Least squares and Bayes methods were used in a cross validation study conducted for comparison purposes. The study applies to situations with the following conditions: predictor data are given on the same scales; criterion data may be given on different scales; and it is necessary to pool data even though criterion scale differences exist. Such a system may be needed for minority group prediction studies or graduate school prediction studies where the group sizes are small. Data for the study were taken from the files of the Validity Study Service of the College Entrance Examination Board. Also a very limited amount of data were supplied by a few American graduate schools. The Bayes method was somewhat better, but it was found that both methods yielded negative regression weights; when the absolute values of the weights were used, both the methods were improved and yielded results which were very similar in terms of evaluative statistics computed in the cross validation sample. (Author/CTM)