Consider the data points (2, 3), (3, 2), (5, 1), (6, 0).
(a) find the equation of the least-squares line y = β0 + β1x which best fits the data.
(b) find the equation of the least-squares parabola y = β0 + β1x + β2x 2 which best fits the data.
(c) calculate how much ‘better’ the parabola fits the data than the line: calculate and compare ~y − xβ~ 2 , which is the sum of squares of the errors terms, for the line and parabola found in parts (a) and (b).