Simulation method of model selection based on Mallows' Cp Criteria in linier regression

Abstract

The selection of models involving many independent variables is one of the studies on linear regression modeling. If there are k independent variables, then there are as many as 2 k the number of models to be observed and selected as good as the final model. The increasing number of all models to be studied with the increase of independent variables is the fundamental issue that needs to be determined in selection criteria. This paper reviews the Mallow's Cp Criteria that is often overestimate the number of independent variables selected in the model. The number of selected variables in the model using Mallow's Cp criteria is performed by simulation. The simulation is run in two cases, one for the case where there is a correlation between some independent variables and one dependent variable, whereas the second case is the absence of correlation between some independent variables and one dependent variable. The simulation results are used to investigate the overestimate number of independent variables selected in the model.