This paper examines the Bayesian estimation of parameters of linear regression model when the assumption of normality is not tenable. Outlier observations have been traced and identified as one of the factors causing departures from normality assumptions. Thus, the Ordinary Least Squares (OLS) estimates are unbiased but the variances are no longer minimum which can hinder the validity of the inferences to be made about the parameters. Nigerian Stock Exchange and Simulated data were used for illustrations. The finding shows that the posterior mean is unbiased, consistent and similar to the results obtained in homoscedasticity version and the degrees-of-freedom obtained are relatively small and the existence of fat tail is confirmed.
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