Chapter 3 Linear models II: model selection, extensions, and diagnostics

Given the response $Y$ and the predictors $X_1,\ldots,X_p,$ many linear models can be built for predicting and explaining $Y.$ In this chapter we will see how to address the problem of selecting the best subset of predictors $X_1,\ldots,X_p$ for explaining $Y.$ Among others, we will also see how to extend the linear model to account for nonlinear relations between $Y$ and $X_1,\ldots,X_p,$ how to check whether the assumptions of the model are realistic in practice, and how to incorporate dimension reduction within linear regression.