practiceprob6_soln

# practiceprob6_soln - Math 235 Assignment 6 Practice...

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Unformatted text preview: Math 235 Assignment 6 Practice Problems Solutions 1. Find a and b to obtain the best fitting equation of the form y = a + bt for the given data. a) t- 2- 1 0 1 2 y 3 5 7 9 10 Solution: Let X T = 1 1 1 1 1- 2- 1 0 1 2 and ~ y T = (3 , 5 , 7 , 9 , 10). Then we get ~a = ( X T X )- 1 X T ~ y = 5 0 10- 1 1 1 1 1 1- 2- 1 0 1 2 3 5 7 9 10 = 1 10 2 0 0 1 34 18 = 6 . 8 1 . 8 Thus a = 6 . 8 and b = 1 . 8. b) t 1 2 3 4 5 y 3 4 5 5 7 Solution: Let X T = 1 1 1 1 1 1 2 3 4 5 and ~ y T = (3 , 4 , 5 , 5 , 7). Then we get ~a = ( X T X )- 1 X T ~ y = 5 15 15 35- 1 1 1 1 1 1 1 2 3 4 5 3 4 5 5 7 = 1 10 11- 3- 3 1 24 81 = 2 . 1 . 9 Thus a = 2 . 1 and b =- . 9. 2 2. Find an ~x that minimizes k A~x- ~ b k where A = 1 1 1 2 1 3 1 4 and ~ b = 2 1 1- 1 . Solution: We have A T A = 1 1 1 1 1 2 3 4 1 1 1 2 1 3 1 4 = 4 10 10 30...
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## This note was uploaded on 11/28/2011 for the course MATH 235 taught by Professor Celmin during the Fall '08 term at Waterloo.

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practiceprob6_soln - Math 235 Assignment 6 Practice...

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