Regarding subset selection in normal linear models, which statement is true?

Best subset selection aims to find the optimal model that includes the best combination of predictors from the potential set, which can encompass all possible combinations of the predictors. This process leads to the creation of nested models; each smaller subset of predictors can be derived from a larger model by removing one or more predictors. Thus, it is possible to evaluate simpler models that are contained within larger ones, supporting the idea that best subset selection indeed results in nested models.

In contrast to this, the residual sum of squares is often a crucial metric in assessing the fit of a model against another model. While it can have limitations in certain contexts, it is frequently used as a tool for model selection. Additionally, forward stepwise selection is a technique designed to gradually build up the model by including predictors one at a time based on predefined criteria, which may not be as effective in high-dimensional settings compared to other methods.

Therefore, acknowledging the concept of nested models is key to understanding best subset selection in the context of normal linear models.