Show that a similar result holds for the Lasso.

3. Centering the data and penalized least squares. Consider the ridge regression problem N 2 Bridge = argmin P BERP+1 yi - Bo rij Bi + 1 B2 j=1 Show that this problem is equivalent to the problem N BC = argmin P 2 P BCERP+1 yi - Bo i= + 1 ) (BE)2 j =1 j=1 where aj = N-Ci Xij. More specifically: (a) Give the correspondence between B and the Bridge. (b) Show that the two predicted output vectors are the same. (c) Give an expression of B using y1, ..., yn. Show that a similar result holds for the Lasso