The feasibility and effectiveness of a Bayesian method for estimating regressions in m groups is studied by application of the method to data from the Basic Research Service of The American College Testing Program. Evidence supports the belief that in many testing applications the collateral information obtained from each subset of m-1 colleges will be useful for the estimation of the regression in the m-th college. Specifically, on cross-validation in a second sample, the Bayesian predictions had a smaller mean squared error in each of 22 colleges, the reduction averaging 9.7%, when compared with the least squares predictions when four predictor variables were used on a quarter sample in the 22 colleges where initial within-college sample sizes ranged from 26 to 184. Furthermore, even when based on the full sample within each college, the least squares predictions had an average cross-validated mean squared error only barely less than the Bayesian predictions based on the quarter sample. The most apparent benefit of the Bayesian method is that it permits regression to be done in subpopulations where sample sizes are small and where the regressions are different in the subpopulations. In the present study, a decrease of more than 10% in mean squared error was obtained using this approach. (Author)