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

The increase in the squared multiple correlation coefficient (DeltaR(2)) as sociated with a variable in a regression equation is a commonly used measur e of importance in regression analysis. The probability that an asymptotic confidence interval will include Delta rho (2) was investigated. With sampl e sizes typically used in regression analyses, when Delta rho (2) = 0.00 an d 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 confid ence 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 pr obability to be at least .925 and to be at least .94.