The main purpose of this paper is to discuss some applications of internally studentized residuals 9n the model selection criterion between two nested and non-nested stochastic linear regression models. Joseph et.al [1] formulated various proposals from a Bayesian decision-theoretic perspective regarding model selection Criterion. Oliver Francois et.al [2] proposed novel approaches to model selection based on predictive distributions and approximations of the deviance. Jerzy szroeter [3] in his paper depicted the development of statistical methods to test non-nested models including regressions, simultaneous equations. In particular new criteria for a model selection between two nested/ non-nested stochastic linear regression models have been suggested here.