A stepwise AIC method for variable selection in linear regression

In this article, we study stepwise AIC method for variable selection comparing with other stepwise method for variable selection, such as, Partial F, Partial Correlation, and Semi-Partial Correlation in linear regression modeling. Then we show mathematically that the stepwise AIC method and other stepwise methods lead to the same method as Partial F. Hence, there are more reasons to use the stepwise AIC method than the other stepwise methods for variable selection, since the stepwise AIC method is a model selection method that call be easily managed and can be widely extended to more generalized models and applied to non normally distributed data. We also treat problems that always appear in applications, that are validation of selected variables and problem of collinearity.