A NEW THEORY IN MULTIPLE LINEAR REGRESSION - Piña-Monarrez, Manuel Roman (International Journal of Industrial Engineering: Theory, Applications and Practice, 2011)
Concepts of the most common collinearity diagnostics (e.g. variance inflation factors (VIF), determinant (Det) and condition number (CI)), do not incorporate the possible relationship between the dependent and independent variable, so they neither check for omission variable bias nor for the effect that the correlation between the response variable and independent variable has over the estimated coefficients. In this paper a new approach for creating the above standard diagnostics in the case of dependent variables is proposed. The constructive computational relation is derived and a discussion of the effectiveness of the complete methodology is presented. The obtained results are applied to Ridge regression (RR) method through the derivation of formulas to estimate the value of k for a desired variance reduction. Finally, the and F statistics index were modified to reflect the advantages that RR has over OLS (in presence of collinearity).