Student GPA (y) ACT (x) y-avg(y) x-avg(x) (y-avg(y))*(x-avg(x)) (x-avg(x))^2 estimated y residual 1 2.8 21 2 3.4 24 3 3.0 26 4 3.5 27 5 3.6 29 6 3.0 25 7 2.7 25 8 3.7 30 9 3.2 23 10 3.0 28 11 3.5 30 12 2.5 20 13 3.8 32 14 2.6 26 15 2.7 23 sum sum n sum(y) sum(x) estimated avg(y) avg(x) beta0 beta1 ##### Sheet/List 2 ##### Student GPA (y) ACT (x) vector y matrix X X' estimated y residual 1 2.8 21 2 3.4 24 3 3.0 26 4 3.5 27 X'X 5 3.6 29 6 3.0 25 7 2.7 25 8 3.7 30 (X'X)^(-1) 9 3.2 23 10 3.0 28 11 3.5 30 12 2.5 20 X'y beta 13 3.8 32 beta0 14 2.6 26 beta1 15 2.7 23 ##### Sheet/List 3 ##### y x vector y matrix X X' estimated y real model y residual disturbance 2 1 6 4 3 2 8 5 X'X (X'X)^(-1) 5 3 4 4 X'y beta real beta0 0 beta1 1.5