Bayesian analysis is a method of making inferences concerning a given process which allows prior beliefs and data concerning the statistical structure of the process to be combined with the results of present trials of the process into a posterior credibility distribution on the parameters characterizing the process. Credibility interval statements from this distribution are often of interest. In this paper, a technique for stating some such intervals for a normal regression model is developed. Section 1 of this paper briefly presents an approach to Bayesian inference, due to Novick and Hall, which provides a technique for quantifying prior beliefs. Section 2 reviews the distribution theory necessary for Bayesian analysis of processes which are of the normal, linear fixed effects model type and presents a method of deriving Bayesian credibility intervals based on this distribution theory. Section 3 demonstrates the application of these methods to three sets of data.