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Model Selection Criteria have become exceedingly popular in the Time Series/Forecasting and Applied Regression Analysis. The problem of model selection has long term of interest statisticians .In the Applied Regression analysis,one is faced with a large number of explanatory variables which are potentially important for the specification of the model.Selecting the best statistical model is an important problem in statistics as well as in any other field that uses regression analysis.The problem of reducing the number of regressors in the prediction equation of Multiple regression analysis has received and shall continue to receive considerable attention in the statistical analysis. In the present research study ,the various Selection Criteria for best regression models have been developed by using studentized residuals.