วิธีการประมาณค่าพารามิเตอร์ในตัวแบบการถดถอยเชิงเส้นพหุคูณเมื่อเกิดพหุสัมพันธ์ - วราภรณ์ บุญยไพศาลเจริญ (จุฬาลงกรณ์มหาวิทยาลัย, 2003)
The objective of this research is to compare multiple regression coefficients estimating methods when having multicollinearity among independent variables. The estimation methods are Principal Component Regression method (PC), Latent Root Regression method (LR) and Restricted Liu Estmator method (RL). The criterion of comparison is the average value of mean square error. This research used sample sizes 15, 20, 30, 40, 50, 60, 70, 80, 90 and 100. The random errors are independent and identically distributed normal with mean zero and standard deviation 1.0, 5.0 and 10.0, respectively. The level of correlations among independent variables X[subscript 1] and X[subscript 2] equal 0.10, 0.30, 0.50, 0.70, 0.80 and 0.90 for the number of independent variables of 3 (X[subscript 1], X[subscript 2] and X[subscript 3]) and are (0.10,0.30), (0.50,0.70) and (0.80,0.90) for correlations of (X[subscript 1] and X[subscript 2], X[subscript 4] and X[subscript 5]) for the number of independent variables of 5. The study used the Monte Carlo Simulation method. The experiment was repeated 1,000 times under each situations. The results of this research showed that level of correlations, sample sizes, number of independent variables and standard deviation have effect to multiple regression coefficients estimates. The average values of mean square error of multiple regression coefficients decreases when sample size increases but it increases when level of correlation or standard deviation increases or the number of dependence variables increases. In case of data are satisfy restriction. In every level of correlation every sample size, the average value of mean square error of Restricted Liu estimator method is smallest, except in the case of standard deviation is small (1.0), the average values of mean square error of the three methods are not different. In case of data are not satisfy restriction. In every level of correlation, sample size, standard deviation and number of independent variables. Principal Component Regression method is smallest average value of mean square error of multiple regression coefficients.