Two Strategies for Removing Multicollinearity

In this paper, two procedures are introduced in multiple linear regression model to deal with multicollinearity: one when variables can be selected and the other when all variables must be included. Nevertheless, both these cases remove multicollinearity. This is the main result of this paper. We use the relation between the correlation matrix (R) and the variance inflation factor( VIF) for detecting multicollinearity and also for selecting variables. The first procedure does not require fitting regression of one explanatory variable on the others for computing the VIF. The second procedure replaces an explanatory variable by the residual from its regression on other explanatory variables. As a result, the final model is without multicollinearity. The performance of these procedures is compared with some recently developed methods. Three examples are used to illustrate these procedures.