Principal components in the problem of multicollineartity

ABSTRACT In this study, principal components regression and ridge regression are examined among the methods used to remedy multicollinearity problem in multiple linear regression model. One of the assumptions in multiple linear regression is that there must be no perfect linear relations among the regressors. The relationship among the regressors is called multicollinearity. In case of multicollinearity, parameter estimations by least square method have large variances and hypothesis tests result in contradictory. There are various methods for dealing with multicollinearity problem. Biased regression methods (BRM) are the ones that can explain the structure of multicollinearity and provide small standard errors among the methods used. In this study two of biased regression methods; principal components regression and ridge regression are examined as theoretically and researched which methods give the best consequence by simulation. In the application, 50 repetitions have been generated for each of the sample sizes of 40, 80 and 120. Least squares, ridge and principal components regression are used for each sample. Regression coefficients for each estimator were computed and the mean and the standard deviation of the estimates were used as statistical comparison criteria. According to comparisons among the estimators the principal components regression has been found to provide better estimates.