A summary of the technical problems encountered in performing Bayesian m group regression is given. Grade-point averages for students entering a vocational-technical program are predicted using ability assessments from the Career Planning Profile (CPP), a development of The American College Testing Program (ACT). The theory derived by Lindley (see Lindley and Smith, in press); a method developed by Jackson Novick, and Thayer (1971); and the cross-validation performed by Novick, Jackson, Thayer, and Cole (in press) are cited; and the relation to conventional least squares is explored. (Author)