2. Consider a multiple linear regression with n = 4 observations and p = 2 explanatory variables: 'i EH1 332'2 91' 1 1 2 68 2 U 1 57 3 U 2 90 4 2 1 1 12 (a) Calculate these matrix products by hand (you can use software to check): X , X' X , X 'Y (b) Obtain the inverse of X ' X . You can use software, but it is doable by hand too. To obtain it by hand, consider augmenting the matrix with the (3 X 3) identity matrix on the right and then carrying out the following sequence of row operations which should leave the identity matrix on the left, and the inverse of X'X on the right (R1, R2, R3 refer to rows 1,2 and 3): R3' : 123/10, R2' : 3R1 4R2, R2' : R2/11,R1' : R1 3R2,R1' : R1/4. (0) Obtain the product (X'X)_1X'Y. What is this vector product called, (in words, not symbols)