Ridge Estimation’s E�ectiveness for Multiple Linear Regression with Multicollinearity: An Investigation Using Monte-Carlo Simulations
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The goal of this research is to compare multiple linear regression coe�cient estimation technique with multicollinearity. In order to quantify
the e�ectiveness of estimations by the mean of average mean square error, the ordinary least squares technique (OLS), modified ridge regression
method (MRR), and generalized Liu-Kejian method (LKM) are compared with the Average Mean Square Error (AMSE). For this study, the
simulation scenarios are 3 and 5 independent variables with zero mean normally distributed random error of variance 1, 5, and 10, three correlation
coe�cient levels; i.e., low (0.2), medium (0.5), and high (0.8) are determined for independent variables, and all combinations are performed with
sample sizes 15, 55, and 95 by Monte Carlo simulation technique for 1,000 times in total. As the sample size rises, the AMSE decreased. The
MRR and LKM both outperformed the OLS. At random error of variance 10, the MRR is the most suitable for all circumstances
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QA Mathematics