This article considers Bayesian inference of the linear regression
model with one change point in observations, provided that the prior distribution of the change
point is the beta-binomial distribution or the power prior introduced by Ibrahim et al. (2003)
and the variances of the observations on two sides of the change point are the same. We get
closed forms of the posterior distributions of the change point, the regression coefficients
and the common variance. This not only generalizes the result of Ferreira (1975) from the the
discrete uniform prior distribution of the change point t to the beta-binomial distribution
which can well describe the shape of the change point distribution, but also can be further
generalized to the power prior distribution of the change point, which included the historical
information. Simulation shows higher performance or accuracy of the Bayesian method when the
change point follows the beta-binomial and power prior.