Confidence Intervals for an Effect Size Measure in Multiple Linear Regression

The increase in the squared multiple correlation coefficient (ΔR 2 ) associated with a variable in a regression equation is a commonly used measure of importance in regression analysis. The coverage probability that an asymptotic and percentile bootstrap confidence interval includes Δρ 2 was investigated. As expected, coverage probability for the asymptotic confidence interval was often inadequate (outside the interval .925 to .975 for a 95% confidence interval), even when sample size was quite large (i.e., 200). However, adequate coverage probability for the confidence interval based on a bootstrap interval could typically be obtained with a sample size of 200 or less, and moreover, this accuracy was obtained with relatively small sample sizes (100 or less) with six or fewer predictors.