Linear Model Selection and Regularization

In the regression setting, the standard linear model $$\displaystyle{ Y =\beta _{0} +\beta _{1}X_{1} + \cdots +\beta _{p}X_{p}+\epsilon }$$ (6.1) is commonly used to describe the relationship between a response Y and a set of variables \(X_{1},X_{2},\ldots,X_{p}\). We have seen in Chapter 3 that one typically fits this model using least squares.