{"id":3559,"date":"2023-07-16T20:16:40","date_gmt":"2023-07-16T20:16:40","guid":{"rendered":"https:\/\/statorials.org\/ar\/ols-%d8%a7%d9%84%d8%a7%d9%86%d8%ad%d8%af%d8%a7%d8%b1-%d8%a8%d9%8a%d8%ab%d9%88%d9%86\/"},"modified":"2023-07-16T20:16:40","modified_gmt":"2023-07-16T20:16:40","slug":"ols-%d8%a7%d9%84%d8%a7%d9%86%d8%ad%d8%af%d8%a7%d8%b1-%d8%a8%d9%8a%d8%ab%d9%88%d9%86","status":"publish","type":"post","link":"https:\/\/statorials.org\/ar\/ols-%d8%a7%d9%84%d8%a7%d9%86%d8%ad%d8%af%d8%a7%d8%b1-%d8%a8%d9%8a%d8%ab%d9%88%d9%86\/","title":{"rendered":"\u0643\u064a\u0641\u064a\u0629 \u062a\u0646\u0641\u064a\u0630 \u0627\u0646\u062d\u062f\u0627\u0631 ols \u0641\u064a \u0628\u0627\u064a\u062b\u0648\u0646 (\u0645\u0639 \u0645\u062b\u0627\u0644)"},"content":{"rendered":"<p><\/p>\n<hr>\n<p style=\";text-align:right;direction:rtl\"><span style=\"color: #000000;\">\u064a\u0639\u062f \u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u0645\u0631\u0628\u0639\u0627\u062a \u0627\u0644\u0635\u063a\u0631\u0649 \u0627\u0644\u0639\u0627\u062f\u064a\u0629 (OLS) \u0637\u0631\u064a\u0642\u0629 \u062a\u0633\u0645\u062d \u0644\u0646\u0627 \u0628\u0627\u0644\u0639\u062b\u0648\u0631 \u0639\u0644\u0649 \u0633\u0637\u0631 \u064a\u0635\u0641 \u0627\u0644\u0639\u0644\u0627\u0642\u0629 \u0628\u064a\u0646 \u0648\u0627\u062d\u062f \u0623\u0648 \u0623\u0643\u062b\u0631 \u0645\u0646 \u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0627\u0644\u062a\u0648\u0642\u0639 <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\">\u0648\u0645\u062a\u063a\u064a\u0631 \u0627\u0644\u0627\u0633\u062a\u062c\u0627\u0628\u0629<\/a> .<\/span><\/p>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">\u062a\u062a\u064a\u062d \u0644\u0646\u0627 \u0647\u0630\u0647 \u0627\u0644\u0637\u0631\u064a\u0642\u0629 \u0625\u064a\u062c\u0627\u062f \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629:<\/span><\/p>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\"><strong>\u0177 = \u0628 <sub>0<\/sub> + \u0628 <sub>1<\/sub> \u0633<\/strong><\/span><\/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>\u0177<\/strong> : \u0642\u064a\u0645\u0629 \u0627\u0644\u0627\u0633\u062a\u062c\u0627\u0628\u0629 \u0627\u0644\u0645\u0642\u062f\u0631\u0629<\/span><\/li>\n<li style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\"><strong>\u0628 <sub>0<\/sub><\/strong> : \u0623\u0635\u0644 \u062e\u0637 \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631<\/span><\/li>\n<li style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\"><strong>\u0628 <sub>1<\/sub><\/strong> : \u0645\u064a\u0644 \u062e\u0637 \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631<\/span><\/li>\n<\/ul>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">\u064a\u0645\u0643\u0646 \u0623\u0646 \u062a\u0633\u0627\u0639\u062f\u0646\u0627 \u0647\u0630\u0647 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0641\u064a \u0641\u0647\u0645 \u0627\u0644\u0639\u0644\u0627\u0642\u0629 \u0628\u064a\u0646 \u0627\u0644\u0645\u062a\u0646\u0628\u0626 \u0648\u0645\u062a\u063a\u064a\u0631 \u0627\u0644\u0627\u0633\u062a\u062c\u0627\u0628\u0629\u060c \u0648\u064a\u0645\u0643\u0646 \u0627\u0633\u062a\u062e\u062f\u0627\u0645\u0647\u0627 \u0644\u0644\u062a\u0646\u0628\u0624 \u0628\u0642\u064a\u0645\u0629 \u0645\u062a\u063a\u064a\u0631 \u0627\u0644\u0627\u0633\u062a\u062c\u0627\u0628\u0629 \u0628\u0645\u0639\u0644\u0648\u0645\u064a\u0629 \u0642\u064a\u0645\u0629 \u0627\u0644\u0645\u062a\u063a\u064a\u0631 \u0627\u0644\u0645\u062a\u0646\u0628\u0626.<\/span><\/p>\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 \u0625\u062c\u0631\u0627\u0621 \u0627\u0646\u062d\u062f\u0627\u0631 OLS \u0641\u064a Python.<\/span><\/p>\n<h2 style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\"><b>\u0627\u0644\u062e\u0637\u0648\u0629 1: \u0625\u0646\u0634\u0627\u0621 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a<\/b><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">\u0641\u064a \u0647\u0630\u0627 \u0627\u0644\u0645\u062b\u0627\u0644\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\u062d\u062a\u0648\u064a \u0639\u0644\u0649 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u064a\u0646 \u0627\u0644\u062a\u0627\u0644\u064a\u064a\u0646 \u0644\u0640 15 \u0637\u0627\u0644\u0628\u064b\u0627:<\/span><\/p>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">\u0625\u062c\u0645\u0627\u0644\u064a \u0639\u062f\u062f \u0627\u0644\u0633\u0627\u0639\u0627\u062a \u0627\u0644\u0645\u062f\u0631\u0648\u0633\u0629<\/span><\/li>\n<li style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">\u0646\u062a\u064a\u062c\u0629 \u0627\u0644\u0625\u0645\u062a\u062d\u0627\u0646<\/span><\/li>\n<\/ul>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">\u0633\u0646\u0642\u0648\u0645 \u0628\u0625\u062c\u0631\u0627\u0621 \u0627\u0646\u062d\u062f\u0627\u0631 OLS\u060c \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0633\u0627\u0639\u0627\u062a \u0643\u0645\u062a\u063a\u064a\u0631 \u0645\u062a\u0648\u0642\u0639 \u0648\u062f\u0631\u062c\u0629 \u0627\u0644\u0627\u0645\u062a\u062d\u0627\u0646 \u0643\u0645\u062a\u063a\u064a\u0631 \u0627\u0644\u0627\u0633\u062a\u062c\u0627\u0628\u0629.<\/span><\/p>\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 \u0625\u0646\u0634\u0627\u0621 \u0645\u062c\u0645\u0648\u0639\u0629 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0627\u0644\u0645\u0632\u064a\u0641\u0629 \u0647\u0630\u0647 \u0641\u064a \u0627\u0644\u0628\u0627\u0646\u062f\u0627:<\/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<span style=\"color: #008080;\">\n#createDataFrame<\/span>\ndf = pd. <span style=\"color: #3366ff;\">DataFrame<\/span> ({' <span style=\"color: #ff0000;\">hours<\/span> ': [1, 2, 4, 5, 5, 6, 6, 7, 8, 10, 11, 11, 12, 12, 14],\n                   ' <span style=\"color: #ff0000;\">score<\/span> ': [64, 66, 76, 73, 74, 81, 83, 82, 80, 88, 84, 82, 91, 93, 89]})\n\n<span style=\"color: #008080;\">#view DataFrame\n<\/span><span style=\"color: #008000;\">print<\/span> (df)\n\n    hours score\n0 1 64\n1 2 66\n2 4 76\n3 5 73\n4 5 74\n5 6 81\n6 6 83\n7 7 82\n8 8 80\n9 10 88\n10 11 84\n11 11 82\n12 12 91\n13 12 93\n14 14 89<\/strong><\/pre>\n<h2 style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\"><b>\u0627\u0644\u062e\u0637\u0648\u0629 2: \u0625\u062c\u0631\u0627\u0621 \u0627\u0646\u062d\u062f\u0627\u0631 OLS<\/b><\/span><\/h2>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">\u0628\u0639\u062f \u0630\u0644\u0643\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0648\u0638\u0627\u0626\u0641 \u0627\u0644\u0645\u0648\u062c\u0648\u062f\u0629 \u0641\u064a \u0648\u062d\u062f\u0629 <a href=\"https:\/\/www.statsmodels.org\/stable\/index.html\" target=\"_blank\" rel=\"noopener\">statsmodels<\/a> \u0644\u0625\u062c\u0631\u0627\u0621 \u0627\u0646\u062d\u062f\u0627\u0631 OLS\u060c \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 <strong>\u0627\u0644\u0633\u0627\u0639\u0627\u062a<\/strong> \u0643\u0645\u062a\u063a\u064a\u0631 \u0645\u062a\u0648\u0642\u0639 \u0648\u0627\u0644\u0646\u062a\u064a\u062c\u0629 \u0643\u0645\u062a\u063a\u064a\u0631 <strong>\u0627\u0644\u0627\u0633\u062a\u062c\u0627\u0628\u0629<\/strong> :<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\"><span style=\"color: #000000;\"><span style=\"color: #008000;\">import<\/span> statsmodels.api <span style=\"color: #008000;\">as<\/span> sm\n<\/span>\n#define predictor and response variables\n<span style=\"color: #000000;\">y = df[' <span style=\"color: #ff0000;\">score<\/span> ']\nx = df[' <span style=\"color: #ff0000;\">hours<\/span> ']<\/span>\n\n#add constant to predictor variables\n<span style=\"color: #000000;\">x = sm. <span style=\"color: #3366ff;\">add_constant<\/span> (x)\n<\/span>\n#fit linear regression model\n<span style=\"color: #000000;\">model = sm. <span style=\"color: #3366ff;\">OLS<\/span> (y,x). <span style=\"color: #3366ff;\">fit<\/span> ()\n<\/span>\n#view model summary\n<span style=\"color: #000000;\"><span style=\"color: #008000;\">print<\/span> ( <span style=\"color: #3366ff;\">model.summary<\/span> ())\n\n                            OLS Regression Results                            \n==================================================== ============================\nDept. Variable: R-squared score: 0.831\nModel: OLS Adj. R-squared: 0.818\nMethod: Least Squares F-statistic: 63.91\nDate: Fri, 26 Aug 2022 Prob (F-statistic): 2.25e-06\nTime: 10:42:24 Log-Likelihood: -39,594\nNo. Observations: 15 AIC: 83.19\nDf Residuals: 13 BIC: 84.60\nModel: 1                                         \nCovariance Type: non-robust                                         \n==================================================== ============================\n                 coef std err t P&gt;|t| [0.025 0.975]\n-------------------------------------------------- ----------------------------\nconst 65.3340 2.106 31.023 0.000 60.784 69.884\nhours 1.9824 0.248 7.995 0.000 1.447 2.518\n==================================================== ============================\nOmnibus: 4,351 Durbin-Watson: 1,677\nProb(Omnibus): 0.114 Jarque-Bera (JB): 1.329\nSkew: 0.092 Prob(JB): 0.515\nKurtosis: 1.554 Cond. No. 19.2\n==================================================== ============================<\/span><\/span><\/strong><\/pre>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">\u0645\u0646 \u0639\u0645\u0648\u062f <strong>coef<\/strong> \u064a\u0645\u0643\u0646\u0646\u0627 \u0631\u0624\u064a\u0629 \u0645\u0639\u0627\u0645\u0644\u0627\u062a \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0648\u0643\u062a\u0627\u0628\u0629 \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u0645\u062c\u0647\u0632\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629:<\/span><\/p>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\"><strong>\u0627\u0644\u0646\u062a\u064a\u062c\u0629 = 65.334 + 1.9824*(\u0633\u0627\u0639\u0627\u062a)<\/strong><\/span><\/p>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">\u0648\u0647\u0630\u0627 \u064a\u0639\u0646\u064a \u0623\u0646 \u0643\u0644 \u0633\u0627\u0639\u0629 \u0625\u0636\u0627\u0641\u064a\u0629 \u062a\u062a\u0645 \u062f\u0631\u0627\u0633\u062a\u0647\u0627 \u062a\u0631\u062a\u0628\u0637 \u0628\u0632\u064a\u0627\u062f\u0629 \u0641\u064a \u0645\u062a\u0648\u0633\u0637 \u062f\u0631\u062c\u0627\u062a \u0627\u0644\u0627\u0645\u062a\u062d\u0627\u0646 \u0628\u0645\u0642\u062f\u0627\u0631 <strong>1.9824<\/strong> \u0646\u0642\u0637\u0629.<\/span><\/p>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">\u062a\u062e\u0628\u0631\u0646\u0627 \u0627\u0644\u0642\u064a\u0645\u0629 \u0627\u0644\u0623\u0635\u0644\u064a\u0629 \u0627\u0644\u0628\u0627\u0644\u063a\u0629 <strong>65,334<\/strong> \u0628\u0645\u062a\u0648\u0633\u0637 \u062f\u0631\u062c\u0627\u062a \u0627\u0644\u0627\u062e\u062a\u0628\u0627\u0631 \u0627\u0644\u0645\u062a\u0648\u0642\u0639\u0629 \u0644\u0644\u0637\u0627\u0644\u0628 \u0627\u0644\u0630\u064a \u064a\u062f\u0631\u0633 \u0644\u0645\u062f\u0629 \u0635\u0641\u0631 \u0633\u0627\u0639\u0629.<\/span><\/p>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">\u064a\u0645\u0643\u0646\u0646\u0627 \u0623\u064a\u0636\u064b\u0627 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0647\u0630\u0647 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0644\u0644\u0639\u062b\u0648\u0631 \u0639\u0644\u0649 \u062f\u0631\u062c\u0629 \u0627\u0644\u0627\u0645\u062a\u062d\u0627\u0646 \u0627\u0644\u0645\u062a\u0648\u0642\u0639\u0629 \u0628\u0646\u0627\u0621\u064b \u0639\u0644\u0649 \u0639\u062f\u062f \u0627\u0644\u0633\u0627\u0639\u0627\u062a \u0627\u0644\u062a\u064a \u064a\u062f\u0631\u0633\u0647\u0627 \u0627\u0644\u0637\u0627\u0644\u0628.<\/span><\/p>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">\u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644\u060c \u0627\u0644\u0637\u0627\u0644\u0628 \u0627\u0644\u0630\u064a \u064a\u062f\u0631\u0633 \u0644\u0645\u062f\u0629 10 \u0633\u0627\u0639\u0627\u062a \u064a\u062c\u0628 \u0623\u0646 \u064a\u062d\u0642\u0642 \u062f\u0631\u062c\u0629 \u0627\u0644\u0627\u0645\u062a\u062d\u0627\u0646 <strong>85.158<\/strong> :<\/span><\/p>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\"><strong>\u0627\u0644\u0646\u062a\u064a\u062c\u0629 = 65.334 + 1.9824*(10) = 85.158<\/strong><\/span><\/p>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">\u0641\u064a\u0645\u0627 \u064a\u0644\u064a \u0643\u064a\u0641\u064a\u0629 \u062a\u0641\u0633\u064a\u0631 \u0628\u0642\u064a\u0629 \u0645\u0644\u062e\u0635 \u0627\u0644\u0646\u0645\u0648\u0630\u062c:<\/span><\/p>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\"><strong>P(&gt;|t|):<\/strong> \u0647\u0630\u0647 \u0647\u064a \u0627\u0644\u0642\u064a\u0645\u0629 p \u0627\u0644\u0645\u0631\u062a\u0628\u0637\u0629 \u0628\u0645\u0639\u0627\u0645\u0644\u0627\u062a \u0627\u0644\u0646\u0645\u0648\u0630\u062c. \u0648\u0628\u0645\u0627 \u0623\u0646 \u0627\u0644\u0642\u064a\u0645\u0629 p <em>\u0644\u0644\u0633\u0627\u0639\u0627\u062a<\/em> (0.000) \u0623\u0642\u0644 \u0645\u0646 0.05\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u0627\u0644\u0642\u0648\u0644 \u0623\u0646 \u0647\u0646\u0627\u0643 \u0639\u0644\u0627\u0642\u0629 \u0630\u0627\u062a \u062f\u0644\u0627\u0644\u0629 \u0625\u062d\u0635\u0627\u0626\u064a\u0629 \u0628\u064a\u0646 <em>\u0627\u0644\u0633\u0627\u0639\u0627\u062a<\/em> <em>\u0648\u0627\u0644\u0646\u062a\u064a\u062c\u0629<\/em> .<\/span><\/li>\n<li style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\"><strong>R-squared:<\/strong> \u064a\u062e\u0628\u0631\u0646\u0627 \u0647\u0630\u0627 \u0623\u0646 \u0646\u0633\u0628\u0629 \u0627\u0644\u062a\u0628\u0627\u064a\u0646 \u0641\u064a \u062f\u0631\u062c\u0627\u062a \u0627\u0644\u0627\u0645\u062a\u062d\u0627\u0646 \u064a\u0645\u0643\u0646 \u062a\u0641\u0633\u064a\u0631\u0647\u0627 \u0628\u0639\u062f\u062f \u0627\u0644\u0633\u0627\u0639\u0627\u062a \u0627\u0644\u0645\u062f\u0631\u0648\u0633\u0629. \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0627\u0644\u0629\u060c \u064a\u0645\u0643\u0646 \u062a\u0641\u0633\u064a\u0631 <strong>83.1%<\/strong> \u0645\u0646 \u0627\u0644\u062a\u0628\u0627\u064a\u0646 \u0641\u064a \u0627\u0644\u062f\u0631\u062c\u0627\u062a \u0645\u0646 \u062e\u0644\u0627\u0644 \u0633\u0627\u0639\u0627\u062a \u0627\u0644\u062f\u0631\u0627\u0633\u0629.<\/span><\/li>\n<li style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\"><strong>\u0625\u062d\u0635\u0627\u0626\u064a\u0629 F \u0648\u0642\u064a\u0645\u0629 p:<\/strong> \u062a\u062e\u0628\u0631\u0646\u0627 \u0625\u062d\u0635\u0627\u0626\u064a\u0629 F ( <strong>63.91<\/strong> ) \u0648\u0627\u0644\u0642\u064a\u0645\u0629 p \u0627\u0644\u0645\u0642\u0627\u0628\u0644\u0629 \u0644\u0647\u0627 ( <strong>2.25e-06<\/strong> ) \u0628\u0627\u0644\u0623\u0647\u0645\u064a\u0629 \u0627\u0644\u0625\u062c\u0645\u0627\u0644\u064a\u0629 \u0644\u0646\u0645\u0648\u0630\u062c \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631\u060c \u0623\u064a \u0645\u0627 \u0625\u0630\u0627 \u0643\u0627\u0646\u062a \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0627\u0644\u0645\u062a\u0648\u0642\u0639\u0629 \u0641\u064a \u0627\u0644\u0646\u0645\u0648\u0630\u062c \u0645\u0641\u064a\u062f\u0629 \u0641\u064a \u062a\u0641\u0633\u064a\u0631 \u0627\u0644\u062a\u0628\u0627\u064a\u0646. \u0641\u064a \u0645\u062a\u063a\u064a\u0631 \u0627\u0644\u0627\u0633\u062a\u062c\u0627\u0628\u0629 \u0646\u0638\u0631\u064b\u0627 \u0644\u0623\u0646 \u0627\u0644\u0642\u064a\u0645\u0629 p \u0641\u064a \u0647\u0630\u0627 \u0627\u0644\u0645\u062b\u0627\u0644 \u0623\u0642\u0644 \u0645\u0646 0.05\u060c \u0641\u0625\u0646 \u0646\u0645\u0648\u0630\u062c\u0646\u0627 \u0630\u0648 \u062f\u0644\u0627\u0644\u0629 \u0625\u062d\u0635\u0627\u0626\u064a\u0629 \u0648\u062a\u0639\u062a\u0628\u0631 <em>\u0627\u0644\u0633\u0627\u0639\u0627\u062a<\/em> \u0645\u0641\u064a\u062f\u0629 \u0641\u064a \u0634\u0631\u062d \u062a\u0628\u0627\u064a\u0646 <em>\u0627\u0644\u0646\u062a\u064a\u062c\u0629<\/em> .<\/span><\/li>\n<\/ul>\n<h2 style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\"><strong>\u0627\u0644\u062e\u0637\u0648\u0629 3: \u062a\u0635\u0648\u0631 \u0627\u0644\u062e\u0637 \u0627\u0644\u0623\u0646\u0633\u0628<\/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 \u062d\u0632\u0645\u0629 \u062a\u0635\u0648\u0631 \u0628\u064a\u0627\u0646\u0627\u062a <strong>matplotlib<\/strong> \u0644\u062a\u0635\u0648\u0631 \u062e\u0637 \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u0645\u0644\u0627\u0626\u0645 \u0644\u0646\u0642\u0627\u0637 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0627\u0644\u0641\u0639\u0644\u064a\u0629:<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\"><span style=\"color: #000000;\"><span style=\"color: #008000;\">import<\/span> matplotlib. <span style=\"color: #3366ff;\">pyplot<\/span> <span style=\"color: #008000;\">as<\/span> plt\n<\/span>\n#find line of best fit\n<span style=\"color: #000000;\">a, b = np. <span style=\"color: #3366ff;\">polyfit<\/span> (df[' <span style=\"color: #ff0000;\">hours<\/span> '], df[' <span style=\"color: #ff0000;\">score<\/span> '], <span style=\"color: #008000;\">1<\/span> )\n<\/span>\n#add points to plot\n<span style=\"color: #000000;\">plt. <span style=\"color: #3366ff;\">scatter<\/span> (df[' <span style=\"color: #ff0000;\">hours<\/span> '], df[' <span style=\"color: #ff0000;\">score<\/span> '], color=' <span style=\"color: #ff0000;\">purple<\/span> ')\n<\/span>\n#add line of best fit to plot\n<span style=\"color: #000000;\">plt. <span style=\"color: #3366ff;\">plot<\/span> (df[' <span style=\"color: #ff0000;\">hours<\/span> '], a*df[' <span style=\"color: #ff0000;\">hours<\/span> ']+b)\n<\/span>\n#add fitted regression equation to plot\n<span style=\"color: #000000;\">plt. <span style=\"color: #3366ff;\">text<\/span> ( <span style=\"color: #008000;\">1<\/span> , <span style=\"color: #008000;\">90<\/span> , 'y = ' + '{:.3f}'.format(b) + ' + {:.3f}'.format(a) + 'x', size= <span style=\"color: #008000;\">12<\/span> )\n\n<span style=\"color: #008080;\">#add axis labels\n<\/span>plt. <span style=\"color: #3366ff;\">xlabel<\/span> (' <span style=\"color: #ff0000;\">Hours Studied<\/span> ')\nplt. <span style=\"color: #3366ff;\">ylabel<\/span> (' <span style=\"color: #ff0000;\">Exam Score<\/span> ')\n<\/span><\/span><\/strong><\/pre>\n<p style=\";text-align:right;direction:rtl\"><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-29456 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/ligne11.jpg\" alt=\"\" width=\"502\" height=\"385\" srcset=\"\" sizes=\"\"><\/p>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">\u062a\u0645\u062b\u0644 \u0627\u0644\u0646\u0642\u0627\u0637 \u0627\u0644\u0623\u0631\u062c\u0648\u0627\u0646\u064a\u0629 \u0646\u0642\u0627\u0637 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0627\u0644\u0641\u0639\u0644\u064a\u0629 \u0648\u064a\u0645\u062b\u0644 \u0627\u0644\u062e\u0637 \u0627\u0644\u0623\u0632\u0631\u0642 \u062e\u0637 \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u0645\u062c\u0647\u0632.<\/span><\/p>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">\u0627\u0633\u062a\u062e\u062f\u0645\u0646\u0627 \u0623\u064a\u0636\u064b\u0627 \u0627\u0644\u062f\u0627\u0644\u0629 <strong>plt.text()<\/strong> \u0644\u0625\u0636\u0627\u0641\u0629 \u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u0645\u062c\u0647\u0632\u0629 \u0625\u0644\u0649 \u0627\u0644\u0632\u0627\u0648\u064a\u0629 \u0627\u0644\u064a\u0633\u0631\u0649 \u0627\u0644\u0639\u0644\u064a\u0627 \u0645\u0646 \u0627\u0644\u0645\u062e\u0637\u0637.<\/span><\/p>\n<p style=\";text-align:right;direction:rtl\"> <span style=\"color: #000000;\">\u0648\u0628\u0627\u0644\u0646\u0638\u0631 \u0625\u0644\u0649 \u0627\u0644\u0631\u0633\u0645 \u0627\u0644\u0628\u064a\u0627\u0646\u064a\u060c \u064a\u0628\u062f\u0648 \u0623\u0646 \u062e\u0637 \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u0645\u0644\u0627\u0626\u0645 \u064a\u062c\u0633\u062f \u0627\u0644\u0639\u0644\u0627\u0642\u0629 \u0628\u064a\u0646 \u0645\u062a\u063a\u064a\u0631 <strong>\u0627\u0644\u0633\u0627\u0639\u0627\u062a<\/strong> \u0648\u0645\u062a\u063a\u064a\u0631 <strong>\u0627\u0644\u0646\u062a\u064a\u062c\u0629<\/strong> \u0628\u0634\u0643\u0644 \u062c\u064a\u062f.<\/span><\/p>\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;\">\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 \u062a\u0646\u0641\u064a\u0630 \u0627\u0644\u0645\u0647\u0627\u0645 \u0627\u0644\u0634\u0627\u0626\u0639\u0629 \u0627\u0644\u0623\u062e\u0631\u0649 \u0641\u064a \u0628\u0627\u064a\u062b\u0648\u0646:<\/span><\/p>\n<p style=\";text-align:right;direction:rtl\"> <a href=\"https:\/\/statorials.org\/ar\/\u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631-\u0627\u0644\u0644\u0648\u062c\u0633\u062a\u064a-\u0628\u064a\u062b\u0648\u0646\/\" target=\"_blank\" rel=\"noopener\">\u0643\u064a\u0641\u064a\u0629 \u062a\u0646\u0641\u064a\u0630 \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u0644\u0648\u062c\u0633\u062a\u064a \u0641\u064a \u0628\u0627\u064a\u062b\u0648\u0646<\/a><br \/> <a href=\"https:\/\/statorials.org\/ar\/\u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631-\u0627\u0644\u0627\u0654\u0633\u064a-\u0628\u064a\u062b\u0648\u0646\/\" target=\"_blank\" rel=\"noopener\">\u0643\u064a\u0641\u064a\u0629 \u062a\u0646\u0641\u064a\u0630 \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u0623\u0633\u064a \u0641\u064a \u0628\u0627\u064a\u062b\u0648\u0646<\/a><br \/> <a href=\"https:\/\/statorials.org\/ar\/aic-\u0641\u064a-\u0628\u064a\u062b\u0648\u0646\/\" target=\"_blank\" rel=\"noopener\">\u0643\u064a\u0641\u064a\u0629 \u062d\u0633\u0627\u0628 AIC \u0644\u0646\u0645\u0627\u0630\u062c \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0641\u064a \u0628\u0627\u064a\u062b\u0648\u0646<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u064a\u0639\u062f \u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u0645\u0631\u0628\u0639\u0627\u062a \u0627\u0644\u0635\u063a\u0631\u0649 \u0627\u0644\u0639\u0627\u062f\u064a\u0629 (OLS) \u0637\u0631\u064a\u0642\u0629 \u062a\u0633\u0645\u062d \u0644\u0646\u0627 \u0628\u0627\u0644\u0639\u062b\u0648\u0631 \u0639\u0644\u0649 \u0633\u0637\u0631 \u064a\u0635\u0641 \u0627\u0644\u0639\u0644\u0627\u0642\u0629 \u0628\u064a\u0646 \u0648\u0627\u062d\u062f \u0623\u0648 \u0623\u0643\u062b\u0631 \u0645\u0646 \u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0627\u0644\u062a\u0648\u0642\u0639 \u0648\u0645\u062a\u063a\u064a\u0631 \u0627\u0644\u0627\u0633\u062a\u062c\u0627\u0628\u0629 . \u062a\u062a\u064a\u062d \u0644\u0646\u0627 \u0647\u0630\u0647 \u0627\u0644\u0637\u0631\u064a\u0642\u0629 \u0625\u064a\u062c\u0627\u062f \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629: \u0177 = \u0628 0 + \u0628 1 \u0633 \u0630\u0647\u0628: \u0177 : \u0642\u064a\u0645\u0629 \u0627\u0644\u0627\u0633\u062a\u062c\u0627\u0628\u0629 \u0627\u0644\u0645\u0642\u062f\u0631\u0629 \u0628 0 : \u0623\u0635\u0644 \u062e\u0637 \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0628 1 : \u0645\u064a\u0644 [&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 \u062a\u0646\u0641\u064a\u0630 \u0627\u0646\u062d\u062f\u0627\u0631 OLS \u0641\u064a \u0628\u0627\u064a\u062b\u0648\u0646 (\u0645\u0639 \u0645\u062b\u0627\u0644) - \u0639\u0644\u0645 \u0627\u0644\u0625\u062d\u0635\u0627\u0621<\/title>\n<meta name=\"description\" content=\"\u064a\u0642\u062f\u0645 \u0647\u0630\u0627 \u0627\u0644\u0628\u0631\u0646\u0627\u0645\u062c \u0627\u0644\u062a\u0639\u0644\u064a\u0645\u064a \u0645\u062b\u0627\u0644\u0627\u064b \u062e\u0637\u0648\u0629 \u0628\u062e\u0637\u0648\u0629 \u0644\u0643\u064a\u0641\u064a\u0629 \u062a\u0646\u0641\u064a\u0630 \u0627\u0646\u062d\u062f\u0627\u0631 \u0627\u0644\u0645\u0631\u0628\u0639\u0627\u062a \u0627\u0644\u0635\u063a\u0631\u0649 \u0627\u0644\u0639\u0627\u062f\u064a\u0629 (OLS) \u0641\u064a \u0628\u0627\u064a\u062b\u0648\u0646.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/statorials.org\/ar\/ols-\u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631-\u0628\u064a\u062b\u0648\u0646\/\" \/>\n<meta property=\"og:locale\" content=\"az_AZ\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u0643\u064a\u0641\u064a\u0629 \u062a\u0646\u0641\u064a\u0630 \u0627\u0646\u062d\u062f\u0627\u0631 OLS \u0641\u064a \u0628\u0627\u064a\u062b\u0648\u0646 (\u0645\u0639 \u0645\u062b\u0627\u0644) - \u0639\u0644\u0645 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