Best (but oft-forgotten) practices: Checking assumptions concerning regression residuals1,2

Abstract

The residuals of a least squares regression model are defined as the observations minus the modeled values. For least squares regression to produce valid CIs and P values, the residuals must be independent, be normally distributed, and have a constant variance. If these assumptions are not satisfied, estimates can be biased and power can be reduced. However, there are ways to assess these assumptions and steps one can take if the assumptions are violated. Here, we discuss both assessment and appropriate responses to violation of assumptions.