In this paper, we propose a two-stage variable selection procedure for multivariate linear regression models. We select appropriate models under a guaranteed probability by using the summation of noncentralities in the first stage. In the second stage, we exclude those models with large individual noncentrality, and then select the best model with the minimum Akaike's information criterion (AIC). Empirical study is provided to show how to achieve our goal in variable selection and to demonstrate the efficiency and usefulness of the procedure in practical applications. In addition, we have built a reasonable model to ''plain and predict the earnings and productivity in Taiwan area.
