Revisiting the Collinear Data Problem: An Assessment of Estimator ‘Ill-Conditioning’ in Linear Regression

Linear regression has gained widespread popularity in the social sciences. However, many applications of linear regression have been in situations in which the model data are collinear or ‘ill-conditioned.’ Collinearity renders regression estimates with inflated standard errors. In this paper, we present a method for precisely identifying coefficient estimates that are ill-conditioned, as well as those that are not involved, or only marginally involved in a linear dependency. Diagnostic tools are presented for a hypothetical regression model with ordinary least squares (OLS). It is hoped that practicing researchers will more readily incorporate these diagnostics into their analyses.