Question 4 (12 marks) We want to fit a multiple linear regression model to a dataset of n = 97 observations and carry out variable selection using Lasso. We find that Amax = 0.9 is a value of the shrinkage parameter / that all the coefficients are shrunk to zero. To find the optimal shrinkage, we create a range of 10 values for A : 0, 0.1, 0.2, ..., 0.9, and compute the Lasso estimates Basso at each of these values. Let o? _ ly-XBass|2 be the estimate of the variance of the error term e. The table below gives the degrees of freedom df , and of A O 0.1 0.2 0.3 0.4 0.5 6 .7 .8 9 def x 8 5 3 3 2 1 0.9033 0.8116 1.8865 4.1080 4.6396 5.1962 5.7991 6.4485 7.1444 7.4611 (a) Find the best value of A among these 10 values using the BIC criterion. (b) Explain why variable selection is often necessary in regression and classification