Generate a MATHLAB code: You are provided with a dataset consisting of x and y values as follows: x = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10] y = [1.0, 3.9, 8.2, 15.0, 24.1, 35.8, 50.0, 66.7, 86.2, 108.0]. Your task is to implement polynomial least squares to fit a quadratic polynomial y = ax2 bx c to the data. (a) Plot the data points y versus x. (b) Implement the polynomial least squares method to fit a quadratic polynomial y = ax2 bx c to the data . i. Substituting the values of x, y in to the polynomial, you will have an overdetermined system: Au = v, (3) where the dimension the matrix A is 10 × 3. Output the matrix A. ii. Use the normal equation method to find the unknowns u in (3). 2iii. Find the singular value decomposition (SVD) for the matrix A by yourself, i.e. A = USV, where U is of 5 × 3, S is of 3 × 3 and V is of 3 × 3. iv. Then use the SVD obtained in (iii) to find the unknows u in (3).
