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.