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