3. (30 points) Given an equation Ax = b, the least-squares solution x is defined to be the solution x such

that ||Ax-b|| is minimized. It can proven that for systems with exactly one least-squares solution, the

least-squares solution is given by the following formula:

x = (MTM)-¹M¹b

Linear regression is an example application of the least-squares problem. Using the formula above, find

constants a and b for the equation given below.

¹ (8)

M

= b with M=

/22.9

30.0 1

27.8 1

24.1 1

28.2

and b

(31.5)

18.3

21.3

28.4

20.7)