Regression residuals and test statistics: Assessing naive outlier deletion

Abstract The authors derive the joint distributions of a studentized deleted residual and various regression quantities, calculated with all the data or with one case deleted. They show that the correlation between the studentized deleted residual and the deleted test statistic has an interesting interpretation in terms of well‐known regression quantities. These results allow them to examine the effect of applying some naive outlier deletion methods before making inferences about a regression parameter.