The impact of collinearity on regression analysis: the asymmetric effect of negative and positive correlations

The purpose of this paper is to ascertain how collinearity in general, and the sign of correlations in specific, affect parameter inference, variable omission bias, and their diagnostic indices in regression. It is found that collinearity can reduce parameter variance estimates and that positive and negative correlation structures have an asymmetric effect on variable omission bias. It is also shown that the effects of collinearity are moderated by the relationship between the dependent variable and the regressors, a consideration not incorporated into most commonly used collinearity diagnostics. The formulae derived enable researchers to assess the sensitivity of regression results to the underlying correlation structure in the data.