ee231_ass9_sol - EE 231_B1 Numerical Analysis for...

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The sum of the squares of the residuals for this case can be written as () = = n i i i i r x a x a y S 1 2 2 2 1 The partial derivatives of this function with respect to the unknown parameters can be determined as [] = i i i i r x x a x a y a S ) ( 2 2 2 1 1 [] = 2 2 2 1 2 ) ( 2 i i i i r x x a x a y a S Setting the derivative equal to zero and evaluating the summations gives ( ) ( ) i i i i y x a x a x = + 2 3 1 2 ( ) ( ) i i i i y x a x a x = + 2 2 4 1 3 which can be solved for () 2 3 4 2 3 2 4 1 = i i i i i i i i i x x x x y x x y x a () 2 3 4 2 3 2 2 2 ∑∑ = i i i i i i i i i x x x x y x y x x a The model can be tested for the data from Table 12.1. x y x 2 x 3 x 4 xy x 2 y 10 25 100 1000 10000 250 2500 20 70 400 8000 160000 1400 28000 30 380 900 27000 810000 11400 342000 40 550 1600 64000 2560000 22000 880000 50 610 2500 125000 6250000 30500 1525000 60 1220 3600 216000 12960000 73200 4392000 70 830 4900 343000 24010000 58100 4067000 80 1450 6400 512000 40960000 116000 9280000 Σ 20400 1296000 87720000 312850 20516500 EE 231_B1 Numerical Analysis for Electrical and Computer Engineering Course Instructor: Dr. Sergiy Vorobyov
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This note was uploaded on 12/20/2010 for the course E E 231 taught by Professor Vorobyov during the Spring '10 term at University of Alberta.

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ee231_ass9_sol - EE 231_B1 Numerical Analysis for...

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