For the given data and for data of your choice find the interpolation polynomial and the least squares approximations (linear, quadratic, etc.). Compare and comment.
(a) (-2, 0), (-1, 0), (0, 1), (1, 0), (2, 0)
(b) (-4, 0), (-3, 0), (-2, 0), (-1, 0), (0, 1), (1, 0), (2, 0), (3, 0), (4, 0)

(c) Choose five points on a straight line, e.g., (0, 0), (1, 1), · · ·, (4, 4). Move one point 1 unit upward and find the quadratic least squares polynomial. Do this for each point. Graph the five polynomials on common axes. Which of the five motions has the greatest effect?