In this Present book Chapter – I is an introductory one. It contains general introduction about the selection of regressors for the linear models. Chapter – II deals with the model selection measures using R square and statistics. It explains properties of these statistics and the relationships between them. Chapter – III describes the criteria for model selection proposed by Mallows (1973) and Amemiya (1990). The generalized mean squared error criterion is also explained in this chapter. Chapter – IV presents different measures for selecting regressors. It deals with step wise regression methods and stopping rules. Several references regarding the criteria for model selection have been presented under a title “BIBLIOGRAPHY”.