In Berger and Pericchi (1993) a general automatic Bayesian method for comparing models, the {\em Intrinsic Bayes Factor\/} (IBF) was proposed. One version, the {\em Arithmetic IBF\/}, was shown to essentially correspond to an actual Bayes factor for a reasonable {\em Intrinsic Prior}. A second version, the {\em Geometric IBF\/}, is justified in Pericchi and Smith (1993), using a prequential type of loss function, without assuming that one of the entertained models is the true sampling model. Here we analyze the general normal linear model, determining the intrinsic Bayes factors for any model comparisons, nested or separate, as well as for multiple model comparisons. In these situations we also calculate the {\em Expected Arithmetic IBF\/}. We also generalize model elaboration ideas to linear models with fixed mean structure but arbitrary error distributions. The method is illustrated on examples and compared with other model selection methods. Postscript File (529kB)