Multicollinearity implies near-linear dependence among regressors and is one of the diagnostics that harms enough the quality and the estimation of the regression models. Among the effects of multicollinearity can be mentioned that parameter estimates could lead to opposite signs or the variables turn out to having insignificant coefficients although it is known from theory or reality that the relationship exists. Also, when other variables are included or removed from the model this can affect the parameter estimates. Usually, multicollinearity is measured with the help of Variance Inflation Factor. A value greater than ten indicates severe multicollinearity in the model. Different approaches are known to reduce or eliminate multicollinearity effects but some of them are not always applicable due to data. The most used methods include addition of more data or elimination of the variable that is highly correlated with other independent variables or the use of the Ridge Regression. In addition to the well known and used models it is proposed here a new approach for the multicollinearity reduction. This method implies creating an index variable as a linear combination of the highly correlated ones. The index coefficients are selected under specific constraints imposed on the variables such that the new variable becomes highly correlated with the response variable but not with the independent ones. The best coefficients can be chosen out of the solution domain using an optimization program. In the new model, the highly correlated variables are replaced by the index one. The quality of the new model is improved by reducing or even eliminating the effects of multicollinearity. The regression model is expected to yield proper estimates. Also, VIF returns appropriate values, lower than ten. The method is exemplified on the BRD stock portfolio. Multicollinearity was eliminated, as showed by a value of one of the VIF and the model is expected to improve.
