A Comparison between Least Squares and Adjusted Ridge Regression Methods with Application

In this paper, the problem of combating multicollinearity between predictor variables in multiple linear regression model has been studied. This treatment has been done by using the adjusted ridge regression which is suggested by Swindle (1976). This method depends on adding a vector of prior information about the vector of regression parameters  to the estimator proposed by (Hoerl & Kennard, 1970). We selected the vector of prior information to represent the average of Ordinary Least Squares estimator for  . The optimal value for ridge parameter that makes the mean square error of the adjusted estimator minimum has been selected. A comparison between the ordinary least squares and the adjusted estimators has been done. A Monte Carlo simulation is made for 15 predictor variables by choosing different sample sizes simple correlation coefficients,  and and we concluded that the adjusted estimators is better than the ordinary least squares estimators . .