What principle does the stepwise regression follow when selecting input variables?

Stepwise regression is a systematic method used for variable selection in regression models. The principle it follows involves evaluating the significance of input variables in relation to the dependent variable. By examining the p-values of the variables, stepwise regression can both add and remove variables during the modeling process.

If a variable has a p-value below a certain threshold (often 0.05), it is considered statistically significant and can be added to the model. Conversely, if a variable’s p-value exceeds that threshold after the model has been constructed, it can be removed. This adaptive approach ensures that only the most relevant predictors remain in the final model, ultimately enhancing the model's predictive power without overfitting.

The other available choices highlight different approaches to variable selection, such as considering all combinations of variables or only focusing on correlation, neither of which accurately describes the iterative and significance-driven process employed in stepwise regression. Thus, the description of adding or removing variables based on p-values captures the essence of the stepwise regression methodology effectively.