Bayesian prediction with random regressors

In this article we analyse the problem of prediction from regression equations with random independent variables. For example, in predicting electricity sales using a regression equation, the independent variables usually include, among others, income, price, and weather variables. To obtain predictions of the dependent variable, predictions of the independent variables are required. Further, inferences about future values of the dependent variable should reflect uncertainty about the future values of the independent variables. Some work on this problem from the sampling theory point of view is reported in Feldstein (1971). Herein we analyse this prediction problem with random independent variables from the Bayesian point of view.