Controlling overestimation of the regression coefficients in nonorthogonal linear models

Abstract

Dealing with nonorthogonal problems, overestimation of the regression coefficients may be caused either by the presence of correlated variables or by the nature of the X'X matrix which may be near singular itself. Adding small values to the diagonal elements of the correlation matrix seems to control satisfactorily this inflation without losing too much precision. The coefficients obtained from the new pertubed system are slightly biased, however, their values tend to be closer to their actual values.