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In the Present book Chapter -I contains the general introduction about the model selection. Chapter-II speaks about the various inferential problems of linear statistical models. The distributional properties of the OLS estimators have been presented in this chapter. It also contains the procedure of testing the general linear hypothesis .Chapter-III deals with the existing criteria for model selection given in the literature. Chapter-IV proposes some new techniques for selection of linear statistical models pertaining both the nested and non-nested linear regression models. Chapter-V epitomizes the conclusions. Various selected references have been documented under a separate caption 'Bibliography'.