observation weight (y) height (x) vector y matrix X pred. weight residual miss gain (residual)^2 1 63 13 63 1 13 61.29 1.71 0 0.5 2.94 2 70.7 23 70.7 1 23 72.67 -1.97 0 0.5 3.86 3 92.3 33 92.3 1 33 84.05 8.25 1 -0.6 68.14 4 89.1 30 89.1 1 30 80.63 8.47 1 -0.6 71.72 5 72.9 25 72.9 1 25 74.94 -2.04 0 0.5 4.17 6 78.3 28 78.3 1 28 78.36 -0.06 0 0.5 0.00 7 67.5 20 67.5 1 20 69.25 -1.75 0 0.5 3.07 8 74.3 23 74.3 1 23 72.67 1.63 0 0.5 2.67 9 76.5 25 76.5 1 25 74.94 1.56 0 0.5 2.43 10 81 30 81 1 30 80.63 0.37 0 0.5 0.14 11 76.5 28 76.5 1 28 78.36 -1.86 0 0.5 3.44 12 72.9 23 72.9 1 23 72.67 0.23 0 0.5 0.06 13 74.3 25 74.3 1 25 74.94 -0.64 0 0.5 0.41 14 81 30 81 1 30 80.63 0.37 0 0.5 0.14 15 72 20 72 1 20 69.25 2.75 0 0.5 7.56 16 69.8 23 69.8 1 23 72.67 -2.87 0 0.5 8.21 17 74.3 25 74.3 1 25 74.94 -0.64 0 0.5 0.41 18 85.5 38 85.5 1 38 89.74 -4.24 0 0.5 17.94 19 83.3 33 83.3 1 33 84.05 -0.75 0 0.5 0.56 20 69.8 28 69.8 1 28 78.36 -8.56 1 -0.6 73.19 n avg(y) avg(x) sum sum sum 20 76.25 26.15 0.00 6.7 271.0 avg 13.55 model from the setup X' beta_0 46.49 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 beta_1 1.14 13 23 33 30 25 28 20 23 25 30 28 23 25 30 20 23 25 38 33 28 matrix X'X matrix (X'X)^(-1) X'y (X'X)^(-1) X'y estimated 20 523 1.22 -0.04 1525 46.49 beta_0 523 14259 -0.04 0.00 40541.7 1.14 beta_1