practiceprob6_soln

practiceprob6_soln - Math 235 Assignment 6 Practice...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

This note was uploaded on 11/28/2011 for the course MATH 235 taught by Professor Celmin during the Fall '08 term at Waterloo.

Page1 / 3

practiceprob6_soln - Math 235 Assignment 6 Practice...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online