(ii) To make a trend analysis of six evenly spaced data points, one can use orthogonal...

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(ii) To make a trend analysis of six evenly spaced data points, one can use orthogonal polynomials with respect to evaluation at the points t = -5,-3, -1,1,3 and 5 (5) (a) Show that the first three orthogonal polynomials are po(t) = 1, p,(t) = t and p2(t) = 2,2 _ 35 (b) Fit a quadratic trend function to the data (-5,1), (-3,1), (–1,4), (1,4), (3,6), (5,8). (ii) To make a trend analysis of six evenly spaced data points, one can use orthogonal polynomials with respect to evaluation at the points t = -5,-3, -1,1,3 and 5 (5) (a) Show that the first three orthogonal polynomials are po(t) = 1, p,(t) = t and p2(t) = 2,2 _ 35 (b) Fit a quadratic trend function to the data (-5,1), (-3,1), (–1,4), (1,4), (3,6), (5,8).