This paper presents a brief synopsis of some recent work of the authors (Braun and Jones, 1981) in connection with the use of regression methods to predict performance in graduate schools of management on the basis of undergraduate grade point average (UGPA) and the Graduate Management Admission Test (GMAT) score. The central problem is how to provide stable unbiased predictions for identifiable subgroups of candidates whose members may be sparsely distributed across the institutions under study. It is shown how empirical Bayes methods provide a workable solution even when classical procedures cannot be implemented. (11pp.)