Comparison of Least Squares Method and Bayesian with Multivariate Normal Prior in Estimating Multiple Regression Parameters

Based on an assumption of multivariate normal priors for parameters of multivariate regression model, this study outlines an algorithm for application of traditional Bayesian method to estimate regression parameters. From a given set of data, a Jackknife sample of least squares regression coefficient estimates are obtained and used to derive estimates of the mean vector and covariance matrix of the assumed multivariate normal prior distribution of the regression parameters. Driven to determine whether Bayesian methods to multivariate regression parameter estimation present a stable and consistent improvement over classical regression modeling or not, the study results indicate that the Bayesian method and Least Squares Method (LSM) produced almost the same estimates for the regression parameters and coefficient of determination (to 4.dp) with the Bayesian method having smaller standard errors.