0646\u0627\u062a \u0641\u064a R.<\/span><\/p>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\"><strong>\u0627\u0644\u062e\u0637\u0648\u0629 1: \u0625\u0646\u0634\u0627\u0621 \u0645\u062c\u0645\u0648\u0639\u0629 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a.<\/strong><\/span><\/p>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">\u0623\u0648\u0644\u0627\u064b\u060c \u0633\u0646\u0642\u0648\u0645 \u0628\u0625\u0646\u0634\u0627\u0621 \u0645\u062c\u0645\u0648\u0639\u0629 \u0628\u064a\u0627\u0646\u0627\u062a \u062a\u0639\u0631\u0636 \u062f\u0631\u062c\u0627\u062a \u0627\u0644\u0627\u062e\u062a\u0628\u0627\u0631 \u0644\u0640 20 \u0637\u0627\u0644\u0628\u064b\u0627\u060c \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0639\u062f\u062f \u0627\u0644\u0633\u0627\u0639\u0627\u062a \u0627\u0644\u062a\u064a \u0642\u0636\u0648\u0647\u0627 \u0641\u064a \u0627\u0644\u062f\u0631\u0627\u0633\u0629\u060c \u0648\u0639\u062f\u062f \u0627\u0644\u0627\u062e\u062a\u0628\u0627\u0631\u0627\u062a \u0627\u0644\u062a\u062f\u0631\u064a\u0628\u064a\u0629 \u0627\u0644\u062a\u064a \u0623\u062c\u0631\u0648\u0647\u0627 \u0648\u062f\u0631\u062c\u0627\u062a\u0647\u0645 \u0627\u0644\u062d\u0627\u0644\u064a\u0629 \u0641\u064a \u0627\u0644\u062f\u0648\u0631\u0629:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#create data<\/span>\ndf = data.frame(score = c(91, 93, 72, 87, 86, 73, 68, 87, 78, 99, 95, 76, 84, 96, 76, 80, 83, 84, 73, 74) ,\n        hours = c(16, 6, 3, 1, 2, 3, 2, 5, 2, 5, 2, 3, 4, 3, 3, 3, 4, 3, 4, 4),\n        prep = c(3, 4, 0, 3, 4, 0, 1, 2, 1, 2, 3, 3, 3, 2, 2, 2, 3, 3, 2, 2),\n        grade = c(70, 88, 80, 83, 88, 84, 78, 94, 90, 93, 89, 82, 95, 94, 81, 93, 93, 90, 89, 89))\n\n<span style=\"color: #008080;\">#view first six rows of data\n<\/span>head(df)\n\n  score hours prep grade\n1 91 16 3 70\n2 93 6 4 88\n3 72 3 0 80\n4 87 1 3 83\n5 86 2 4 88\n6 73 3 0 84\n<\/strong><\/pre>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\"><strong>\u0627\u0644\u062e\u0637\u0648\u0629 2: \u0627\u062d\u0633\u0628 \u0645\u0633\u0627\u0641\u0629 \u0627\u0644\u0645\u0647\u0627\u0644\u0627\u0646\u0648\u0628\u064a\u0633 \u0644\u0643\u0644 \u0645\u0644\u0627\u062d\u0638\u0629.<\/strong><\/span><\/p>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">\u0628\u0639\u062f \u0630\u0644\u0643\u060c \u0633\u0648\u0641 \u0646\u0633\u062a\u062e\u062f\u0645 \u0627\u0644\u062f\u0627\u0644\u0629 <a href=\"https:\/\/stat.ethz.ch\/R-manual\/R-devel\/library\/stats\/html\/mahalanobis.html\" target=\"_blank\" rel=\"noopener noreferrer\">mahalanobis()<\/a> \u0627\u0644\u0645\u0636\u0645\u0646\u0629 \u0641\u064a R \u0644\u062d\u0633\u0627\u0628 \u0645\u0633\u0627\u0641\u0629 Mahalanobis \u0644\u0643\u0644 \u0645\u0644\u0627\u062d\u0638\u0629\u060c \u0648\u0627\u0644\u062a\u064a \u062a\u0633\u062a\u062e\u062f\u0645 \u0627\u0644\u0635\u064a\u063a\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629:<\/span><\/p>\n<p style=\";text-align:right;direction:rtl\"> <strong><span style=\"color: #000000;\">\u0645\u0627\u0647\u0627\u0644\u0627\u0646\u0648\u0628\u064a\u0633 (x\u060c \u0645\u0631\u0643\u0632\u060c \u0643\u0648\u0641)<\/span><\/strong><\/p>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">\u0630\u0647\u0628:<\/span><\/p>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\"><strong>\u0633:<\/strong> \u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a<\/span><\/li>\n<li style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\"><strong>\u0627\u0644\u0645\u0631\u0643\u0632:<\/strong> \u0645\u062a\u0648\u0633\u0637 \u0646\u0627\u0642\u0644 \u0627\u0644\u062a\u0648\u0632\u064a\u0639<\/span><\/li>\n<li style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\"><strong>cov:<\/strong> \u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u062a\u063a\u0627\u064a\u0631 \u0627\u0644\u062a\u0648\u0632\u064a\u0639\u064a<\/span><\/li>\n<\/ul>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">\u064a\u0648\u0636\u062d \u0627\u0644\u0643\u0648\u062f \u0627\u0644\u062a\u0627\u0644\u064a \u0643\u064a\u0641\u064a\u0629 \u062a\u0646\u0641\u064a\u0630 \u0647\u0630\u0647 \u0627\u0644\u0648\u0638\u064a\u0641\u0629 \u0644\u0645\u062c\u0645\u0648\u0639\u0629 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0627\u0644\u062e\u0627\u0635\u0629 \u0628\u0646\u0627:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#calculate Mahalanobis distance for each observation<\/span>\nmahalanobis(df, colMeans(df), cov(df))\n\n [1] 16.5019630 2.6392864 4.8507973 5.2012612 3.8287341 4.0905633\n [7] 4.2836303 2.4198736 1.6519576 5.6578253 3.9658770 2.9350178\n[13] 2.8102109 4.3682945 1.5610165 1.4595069 2.0245748 0.7502536\n[19] 2.7351292 2.2642268\n<\/strong><\/pre>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\"><strong>\u0627\u0644\u062e\u0637\u0648\u0629 3: \u0627\u062d\u0633\u0628 \u0627\u0644\u0642\u064a\u0645\u0629 p \u0644\u0643\u0644 \u0645\u0633\u0627\u0641\u0629 \u0645\u0627\u0647\u0627\u0644\u0627\u0646\u0648\u0628\u064a\u0633.<\/strong><\/span> <\/p>\n<div id=\"mv-first-video\" class=\"mv-video-target mv-video__featured mv-video__optimized mv-video__embedded\" data-video-id=\"tmdycgxksxqpmqpu0vbx\" data-autoplay=\"true\" data-automobile=\"true\" data-muted=\"true\" data-sticky=\"true\" data-autoinsert=\"true\" data-disable-jsonld=\"true\" data-video-placement-inited=\"true\" style=\";text-align:right;direction:rtl\">\n<div id=\"mediavine-video__target-div__8330b88d-7ed9-463c-85d3-dc370a4c9ab3\" class=\"mediavine-video__target-div\" style=\";text-align:right;direction:rtl\">\n<div class=\"mediavine-video__root-container\" style=\";text-align:right;direction:rtl\">\n<div class=\"mediavine-video__placement-container mediavine-video__bottom mediavine-video__right mediavine-video__dark-theme\" style=\";text-align:right;direction:rtl\">\n<div class=\"mediavine-video__title-bar\" style=\";text-align:right;direction:rtl\">\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">\u064a\u0645\u0643\u0646\u0646\u0627 \u0623\u0646 \u0646\u0631\u0649 \u0623\u0646 \u0628\u0639\u0636 \u0645\u0633\u0627\u0641\u0627\u062a \u0645\u0627\u0647\u0627\u0644\u0627\u0646\u0648\u0628\u064a \u0623\u0643\u0628\u0631 \u0628\u0643\u062b\u064a\u0631 \u0645\u0646 \u063a\u064a\u0631\u0647\u0627.<\/span><\/p>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">\u0644\u062a\u062d\u062f\u064a\u062f \u0645\u0627 \u0625\u0630\u0627 \u0643\u0627\u0646\u062a \u0623\u064a \u0645\u0646 \u0627\u0644\u0645\u0633\u0627\u0641\u0627\u062a \u0630\u0627\u062a \u062f\u0644\u0627\u0644\u0629 \u0625\u062d\u0635\u0627\u0626\u064a\u0629\u060c \u0646\u062d\u062a\u0627\u062c \u0625\u0644\u0649 \u062d\u0633\u0627\u0628 <a href=\"https:\/\/statorials.org\/ar\/\u0641-\u0627\u0644\u0642\u064a\u0645-\u0627\u0654\u0647\u0645\u064a\u0629-\u0627\u0655\u062d\u0635\u0627\u064a\u0654\u064a\u0629\/\" target=\"_blank\" rel=\"noopener\">\u0642\u064a\u0645\u0647\u0627 \u0627\u0644\u0627\u062d\u062a\u0645\u0627\u0644\u064a\u0629<\/a> .<\/span><\/p>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">\u064a\u062a\u0645 \u062d\u0633\u0627\u0628 \u0627\u0644\u0642\u064a\u0645\u0629 p \u0644\u0643\u0644 \u0645\u0633\u0627\u0641\u0629 \u0639\u0644\u0649 \u0623\u0646\u0647\u0627 \u0627\u0644\u0642\u064a\u0645\u0629 p \u0627\u0644\u062a\u064a \u062a\u062a\u0648\u0627\u0641\u0642 \u0645\u0639 \u0625\u062d\u0635\u0627\u0626\u064a\u0629 \u0645\u0631\u0628\u0639 \u0643\u0627\u064a \u0644\u0645\u0633\u0627\u0641\u0629 Mahalanobis \u0645\u0639 \u062f\u0631\u062c\u0627\u062a \u062d\u0631\u064a\u0629 k-1\u060c \u062d\u064a\u062b k = \u0639\u062f\u062f \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a.<\/span><\/p>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">\u0644\u0630\u0644\u0643 \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0627\u0644\u0629 \u0633\u0648\u0641 \u0646\u0633\u062a\u062e\u062f\u0645 \u062f\u0631\u062c\u0627\u062a \u0627\u0644\u062d\u0631\u064a\u0629 4-1 = 3.<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#create new column in data frame to hold Mahalanobis distances<\/span>\ndf$mahal &lt;- mahalanobis(df, colMeans(df), cov(df))\n\n<span style=\"color: #008080;\">#create new column in data frame to hold p-value for each Mahalanobis distance\n<\/span>df$p &lt;- <span style=\"color: #3366ff;\">pchisq<\/span> (df$mahal, df= <span style=\"color: #339966;\">3<\/span> , lower.tail=FALSE)\n\n<span style=\"color: #008080;\">#view data frame\n<\/span>df\n\n   score hours prep grade mahal p\n1 91 16 3 70 16.5019630 0.0008945642\n2 93 6 4 88 2.6392864 0.4506437265\n3 72 3 0 80 4.8507973 0.1830542407\n4 87 1 3 83 5.2012612 0.1576392526\n5 86 2 4 88 3.8287341 0.2805615121\n6 73 3 0 84 4.0905633 0.2518495222\n7 68 2 1 78 4.2836303 0.2324211504\n8 87 5 2 94 2.4198736 0.4899458807\n9 78 2 1 90 1.6519576 0.6476670033\n10 99 5 2 93 5.6578253 0.1294978092\n11 95 2 3 89 3.9658770 0.2651724541\n12 76 3 3 82 2.9350178 0.4017530495\n13 84 4 3 95 2.8102109 0.4218217836\n14 96 3 2 94 4.3682945 0.2243432904\n15 76 3 2 81 1.5610165 0.6682610031\n16 80 3 2 93 1.4595069 0.6916471506\n17 83 4 3 93 2.0245748 0.5673218169\n18 84 3 3 90 0.7502536 0.8613248635\n19 73 4 2 89 2.7351292 0.4342904353\n20 74 4 2 89 2.2642268 0.5194087143\n<\/strong><\/pre>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">\u0628\u0634\u0643\u0644 \u0639\u0627\u0645\u060c \u062a\u0639\u062a\u0628\u0631 \u0627\u0644\u0642\u064a\u0645\u0629 p <strong>\u0627\u0644\u0623\u0642\u0644 \u0645\u0646 0.001<\/strong> \u0642\u064a\u0645\u0629 \u0645\u062a\u0637\u0631\u0641\u0629.<\/span><\/p>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">\u064a\u0645\u0643\u0646\u0646\u0627 \u0623\u0646 \u0646\u0631\u0649 \u0623\u0646 \u0627\u0644\u0645\u0644\u0627\u062d\u0638\u0629 \u0627\u0644\u0623\u0648\u0644\u0649 \u062a\u0639\u062a\u0628\u0631 \u063a\u0631\u064a\u0628\u0629 \u0641\u064a \u0645\u062c\u0645\u0648\u0639\u0629 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0644\u0623\u0646\u0647\u0627 \u062a\u062d\u062a\u0648\u064a \u0639\u0644\u0649 \u0642\u064a\u0645\u0629 p \u0623\u0642\u0644 \u0645\u0646 0.001.<\/span><\/p>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">\u0627\u0639\u062a\u0645\u0627\u062f\u064b\u0627 \u0639\u0644\u0649 \u0633\u064a\u0627\u0642 \u0627\u0644\u0645\u0634\u0643\u0644\u0629\u060c \u0642\u062f \u062a\u0642\u0631\u0631 \u0625\u0632\u0627\u0644\u0629 \u0647\u0630\u0647 \u0627\u0644\u0645\u0644\u0627\u062d\u0638\u0629 \u0645\u0646 \u0645\u062c\u0645\u0648\u0639\u0629 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0644\u0623\u0646\u0647\u0627 \u062a\u0645\u062b\u0644 \u0642\u064a\u0645\u0629 \u0645\u062a\u0637\u0631\u0641\u0629 \u0648\u064a\u0645\u0643\u0646 \u0623\u0646 \u062a\u0624\u062b\u0631 \u0639\u0644\u0649 \u0646\u062a\u0627\u0626\u062c \u0627\u0644\u062a\u062d\u0644\u064a\u0644.<\/span><\/p>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\"><span style=\"color: #000000;\"><b>\u0630\u0627\u062a \u0635\u0644\u0629:<\/b><\/span> <a 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