This paper discusses Bayesian m-group regression where the groups are arranged in a two-way layout into m rows and n columns, there still being a regression of y on the x's within each group. The mathematical model is then provided as applied to the case where the rows correspond to high schools and the columns to colleges: the predictor variables might be the performances in various course area taken while at high school and the random variable the first-year performance at college. Then "cell" (i,j) of the two-way table will contain data on the performances of those subjects who passed from high school i to college j. Eighteen equations are given. (DB)