Recent work on the analysis of growth curves has concentrated on the generalized growth model put forward by Potthoff & Roy (1964), the model being studied from a Bayesian viewpoint by Geisser (1970). The analysis of such data however falls naturally within the scope of the general Bayesian linear model proposed and analyzed by Lindley & Smith (1972). Here we apply the theory developed by Lindley & Smith to the estimation problem for growth curves, and also consider the problem of prediction, given a sample from this model.