The squared correlation coefficient,w2, between an empirically chosen linear function of predictors, B̂0+ B̂′x, and a criterion,y, is employed as a measure of predictive precision. This coefficient is defined over the entire population but is conditional on B̂. Assuming a multinormal distribution for x and y, approximations for the expected value and variance ofw2are derived. If too many predictors are employed, precision of prediction can decrease. This is illustrated by means of an example of a sequence of values of ℰ (w2). A function of the sample squared multiple correlation coefficient,r2, is proposed as an estimator ofw2. Results of Monte Carlo experiments are employed to give an impression of the precision of the estimates ofw2, and the accuracy of the approximations for ℰ (w2) and