Multiple linear regression with correlations among the predictor variables. Theory and computer algorithm ridge (FORTRAN 77)

Abstract

Application of ridge regression in geoscience usually is a more appropriate technique than ordinary least-squares regression, especially in the situation of highly intercorrelated predictor variables. A FORTRAN 77 program RIDGE for ridged multiple linear regression is presented. The theory of linear regression and ridge regression is treated, to allow for a careful interpretation of the results and to understand the structure of the program. The program gives various parameters to evaluate the extent of multicollinearity within a given regression problem, such as the correlation matrix, multiple correlations among the predictors, variance inflation factors, eigenvalues, condition number, and the determinant of the predictors correlation matrix. The best method for the optimum choice of the ridge parameter with ridge regression has not been established yet. Estimates of the ridge bias, ridged variance inflation factors, estimates, and norms for the ridge parameter therefore are given as output by RIDGE and should complement inspection of the ridge traces. Application within the earth sciences is discussed.