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 -0.33 -4.93 1.64 24.34 2.67 0.13 2 3.4 24 0.27 -1.93 -0.52 3.74 2.95 0.45 3 3.0 26 -0.13 0.07 -0.01 0.00 3.14 -0.14 4 3.5 27 0.37 1.07 0.39 1.14 3.23 0.27 5 3.6 29 0.47 3.07 1.43 9.40 3.42 0.18 6 3.0 25 -0.13 -0.93 0.12 0.87 3.04 -0.04 7 2.7 25 -0.43 -0.93 0.40 0.87 3.04 -0.34 8 3.7 30 0.57 4.07 2.30 16.54 3.52 0.18 9 3.2 23 0.07 -2.93 -0.20 8.60 2.86 0.34 10 3.0 28 -0.13 2.07 -0.28 4.27 3.33 -0.33 11 3.5 30 0.37 4.07 1.49 16.54 3.52 -0.02 12 2.5 20 -0.63 -5.93 3.76 35.20 2.57 -0.07 13 3.8 32 0.67 6.07 4.04 36.80 3.71 0.09 14 2.6 26 -0.53 0.07 -0.04 0.00 3.14 -0.54 15 2.7 23 -0.43 -2.93 1.27 8.60 2.86 -0.16 n sum(y) sum(x) sum sum 15 47.0 389 15.83 166.93 avg(y) avg(x) 3.13 25.93 estimated beta_0 0.67 beta_1 0.09 ##### Sheet/List 2 ##### 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 -0.33 -4.93 1.64 24.34 2.67 0.13 2 3.4 24 0.27 -1.93 -0.52 3.74 2.95 0.45 3 3.0 26 -0.13 0.07 -0.01 0.00 3.14 -0.14 4 3.5 27 0.37 1.07 0.39 1.14 3.23 0.27 5 3.6 29 0.47 3.07 1.43 9.40 3.42 0.18 6 3.0 25 -0.13 -0.93 0.12 0.87 3.04 -0.04 7 2.7 25 -0.43 -0.93 0.40 0.87 3.04 -0.34 8 3.7 30 0.57 4.07 2.30 16.54 3.52 0.18 9 3.2 23 0.07 -2.93 -0.20 8.60 2.86 0.34 10 3.0 28 -0.13 2.07 -0.28 4.27 3.33 -0.33 11 3.5 30 0.37 4.07 1.49 16.54 3.52 -0.02 12 2.5 20 -0.63 -5.93 3.76 35.20 2.57 -0.07 13 3.8 32 0.67 6.07 4.04 36.80 3.71 0.09 14 2.6 26 -0.53 0.07 -0.04 0.00 3.14 -0.54 15 2.7 23 -0.43 -2.93 1.27 8.60 2.86 -0.16 n sum(y) sum(x) sum sum 15 47 389 15.83 166.93 avg(y) avg(x) 3.13 25.93 estimated beta_0 0.67 beta_1 0.09 ##### Sheet/List 3 ##### student GPA (y) ACT (x) vector y matrix X X' estimated y residual 1 2.8 21 2.8 1 21 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2.67 0.13 2 3.4 24 3.4 1 24 21 24 26 27 29 25 25 30 23 28 30 20 32 26 23 2.95 0.45 3 3.0 26 3.0 1 26 3.14 -0.14 4 3.5 27 3.5 1 27 X'X 3.23 0.27 5 3.6 29 3.6 1 29 15 389 "Hint for Windows: Expand to the size of the matrix & Press F2, then Ctrl+Shift+Enter (use ""MMULT"")" 3.42 0.18 6 3.0 25 3.0 1 25 389 10255 "Hint for Mac: Expand to the size of the matrix & press CONTROL+U, and then press ⌘+RETURN" 3.04 -0.04 7 2.7 25 2.7 1 25 3.04 -0.34 8 3.7 30 3.7 1 30 (X'X)^(-1) 3.52 0.18 9 3.2 23 3.2 1 23 4.10 -0.16 "Hint for Windows: Expand to the size of the matrix & Press F2, then Ctrl+Shift+Enter (use ""MINVERSE"")" 2.86 0.34 10 3.0 28 3.0 1 28 -0.16 0.01 "Hint for Mac: Expand to the size of the matrix & press CONTROL+U, and then press ⌘+RETURN" 3.33 -0.33 11 3.5 30 3.5 1 30 3.52 -0.02 12 2.5 20 2.5 1 20 X'y estim. 2.57 -0.07 13 3.8 32 3.8 1 32 47 beta_0 0.67 3.71 0.09 14 2.6 26 2.6 1 26 1235 beta_1 0.09 3.14 -0.54 15 2.7 23 2.7 1 23 2.86 -0.16 ##### Sheet/List 4 ##### student GPA (y) ACT (x) vector y matrix X X' estimated y residual 1 2.8 21 2.8 1 21 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2.67 0.13 2 3.4 24 3.4 1 24 21 24 26 27 29 25 25 30 23 28 30 20 32 26 23 2.95 0.45 3 3.0 26 3.0 1 26 3.14 -0.14 4 3.5 27 3.5 1 27 X'X 3.23 0.27 5 3.6 29 3.6 1 29 15 389 "Hint for Windows: Expand to the size of the matrix & Press F2, then Ctrl+Shift+Enter (use ""MMULT"")" 3.42 0.18 6 3.0 25 3.0 1 25 389 10255 "Hint for Mac: Expand to the size of the matrix & press CONTROL+U, and then press ⌘+RETURN" 3.04 -0.04 7 2.7 25 2.7 1 25 3.04 -0.34 8 3.7 30 3.7 1 30 (X'X)^(-1) 3.52 0.18 9 3.2 23 3.2 1 23 4.10 -0.16 "Hint for Windows: Expand to the size of the matrix & Press F2, then Ctrl+Shift+Enter (use ""MINVERSE"")" 2.86 0.34 10 3.0 28 3.0 1 28 -0.16 0.01 "Hint for Mac: Expand to the size of the matrix & press CONTROL+U, and then press ⌘+RETURN" 3.33 -0.33 11 3.5 30 3.5 1 30 3.52 -0.02 12 2.5 20 2.5 1 20 X'y estim. 2.57 -0.07 13 3.8 32 3.8 1 32 47 beta_0 0.67 3.71 0.09 14 2.6 26 2.6 1 26 1235 beta_1 0.09 3.14 -0.54 15 2.7 23 2.7 1 23 2.86 -0.16 ##### Sheet/List 5 ##### y x y-avg(y) x-avg(x) (y-avg(y))*(x-avg(x)) (x-avg(x))^2 estimated y true model y residual disturbance 2 1 -2.67 -2.17 5.78 4.69 1.80 1.5 0.20 0.5 6 4 1.33 0.83 1.11 0.69 5.77 6.0 0.23 0.0 3 2 -1.67 -1.17 1.94 1.36 3.12 3.0 -0.12 0.0 8 5 3.33 1.83 6.11 3.36 7.09 7.5 0.91 0.5 5 3 0.33 -0.17 -0.06 0.03 4.45 4.5 0.55 0.5 4 4 -0.67 0.83 -0.56 0.69 5.77 6.0 -1.77 -2.0 sum(y) sum(x) sum sum 28 19 14.33 10.83 avg(y) avg(x) 4.67 3.17 estimated true beta_0 0.48 0 beta_1 1.32 1.5 ##### Sheet/List 6 ##### y x vector y matrix X X' estimated y true model y residual disturbance 2 1 2 1 1 1 1 1 1 1 1 1.80 1.5 0.20 0.5 6 4 6 1 4 1 4 2 5 3 4 5.77 6.0 0.23 0.0 3 2 3 1 2 3.12 3.0 -0.12 0.0 8 5 8 1 5 X'X (X'X)^(-1) 7.09 7.5 0.91 0.5 5 3 5 1 3 6 19 1.09 -0.29 4.45 4.5 0.55 0.5 4 4 4 1 4 19 71 -0.29 0.09 5.77 6.0 -1.77 -2.0 X'y estim. true 28.0 beta_0 0.48 0 103.0 beta_1 1.32 1.5