Constant predictions 3. (9 points) One model that is even simpler than the linear model we talked about in lecture is the constant model 3} = a, i.e. we predict exactly the same 3; for every observation. We might do this if we had no predictor variables. Or, if our predictor variable were categorical (eg, gender; or treatment vs. control group), we might make a different prediction for each gender, estimating a constant model within each group. One benet of studying the constant model is that it is a simple context in which we can build our intuition for how different loss functions differ from each other. Assume that we observe yl, . . . ,yn, and we choose a to minimize the empirical risk of predicting a for every single 3;: so) = igloo) (a) (2 points) If we use the L2 loss L(y, 3}) = (gomg, show that the best-tting estimate is the sample mean; i.e., ti = 3]. (b) (3 points) If we use the L1 loss L(y, 3}) = |y jr}|, show that the besttting estimate is the sample median. To simplify the problem, you may assume that n is odd, so the median is well-dened