5. Given data points as follows: Yi Wi (c) 1.0 2.3 1.0 2.0 3.8 1.8 3.0 6.2 0.5 where w, is the weighting factor to represent the reliability of the i-th data point. Use least-squares method to best fit these data points by the form of f(x) = co + Cx + x (a) Derive the normal equations (including the weighting factors). (5 pts) (b) 4.0 9.8 0.7 Use the normal equations developed in part (a) and the Gauss-Jordan direct method to compute the solution (digits aligned with given data through rounding - step-by-step for the coefficients: Co, C, and C; and the deviation E (Co 2/3 -2- pt) Use the normal equations developed in part (a) and the Gauss-Seidal indirect method to write a MATLAB code to compute coefficients: Co, C, and C; and the deviation E (C, C, C). Three iterations only and the initial guesses for Co, C, and C are all zeros. (10 pts) (d) Follow your computer program developed in part (c), use hand calculations to check your computational results. Also compare your computation results with those obtained in part (b). (5 pts) -9 [9] = C. 1.74 C1 = 0.063 10.5011 f (x) = 1.74 +0.063x +0.501x 3 E (C, C, C) = W [ (xi) y;] = 4.176 10 => wi i=0