This report addresses the problem of sample size in developing prediction equations for college freshman grade averages under the American College Testing (ACT) Assessment Program. For the ACT Assessment, the prediction weights are estimated by standard least squares procedures. Because prediction weights are estimated regression coefficients whose accuracy depends on the size of the base sample used to estimate them and because error in estimating the weights propagates error in prediction, sample size affects prediction accuracy. This issue is examined from both theoretical and empirical viewpoints. The expectation that total group predictions based on 50 or more cases and eight or fewer predictor variables have nearly the same accuracy as predictions based on larger samples is supported. Moreover, two-variable prediction equations based on as few as 20-29 cases would have essentially the same accuracy as prediction equations based on larger samples. On the other hand, the results from separate-sex prediction equations strongly suggest that eight-variable prediction equations based on much fewer than 50 cases would be noticeably less accurate. Four data tables are provided. (TJH)