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Lecture 29

# Lecture 29 - >>[a r2 = linregr(x,y a = 19.4702-234.2857...

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Wednesday, 11/03/2010 Giving back midterm exam papers

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Untransformed power equation x vs. y transformed data log x vs. log y Linear now! ( log : Base-10) 2 2 y x β α = 2 2 log y log log x α β = + Linearization of Power Function
Linearization of Nonlinear Relationships Exponential equation ( 29 ( 29 i i i i 1 1 x 1 y x of instead y x use x y e y 1 , ln , ln ln β α α β + = =

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Linearization of Nonlinear Relationships Saturation-growth-rate equation Rational function ( 29 i i i i 4 4 4 4 y x of instead y 1 x use x y 1 x 1 y , , + = + = β α β α ( 29 i i i i 3 3 3 3 3 y x of instead y 1 x 1 use x 1 1 y 1 x x y , , + = + = α β α β α
Power equation fit along with the data x vs. y Transformed Data log x i vs. log y i Example 13.4: Power Equation y = α 2 x β 2

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12-12 >> x=[10 20 30 40 50 60 70 80];

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Unformatted text preview: >> [a, r2] = linregr(x,y) a = 19.4702 -234.2857 r2 = 0.8805 y = 19.4702x -234.2857 12-13 >> x=[10 20 30 40 50 60 70 80]; >> y = [25 70 380 550 610 1220 830 1450]; >> linregr(log10(x),log10(y)) r2 = 0.9481 ans = 1.9842 -0.5620 log x vs. log y log y = 1.9842 log x – 0.5620 y = ( 10 –0.5620 ) x 1.9842 = 0.2742 x 1.9842 ◗ Least-square fit of nth-order polynomial p = polyfit(x,y,n) ◗ Evaluate the value of polynomial using y = polyval(p,x) MATLAB Functions n 1 n 2 n 2 1 n 1 p x p x p x p x f + + + + =--- ) (...
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