Write down the least squares problem associated to finding the cubic best fit using all six points

3. [Polynomial interpolation versus least squares fitting. 3+1pts] Recall how Q8 in HW3 required you to find the cubic best fit to six given data points. This led to a least squares optimization problem. We are given the same points as in HW3: i 0 1 2 3 4 5 x Inn-- 2.5 Y mun-- 0-33 (3) Write down the least squares problem associated to finding the cubic best fit using (i) all six points, (ii) only the data for 2' = 0,1,2,3,4, and (iii) i = 0,1,2,3. In each case solve the system and plot both the data and the polynomial. Why is case (iii) not a least squares problem? (b) What is the degree of the polynomial you would have to use so that the solution interpolates (i.e., goes through) all six data points