Regression: Determining Which of p Independent Variables Has the Largest or Smallest Correlation With the Dependent Variable, Plus Results on Ordering the Correlations Winsorized

Abstract

In a regression context, consider p independent variables and a single dependent variable. The paper addresses two goals. The first is to determine the extent it is reasonable to make a decision about whether the largest estimate of the Winsorized correlations corresponds to the independent variable that has the largest population Winsorized correlation. The second is to determine the extent it is reasonable to decide that the order of the estimates of the Winsorized correlations correctly reflects the true ordering. Both goals are addressed by testing relevant hypotheses. Results in Wilcox (in press a) suggest using a multiple comparisons procedure designed specifically for the situations just described, but execution time can be quite high. A modified method for dealing with this issue is proposed.