Question: 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.

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?

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