Additional homework problems due Feb. 8:
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
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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