Use Algorithm 6. 8.1 from Exercise 16 to write Python code that computes the ridge regression coefficient \(\boldsymbol{\beta}\) in (6.5) and use it to replicate the results on Figure 6.1. The following pseudo-code (with running cost of \(O\left((n+p) p^{2}\right)\) ) may help with the writing of the Python code.

Algorithm 6.8.2: Ridge Regression Coefficients via Sherman-Morrison Formula input: Training set (x, y) and regularization parameter y > 0. output: Solution B (nyIp + XTX)-'X'y. 1 Set A to be an n xp matrix of zeros and B + nyIp. 2 for j 1,..., p do 3 4 L Set w to be the j-th column of X. Update {A, B} via Algorithm 6.8.1 with inputs (A, B, j, w}. 5 B+B(XTy) 6 return