Multiple Regression Models, Variable Selection Problem

Regression analysis is the most popular method be used in the all of the meth-ods of multiple statistical analysis. It is a mathematical statistical method to deal with the dependence of the plentiful variables. The main method of regression anal-ysis is building good imitation regression models on the basis of data has known. It is very important problem in building regression models process is how to selec-tion important variables in the plentiful explanation variables, is namely variable selection.In this paper, the problem of variable selection in regression is considered. This paper is divided into five chapters. Firstly, based on the multivariate regression, we introduce the multivariate regression model. Secondly, about the problem of multivariate regression, we introduce several methods of variable selection usually used. Thirdly, about the methods of variable selection, we introduce and study several important variable selection criteria. fourthly, we give the brief introduction of some characters about common criteria. fifthly, on the base of study and contrast, we use Fisher information and Kullback-Leiber information to improve the AIC criteria, and apply the data of random simulation to validate the new criteria is suitable.