Comparison Between the Two Methods of Ridge Regression and Principal Components Regression Using the Monte Carlo Simulation by MSE

Abstract

In the multiple linear regression model the regression variables are supposed to be independent with each other when the regression variables are non-independent of each other and there is a linear relationship which renders the model inappropriate and therefore the results may be inaccurate, so two regression methods Biased: the method of Ridge regression and the method of Principal Components regression to obtain more accurate results. In this research the monte Carlo simulation was used to evaluate the performance of both the method of Ridge regression and the method of Principal component in the case of the problem of linear multiplicity, the mean squares error were used as the criterion for determining the best performance methods. The research found that the method of Ridge regression a better performance than the method of Principal Components regression in the case of the problem of linear multiplicity, the results of the comparison between different RR methods showed that the K_GM method was the best performance at the level of correlation (0.09 , 0.25 , 0.94) and the research concluded that the way K_AM performed better at the level of correlation (0.16) while provided K_HKB better performance at correlation level (0.49) and K_DK was the best at correlation level (0.81) and found that the K_KS method provided the best performance at correlation level (0.98).