Question 4 It is well-known that ridge regression tends to give similar coefficient values to correlated variables, whereas the lasso may give quite different coefficient values to correlated variables. We will now explore this property in a very simple setting. Suppose that n = 2, p = 2, X11 = X12, X21 = X22. Furthermore, suppose that y₁+y2 = 0 and X11+X21 = 0 and X12+x22 = 0, so that the estimate for the intercept in a least-squares, ridge regression, or lasso model is zero: Bo = 0 a) Write out the ridge regression optimization problem in this setting, 1 b) Argue that is this setting the ridge coefficient estimates satisfy ß₁ = ß ₂ c) Write out the lasso optimization problem is this setting

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