TEST-3-Answers - TEST 3 ENGR 3723 PROBLEM 1(10 points...

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TEST # 3 ENGR 3723 PROBLEM 1 (10 points) Define the coefficient of regression. ANSWER: 2 2 2 2 1 0 2 ) ( ) ( = = = i i t i i i i r t r t y y S x a x a a y S S S S r PROBLEM 2 (25 points) Consider 3 . 80 6 9 . 40 4 2 . 27 3 6 . 13 2 7 . 7 1 1 . 2 0 i i y x A) (5 points) Make a linear regression ) ( 1 0 x a a y + = . Calculate the coefficient of regression. ANSWER: 2 1 0 ) ( = i i i r x a a y S
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= = = = i i i i r i i i r x x a a y a S x a a y a S 0 ) ( 2 0 ) ( 2 1 0 1 1 0 0 + = + = i i i i i i i i i i i x a x a x y x a na y Then 2 1 0 1 0 Solve for 0 a and 1 a B) (5 points) Make a second degree polynomial regression. Calculate the coefficient of regression ANSWER: = = = = = = = i i i i i r i i i i i r i i i i r i i i i r x x a x a a y a S x x a x a a y a S x a x a a y a S x a x a a y S 0 ) ( 2 0 ) ( 2 0 ) ( 2 ) ( 2 2 2 1 0 2 2 2 1 0 1 2 2 1 0 0 2 2 2 1 0
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∑∑ ∀∀ + + = + + = + + = ii i i i i i i i i i i i i i i i i i i i i x a x a x a x y x a x a x a x y x a x a na y Then 4 2 3 1 2 0 2 3 2 2 1 0 2 2 1 0 Solve for 0 a , 1 a and 2 a . See attached file. C) (10 points) Make a regression using the exponential fit ) ( 1 0 x a e a y = Calculate the coefficient of regression ANSWER: i i i i y z call then bx a y ln ln ln = + = and get i i bx a z + = ' . See attached file D) (5 points) Which regression is the best. Explain why. ANSWER: We judge the “goodness of fit” by the values of the coefficient of regression. The second order polynomial is better than the other two (the exponential is actually very bad) .
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PROBLEM 3 (20 points)
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This note was uploaded on 08/31/2011 for the course ENGR 3723 taught by Professor Staff during the Summer '11 term at Oklahoma State.

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TEST-3-Answers - TEST 3 ENGR 3723 PROBLEM 1(10 points...

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