Sample sizes for confidence intervals on the increase in the squared multiple correlation coefficient

The increase in the squared multiple correlation coefficient (DeltaR(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 Delta rho (2) was investigated. With sample sizes typically used in regression analyses, when Delta rho (2) = 0.00 and the confidence level is .95 or greater, the probability will be at least .999. For Delta rho (2) greater than or equal to .01 and a confidence level of .95 or greater, the probability will be smaller than the nominal confidence level. For Delta rho (2) greater than or equal to .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.