Question 11.1
Using the crime data set uscrime.txt from Questions 8.2, 9.1, and 10.1, build a regression model using:
1. Stepwise regression
2. Lasso
3. Elastic net
For Parts 2 and 3, remember to scale the data first – otherwise, the regression coefficients will be on different scales and the constraint won’t have the desired effect.
For Parts 2 and 3, use the glmnet function in R.
Notes on R:
• For the elastic net model, what we called λ in the videos, glmnet calls “alpha”; you can get a range of results by varying alpha from 1 (lasso) to 0 (ridge regression) [and, of course, other values of alpha in between].
• In a function call like glmnet(x,y,family=”mgaussian”,alpha=1) the predictors x need to be in R’s matrix format, rather than data frame format. You can convert a data frame to a matrix using as.matrix – for example, x <- as.matrix(data[,1:n-1])
• Rather than specifying a value of T, glmnet returns models for a variety of values of T.
