A Sub-Model Theorem for Ordinary Least Squares | Watagoda | International Journal of Statistics and Probability | CCSE

Variable selection or subset selection is an important step in the process of model fitting. There are many ways to select the best subset of variables including Forward selection, Backward elimination, etcetera. Ordinary least squares (OLS) is one of the most commonly used methods of fitting the final model. Final sub-model can perform poorly if the variable selection process failed to choose the right number of variables. This paper gives a new theorem and a mathematical proof to illustrate the reason for the poor performances, when using the least squares method after variable selection