The use of prior information in linear regression analysis
For the usual linear model , where the e's are NID(0,1), we have considered the use of prior information for β of the form where the e0i are independent of the a's and are NID (mi,σ2). However, the experimenter assumes the e0i are NID (0, σ2 i0). The variances of the usual least squares estimators of the β's are compared to the mean square errors of the corresponding estimators using both fixed (σ2=0) and random priors (σ2=1,4,10) for r = 1,2,3 and selected values of mi, σ2 i0and the correlation betveen the X′s.