Resampling techniques are now-a-days widely used for model assessment and comparison. In the literature, many variable selection methods for regression modeling have been developed whose performance depends critically on the stopping rules. In this book, resampling application for variable selection on the basis of optimum choice of stopping rules for each data set and model simplification in various regression models are addressed. We propose a general approach of resampling techniques in regression analysis that allows us to 'choose' the stopping criterion's for each data set. Our selection method first choosing appropriate cutoff values/stopping criterion's and results in selecting a good subset regression model. We focus on optimizing cutoff values or stopping criterion's in automated model selection methods in regression analysis due to the interest in holding only authentic predictor variables in the regression models. We first focus on linear regression model, and then extended our approach to generalized regression, cox regression and finally robust regression.