This paper considers the application of Bayesian techniques for simultaneous estimation to the specification of regression weights for selection tests used in various technical training courses in the Marine Corps. Results of a method for m-group regression developed by Molenaar and Lewis (1979) suggest that common weights for training courses belonging to certain general categories are justified in many cases. However, such commonality of regression weights does not appear to hold for all courses in these categories--weights for some training courses remain distinct even after the application of the simultaneous estimation procedure. Thus, a hypothesis of validity generalization across training courses in a given category would only be retained for a carefully selected subset of courses and not for all groups included in the analyses. (Author)