Revisiting the Collinear Data Problem: An Assessment of Estimator 'Ill-Conditioning' in Linear Regression - Practical Assessment, Research & Evaluation

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.