A general linear model (GLM), using least-squares techniques, was used to develop a criterion measure to replace freshman year grade point average (GPA) in college admission predictive validity studies. Problems with the use of GPA include those associated with the combination of grades from different courses and disciplines into a single measure, the incompatibility of grades across courses, and adjustments for differences in grading standards at the course level. Freshman year GPA has the added disadvantage of being an insufficient and inadequate sample of a student's achievement through four years of college. Data for this study were taken from all 1,564 students who entered Stanford University (California) as freshmen in the autumn of 1982. Data include: sex, ethnicity, scores on the verbal and mathematics tests of the Scholastic Aptitude Test, high school GPA, high school rank in class, and data on courses taken at Stanford University. Estimates of each student's ability were obtained based on performance in college courses representing each of three substantive areas. Ability estimation was accomplished using the PROC GLM procedure in Statistical Analysis System. The data matrix for each area consisted of students as rows and courses as columns, with each cell of the matrix representing a student's grade in a particular course. The GLM produces an estimate of the least-squares mean for each student, which is the mean grade that would have resulted if the data matrix was complete. Ability estimates are used as separate outcome measures in a series of predictive validity studies and compared with the usually computed GPA. Multiple regression analysis was conducted using other traditional preadmissions measures. Results indicate that this approach yields a predictable criterion. Fifteen data tables are included. (TJH)