forward stepwise regression VS backward stepwise regression

Backward stepwise regression, also known as backward elimination, operates by iteratively refining the model, beginning with a full model containing all potential predictor variables. At each step, it systematically eliminates the least statistically significant variables until reaching an optimal reduced model. This method ensures that the final model includes only variables that significantly contribute to explaining the variation in the response variable, thereby enhancing interpretability and reducing overfitting. For instance, suppose we are examining factors influencing housing prices. Initially, the model may include variables such as square footage, number of bedrooms, bathrooms, location, and proximity to amenities. Through backward stepwise regression, variables with the weakest impact, such as proximity to amenities, may be removed if their contributions are statistically insignificant. The final model could then focus on key predictors like square footage and location, providing a more concise and meaningful interpretation of housing price determinants. By iteratively removing variables based on statistical criteria, backward stepwise regression guards against the inclusion of irrelevant or redundant predictors, resulting in a more parsimonious and interpretable model. This approach is particularly advantageous when dealing with datasets containing numerous potential predictors, as it efficiently identifies the most influential variables while avoiding multicollinearity issues that may arise in forward selection methods.

Forward stepwise regression, in stark contrast, adopts an incremental approach by starting from a null model and successively adding variables that improve model fit. However, this method lacks the systematic refinement inherent in backward stepwise regression, potentially leading to the inclusion of extraneous variables that inflate model complexity and obscure meaningful relationships. For example, in the housing price prediction scenario, forward stepwise regression may add variables such as proximity to amenities without thoroughly evaluating their statistical significance relative to other predictors. This indiscriminate variable addition can result in a bloated model with diminished interpretability, as non-essential factors may distort the true relationship between predictors and the response variable. Moreover, forward stepwise regression may overlook interactions or nonlinear relationships between variables, as it focuses solely on incremental improvements in model fit without considering the broader context of variable interplay. Consequently, the final model may fail to capture the nuanced dynamics of the underlying data, limiting its predictive accuracy and generalizability.