Sample Sizes for Confidence Intervals on the Increase in the Squared Multiple Correlation Coefficient

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 probability that an asymptotic confidence interval will include δρ2 was investigated. With sample sizes typically used in regression analyses, when δρ2 = 0.00 and the confidence level is .95 or greater, the probability will be at least .999. For δρ2≥ .01 and a confidence level of .95 or greater, the probability will be smaller than the nominal confidence level. For δρ2≥ .05 and a confidence level of .95, tables are provided for the sample size necessary for the probability to be at least .925 and to be at least .94.