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. a. Show that the first three orthogonal polynomials are Po(t) = 1, p₁(t) = 1, and p2(1) = 1²-35 (The polynomial p₂ has been scaled so that its values at the evaluation points are small integers.) b. Fit a quadratic trend function to the data (-5, 1), (-3, 1), (-1,4), (1,4), (3,6). (5.8)
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. a. Show that the first three orthogonal polynomials are Po(t) = 1, p₁(t) = 1, and p2(1) = 1²-35 (The polynomial p₂ has been scaled so that its values at the evaluation points are small integers.) b. Fit a quadratic trend function to the data (-5, 1), (-3, 1), (-1,4), (1,4), (3,6). (5.8)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Solve both parts a and b
Transcribed Image Text:4. 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.
a. Show that the first three orthogonal polynomials are
35
Po(t) = 1, Pi(t) = 1, and p2(1) = 1²-¹3 8
(The polynomial p2 has been scaled so that its values at
the evaluation points are small integers.)
b. Fit a quadratic trend function to the data
(-5, 1), (-3, 1), (-1,4), (1, 4). (3,6). (5.8)
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