Question 4 Suppose we want to best-fit a quadratic function y(x) = ax² + b to three data points as shown below. This means we want to find the values of constants a and b such that the best-fit curve is 'closest to the three points given. (a) (b) စာ -2 data point y(x) = ax²+ b Given that the error, di, between each data point (xi, yi) and the best-fit curve is di = y(xi) y = (ax² + b) — Yi, - show that the sum of squared errors (SSE) is - SSE(a,b) = d = (b − 1)² + (4a + b − 2)² + (9a + b − 4)². (3 marks) The best-fit curve occurs when the SSE is at a minimum. Solve for the constants a and b of the best-fit curve and apply derivative tests to show that both the local & global minimum value of the SSE occurs at these constant values. (12 marks)

Fig: 1