We would like to find the equation of the closest possible cubic polynomial, that is an equation in the form y = a x3+ b x2+ c x + d, to the points (0,-3), (1, 2), (2,3), (3,1), (4,2) and (5,6).
(a) Set up a system of linear equations which would find a, b, c and d if all these points lay on the curve.
(b) Find a new system of linear equations whose solution is the least squares solution for this problem.
Next, solve the system to find the least squares solution.
(c) Find the equation for the cubic polynomial that best fits these points. Plot the points and the curve together on Mathematica and include a printout of the picture."