Due next week on Friday, 4/17, by 5pm in Yue's office hours.

from chapter 3 in the book
6, 11, 14, 21
for 14(g) also write the dual problem.

and the following additional problem:

A) Consider the data below.  y approximately equals a x + b.  
a) Formulate the least squares regression (to determine a and b) as an optimization problem and solve.  
b) Formulate the regression problem as a linear program where you minimize the sum of the absolute errors (instead of the sum of the squared errors).
c) Suppose you want to reduce times when the linear fit overestimates the data (e.g., you want to use the regression to make decisions and overestimates are more costly than underestimates).  Formulate a variant of the LP in part b where overestimates are penalized 10x as much as underestimates.

For parts a-c plot the data and the linear fits.

data:
x	y
0.1	6.0
3	8.4
4	9.8
4.5	10.5
5	8.5
8	10.8
9	11.9
11	11.2
20	17.1
24	15.4
43	31.7
44	27.3
90	48.2
102	63.8