{"id":2447,"date":"2023-07-22T05:51:57","date_gmt":"2023-07-22T05:51:57","guid":{"rendered":"https:\/\/statorials.org\/ar\/sst-ssr-sse-%d9%81%d9%8a-%d8%a8%d9%8a%d8%ab%d9%88%d9%86\/"},"modified":"2023-07-22T05:51:57","modified_gmt":"2023-07-22T05:51:57","slug":"sst-ssr-sse-%d9%81%d9%8a-%d8%a8%d9%8a%d8%ab%d9%88%d9%86","status":"publish","type":"post","link":"https:\/\/statorials.org\/ar\/sst-ssr-sse-%d9%81%d9%8a-%d8%a8%d9%8a%d8%ab%d9%88%d9%86\/","title":{"rendered":"\u0643\u064a\u0641\u064a\u0629 \u062d\u0633\u0627\u0628 sst \u0648ssr \u0648sse \u0641\u064a \u0628\u0627\u064a\u062b\u0648\u0646"},"content":{"rendered":"<p><\/p>\n<hr>\n<p style=\";text-align:right;direction:rtl\"><span style=\"color: #000000;\">\u063a\u0627\u0644\u0628\u064b\u0627 \u0645\u0627 \u0646\u0633\u062a\u062e\u062f\u0645 \u062b\u0644\u0627\u062b\u0629 <a href=\"https:\/\/statorials.org\/ar\/\u0637\u0627\u064a\u0654\u0631\u0629-\u0627\u0654\u0633\u0631\u0639-\u0645\u0646-\u0627\u0644\u0635\u0648\u062a-ssr\/\" target=\"_blank\" rel=\"noopener\">\u0645\u062c\u0645\u0648\u0639\u0627\u062a \u0645\u062e\u062a\u0644\u0641\u0629 \u0645\u0646 \u0642\u064a\u0645 \u0627\u0644\u0645\u0631\u0628\u0639\u0627\u062a<\/a> \u0644\u0642\u064a\u0627\u0633 \u0645\u062f\u0649 \u0645\u0644\u0627\u0621\u0645\u0629 <a href=\"https:\/\/statorials.org\/ar\/\u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631-\u0627\u0644\u062e\u0637\u064a-1\/\" target=\"_blank\" rel=\"noopener\">\u062e\u0637 \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631<\/a> \u0644\u0645\u062c\u0645\u0648\u0639\u0629 \u0645\u0646 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a:<\/span><\/p>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\"><strong>1. \u0645\u062c\u0645\u0648\u0639 \u0627\u0644\u0645\u0631\u0628\u0639\u0627\u062a \u0627\u0644\u0625\u062c\u0645\u0627\u0644\u064a\u0629 (SST) \u2013<\/strong> \u0645\u062c\u0645\u0648\u0639 \u0645\u0631\u0628\u0639\u0627\u062a \u0627\u0644\u0627\u062e\u062a\u0644\u0627\u0641\u0627\u062a \u0628\u064a\u0646 \u0646\u0642\u0627\u0637 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0627\u0644\u0641\u0631\u062f\u064a\u0629 (y <sub>i<\/sub> ) \u0648\u0645\u062a\u0648\u0633\u0637 \u0645\u062a\u063a\u064a\u0631 \u0627\u0644\u0627\u0633\u062a\u062c\u0627\u0628\u0629 ( <span style=\"border-top: 1px solid black;\">y<\/span> ).<\/span><\/p>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">\u062f\u0631\u062c\u0629 \u062d\u0631\u0627\u0631\u0629 \u0633\u0637\u062d \u0627\u0644\u0628\u062d\u0631 = \u03a3(\u0635 <sub>\u0637<\/sub> \u2013 <span style=\"border-top: 1px solid black;\">\u0630<\/span> ) <sup>2<\/sup><\/span><\/li>\n<\/ul>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\"><strong>2. \u0627\u0646\u062d\u062f\u0627\u0631 \u0645\u062c\u0645\u0648\u0639 \u0627\u0644\u0645\u0631\u0628\u0639\u0627\u062a (SSR)<\/strong> \u2013 \u0645\u062c\u0645\u0648\u0639 \u0645\u0631\u0628\u0639\u0627\u062a \u0627\u0644\u0627\u062e\u062a\u0644\u0627\u0641\u0627\u062a \u0628\u064a\u0646 \u0646\u0642\u0627\u0637 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0627\u0644\u0645\u062a\u0648\u0642\u0639\u0629 (\u0177 <sub>i<\/sub> ) \u0648\u0645\u062a\u0648\u0633\u0637 \u0645\u062a\u063a\u064a\u0631 \u0627\u0644\u0627\u0633\u062a\u062c\u0627\u0628\u0629 ( <span style=\"border-top: 1px solid black;\">y<\/span> ).<\/span><\/p>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">SSR = \u03a3(\u0177 <sub>i<\/sub> &#8211; <span style=\"border-top: 1px solid black;\">y<\/span> ) <sup>2<\/sup><\/span><\/li>\n<\/ul>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\"><strong>3. \u0645\u062c\u0645\u0648\u0639 \u0645\u0631\u0628\u0639\u0627\u062a \u0627\u0644\u062e\u0637\u0623 (SSE)<\/strong> \u2013 \u0645\u062c\u0645\u0648\u0639 \u0645\u0631\u0628\u0639\u0627\u062a \u0627\u0644\u0627\u062e\u062a\u0644\u0627\u0641\u0627\u062a \u0628\u064a\u0646 \u0646\u0642\u0627\u0637 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0627\u0644\u0645\u062a\u0648\u0642\u0639\u0629 (\u0177 <sub>i<\/sub> ) \u0648\u0646\u0642\u0627\u0637 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0627\u0644\u0645\u0631\u0635\u0648\u062f\u0629 (y <sub>i<\/sub> ).<\/span><\/p>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">SSE = \u03a3(\u0177 <sub>i<\/sub> \u2013 y <sub>i<\/sub> ) <sup>2<\/sup><\/span><\/li>\n<\/ul>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">\u064a\u0648\u0636\u062d \u0627\u0644\u0645\u062b\u0627\u0644 \u0627\u0644\u062a\u0627\u0644\u064a \u062e\u0637\u0648\u0629 \u0628\u062e\u0637\u0648\u0629 \u0643\u064a\u0641\u064a\u0629 \u062d\u0633\u0627\u0628 \u0643\u0644 \u0645\u0646 \u0647\u0630\u0647 \u0627\u0644\u0645\u0642\u0627\u064a\u064a\u0633 \u0644\u0646\u0645\u0648\u0630\u062c \u0627\u0646\u062d\u062f\u0627\u0631 \u0645\u062d\u062f\u062f \u0641\u064a Python.<\/span><\/p>\n<h2 style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\"><strong>\u0627\u0644\u062e\u0637\u0648\u0629 1: \u0625\u0646\u0634\u0627\u0621 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a<\/strong><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">\u0623\u0648\u0644\u0627\u064b\u060c \u0644\u0646\u0642\u0645 \u0628\u0625\u0646\u0634\u0627\u0621 \u0645\u062c\u0645\u0648\u0639\u0629 \u0628\u064a\u0627\u0646\u0627\u062a \u062a\u062d\u062a\u0648\u064a \u0639\u0644\u0649 \u0639\u062f\u062f \u0633\u0627\u0639\u0627\u062a \u0627\u0644\u062f\u0631\u0627\u0633\u0629 \u0648\u062f\u0631\u062c\u0627\u062a \u0627\u0644\u0627\u0645\u062a\u062d\u0627\u0646\u0627\u062a \u0627\u0644\u062a\u064a \u062a\u0645 \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u064a\u0647\u0627 \u0644\u0640 20 \u0637\u0627\u0644\u0628\u064b\u0627 \u0645\u062e\u062a\u0644\u0641\u064b\u0627 \u0641\u064a \u062c\u0627\u0645\u0639\u0629 \u0645\u0639\u064a\u0646\u0629:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008000;\">import<\/span> pandas <span style=\"color: #008000;\">as<\/span> pd\n\n<span style=\"color: #008080;\">#create pandas DataFrame\n<\/span>df = pd. <span style=\"color: #3366ff;\">DataFrame<\/span> ({' <span style=\"color: #ff0000;\">hours<\/span> ': [1, 1, 1, 2, 2, 2, 2, 2, 3, 3,\n                             3, 4, 4, 4, 5, 5, 6, 7, 7, 8],\n                   ' <span style=\"color: #ff0000;\">score<\/span> ': [68, 76, 74, 80, 76, 78, 81, 84, 86, 83,\n                             88, 85, 89, 94, 93, 94, 96, 89, 92, 97]})\n\n<span style=\"color: #008080;\">#view first five rows of DataFrame\n<\/span>df. <span style=\"color: #3366ff;\">head<\/span> ()\n\n\thours score\n0 1 68\n1 1 76\n2 1 74\n3 2 80\n4 2 76\n<\/strong><\/pre>\n<h2 style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\"><strong>\u0627\u0644\u062e\u0637\u0648\u0629 2: \u062a\u0646\u0627\u0633\u0628 \u0646\u0645\u0648\u0630\u062c \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631<\/strong><\/span><\/h2>\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 <strong>OLS()<\/strong> \u0645\u0646 \u0645\u0643\u062a\u0628\u0629 <a href=\"https:\/\/www.statsmodels.org\/devel\/generated\/statsmodels.regression.linear_model.OLS.html\" target=\"_blank\" rel=\"noopener\">statsmodels<\/a> \u0644\u062a\u0646\u0627\u0633\u0628 \u0646\u0645\u0648\u0630\u062c \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u062e\u0637\u064a \u0627\u0644\u0628\u0633\u064a\u0637 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0646\u062a\u064a\u062c\u0629 \u0643\u0645\u062a\u063a\u064a\u0631 \u0627\u0644\u0627\u0633\u062a\u062c\u0627\u0628\u0629 \u0648\u0627\u0644\u0633\u0627\u0639\u0627\u062a \u0643\u0645\u062a\u063a\u064a\u0631 \u0645\u062a\u0648\u0642\u0639:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008000;\">import<\/span> statsmodels. <span style=\"color: #3366ff;\">api<\/span> <span style=\"color: #008000;\">as<\/span> sm\n\n<span style=\"color: #008080;\">#define response variable\n<\/span>y = df[' <span style=\"color: #ff0000;\">score<\/span> ']\n\n<span style=\"color: #008080;\">#define predictor variable\n<\/span>x = df[[' <span style=\"color: #ff0000;\">hours<\/span> ']]\n\n<span style=\"color: #008080;\">#add constant to predictor variables\n<\/span>x = sm. <span style=\"color: #3366ff;\">add_constant<\/span> (x)\n\n<span style=\"color: #008080;\">#fit linear regression model\n<\/span>model = sm. <span style=\"color: #3366ff;\">OLS<\/span> (y,x). <span style=\"color: #3366ff;\">fit<\/span> ()\n<\/strong><\/pre>\n<h2 style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\"><strong>\u0627\u0644\u062e\u0637\u0648\u0629 3: \u062d\u0633\u0627\u0628 SST\u060c SSR \u0648SSE<\/strong><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">\u0623\u062e\u064a\u0631\u064b\u0627\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0635\u064a\u063a \u0627\u0644\u062a\u0627\u0644\u064a\u0629 \u0644\u062d\u0633\u0627\u0628 \u0642\u064a\u0645 SST \u0648SSR \u0648SSE \u0644\u0644\u0646\u0645\u0648\u0630\u062c:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008000;\">import<\/span> numpy <span style=\"color: #008000;\">as<\/span> np\n\n<span style=\"color: #008080;\">#calculate\n<\/span>sse = np. <span style=\"color: #3366ff;\">sum<\/span> ((model. <span style=\"color: #3366ff;\">fitted values<\/span> - df. <span style=\"color: #3366ff;\">score<\/span> ) <span style=\"color: #800080;\">**<\/span> 2)\n<span style=\"color: #008000;\">print<\/span> (sse)\n\n331.07488479262696\n\n<span style=\"color: #008080;\">#calculate ssr\n<\/span>ssr = np. <span style=\"color: #3366ff;\">sum<\/span> ((model. <span style=\"color: #3366ff;\">fitted values<\/span> - df. <span style=\"color: #3366ff;\">score<\/span> . <span style=\"color: #3366ff;\">mean<\/span> ()) <span style=\"color: #800080;\">**<\/span> 2)\n<span style=\"color: #008000;\">print<\/span> (ssr)\n\n917.4751152073725\n\n<span style=\"color: #008080;\">#calculate sst\n<\/span>sst = ssr + sse\n<span style=\"color: #008000;\">print<\/span> (sst)\n\n1248.5499999999995\n<\/strong><\/pre>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">\u0627\u0644\u0645\u0642\u0627\u064a\u064a\u0633 \u062a\u062a\u062d\u0648\u0644 \u0625\u0644\u0649:<\/span><\/p>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\"><strong>\u0645\u062c\u0645\u0648\u0639 \u0627\u0644\u0645\u0631\u0628\u0639\u0627\u062a (SST):<\/strong> 1248.55<\/span><\/li>\n<li style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\"><strong>\u0645\u062c\u0645\u0648\u0639 \u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u0645\u0631\u0628\u0639\u0627\u062a (SSR):<\/strong> 917.4751<\/span><\/li>\n<li style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\"><strong>\u0645\u062c\u0645\u0648\u0639 \u0645\u0631\u0628\u0639\u0627\u062a \u0627\u0644\u062e\u0637\u0623 (SSE):<\/strong> 331.0749<\/span><\/li>\n<\/ul>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">\u064a\u0645\u0643\u0646\u0646\u0627 \u0627\u0644\u062a\u062d\u0642\u0642 \u0645\u0646 \u0623\u0646 SST = SSR + SSE:<\/span><\/p>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">\u0637\u0627\u0626\u0631\u0629 \u0623\u0633\u0631\u0639 \u0645\u0646 \u0627\u0644\u0635\u0648\u062a = SSR + SSE<\/span><\/li>\n<li style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">1248.55 = 917.4751 + 331.0749<\/span><\/li>\n<\/ul>\n<h2 style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\"><strong>\u0645\u0635\u0627\u062f\u0631 \u0625\u0636\u0627\u0641\u064a\u0629<\/strong><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">\u064a\u0645\u0643\u0646\u0643 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0622\u0644\u0627\u062a \u0627\u0644\u062d\u0627\u0633\u0628\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629 \u0644\u062d\u0633\u0627\u0628 SST \u0648SSR \u0648SSE \u062a\u0644\u0642\u0627\u0626\u064a\u064b\u0627 \u0644\u0623\u064a \u062e\u0637 \u0627\u0646\u062d\u062f\u0627\u0631 \u062e\u0637\u064a \u0628\u0633\u064a\u0637:<\/span><\/p>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> \u0622\u0644\u0629 \u062d\u0627\u0633\u0628\u0629 SST<\/li>\n<li style=\";text-align:right;direction:rtl\"> \u062d\u0627\u0633\u0628\u0629 \u0622\u0631 \u0625\u0633 \u0625\u0633<\/li>\n<li style=\";text-align:right;direction:rtl\"> \u062d\u0627\u0633\u0628\u0629 ESS<\/li>\n<\/ul>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">\u062a\u0634\u0631\u062d \u0627\u0644\u0628\u0631\u0627\u0645\u062c \u0627\u0644\u062a\u0639\u0644\u064a\u0645\u064a\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629 \u0643\u064a\u0641\u064a\u0629 \u062d\u0633\u0627\u0628 SST \u0648SSR \u0648SSE \u0641\u064a \u0628\u0631\u0627\u0645\u062c \u0625\u062d\u0635\u0627\u0626\u064a\u0629 \u0623\u062e\u0631\u0649:<\/span><\/p>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> <a href=\"https:\/\/statorials.org\/ar\/\u0637\u0627\u064a\u0654\u0631\u0629-\u0627\u0654\u0633\u0631\u0639-\u0645\u0646-\u0627\u0644\u0635\u0648\u062a-ssr-sse-\u0641\u064a-\u0635\/\" target=\"_blank\" rel=\"noopener\">\u0643\u064a\u0641\u064a\u0629 \u062d\u0633\u0627\u0628 SST \u0648SSR \u0648SSE \u0641\u064a R<\/a><\/li>\n<li style=\";text-align:right;direction:rtl\"> <a href=\"https:\/\/statorials.org\/ar\/sst-ssr-sse-\u0641\u064a-\u0627\u0644\u062a\u0641\u0648\u0642\/\" target=\"_blank\" rel=\"noopener\">\u0643\u064a\u0641\u064a\u0629 \u062d\u0633\u0627\u0628 SST\u060c SSR \u0648SSE \u0641\u064a Excel<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>\u063a\u0627\u0644\u0628\u064b\u0627 \u0645\u0627 \u0646\u0633\u062a\u062e\u062f\u0645 \u062b\u0644\u0627\u062b\u0629 \u0645\u062c\u0645\u0648\u0639\u0627\u062a \u0645\u062e\u062a\u0644\u0641\u0629 \u0645\u0646 \u0642\u064a\u0645 \u0627\u0644\u0645\u0631\u0628\u0639\u0627\u062a \u0644\u0642\u064a\u0627\u0633 \u0645\u062f\u0649 \u0645\u0644\u0627\u0621\u0645\u0629 \u062e\u0637 \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0644\u0645\u062c\u0645\u0648\u0639\u0629 \u0645\u0646 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a: 1. \u0645\u062c\u0645\u0648\u0639 \u0627\u0644\u0645\u0631\u0628\u0639\u0627\u062a \u0627\u0644\u0625\u062c\u0645\u0627\u0644\u064a\u0629 (SST) \u2013 \u0645\u062c\u0645\u0648\u0639 \u0645\u0631\u0628\u0639\u0627\u062a \u0627\u0644\u0627\u062e\u062a\u0644\u0627\u0641\u0627\u062a \u0628\u064a\u0646 \u0646\u0642\u0627\u0637 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0627\u0644\u0641\u0631\u062f\u064a\u0629 (y i ) \u0648\u0645\u062a\u0648\u0633\u0637 \u0645\u062a\u063a\u064a\u0631 \u0627\u0644\u0627\u0633\u062a\u062c\u0627\u0628\u0629 ( y ). \u062f\u0631\u062c\u0629 \u062d\u0631\u0627\u0631\u0629 \u0633\u0637\u062d \u0627\u0644\u0628\u062d\u0631 = \u03a3(\u0635 \u0637 \u2013 \u0630 ) 2 2. \u0627\u0646\u062d\u062f\u0627\u0631 \u0645\u062c\u0645\u0648\u0639 \u0627\u0644\u0645\u0631\u0628\u0639\u0627\u062a (SSR) [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u0643\u064a\u0641\u064a\u0629 \u062d\u0633\u0627\u0628 SST \u0648SSR \u0648SSE \u0641\u064a \u0628\u0627\u064a\u062b\u0648\u0646 - \u0639\u0644\u0645 \u0627\u0644\u0625\u062d\u0635\u0627\u0621<\/title>\n<meta name=\"description\" content=\"\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\u062c\u0627\u0645\u064a\u0639 \u0627\u0644\u0645\u0631\u0628\u0639\u0627\u062a \u0627\u0644\u0645\u062e\u062a\u0644\u0641\u0629 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