1. Prove that the sum of the absolute residuals cost function is convex as a function of (beta_0, beta_1).

2. When is the minimum of the SSE unique as a function of (beta_0, beta_1)? Interpret your answer geometrically. (Hint: when is the SSE strictly convex?)

3. Plot the a) maximum absolute residual, b) SSE, and c) sum of absolute residuals as a function of (beta_0, beta_1), for the data in problem 13 in chapter 2 of the book. (You can use a contour plot or a grayscale plot, whichever is more aesthetically pleasing / clear.) Interpret the differences (if any) in the locations of the minima (i.e., the optimal estimates) of these three cost functions.

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