Problem 3:
Now we will use the methods of ridge regression and lasso to solve our models.
1. The ridge regression cost function we will use is of the form
$$L(X, y, \alpha, s) = \frac{1}{n}||Xa - y||_2^2 + s||\alpha||_2^2$$
We can solve the normal equations directly to obtain our model parameters using
$$\alpha = (X^TX + (s/n)I)^{-1}X^Ty$$
Write a python function `ridge(X, y, s)` which returns the model parameters as a numpy array.