13.20 Penalized regression

• dropping some controls
• \(argmin_\beta \{\sum(Y - \hat{Y})^2 + \lambda F(\beta)\}\)
• minmize sum of squared residuals AND make \(\beta\) function small
• implementation: LASSO, ridge regression, elastic net regression (LASSO + ridge)
• throw out variables that LASSO thinks are unimportant
• watch out: standardize all variables
• choose \(\lambda\) as you want; higher value –> toss out more variables