Criterion and selection of optimal subsets in the linear regression,two stage procedures

In many practical situation the regression analysis with stochastic regressors is used. The estimations of this model are often influenced by a high degree of multicollinearity. For avoidance of this fact a criterion and a procedure for the selection of an optimal subset for regression will be derived on the base of the partition of the moments of the conditional normal distribution of the regressand under the condition of the regressors. Further two stage procedures improving the result of the subset regression. based also on the partition of the conditional moments will be given.