Not sure how to start this problem.

1. The lasso estimator can be hard to understand because there is no closed-form ex- pression. But there are simpler cases for which a closed-form expression is available, and that can shed some light on what lasso is doing. Here is one such case. (a) Suppose we have just one observation from the model y = 8 + 6, and we want to use lasso to estimate B. Define the function gx(b) = (y - b)? + Ab|, where A > 0 is fixed, so that Bx = arg mine gx (b). Show that Bx = sign(y) . (ly| - >/2)+, where r, = max( 0, sign () = >/2 and ly| /2 separately. (b) For a fixed value of A, say, A = 1, draw a plot of B, as a function of y. On top of this plot, overlay the diagonal "y = a" line. Explain in what sense lasso achieves both shrinkage and selection. Hint: To deal with the "positive part" in plotting Bx, it'll help to use the R command pmax