Non-Linear Regression Models B

Non-Linear Regression Models B - Fitting Non-Linear...

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Fitting Non-Linear Regression Oy Mae Louie Bessie Nguyen Gina Piscitelli
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When do we use a non-linear regression model? When at least one of the parameters is not linear The general form of a non-linear regression model is y=η(x,β) + ε where ε ~N(0, σ 2 )
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Plot of Weight Loss vs Days for an Obese Patient oldpar<-par(mar=c(5.1,4.1,4.1,4.1)) plot(Days,Weight,type="p",ylab="Weight(kg)") Wt.lbs<-pretty(range(Weight*2.2025)) axis(side=4,at=Wt.lbs/2.205,lab=Wt.lbs,srt=90) mtext("Weight(lb)",side=4,line=3)
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Weight Loss Dataset Model: y = β o + β 1 *2 -t/θ + ε The parameters: β o : ultimate lean weight β 1 : total amount of weight to be lost θ: time taken to lose half the amount of weight remaining to be lost
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Method Used to Analyze Data Iterative procedure The number of iterations depend on how quickly the parameters converge. The converged parameters are close approximates for βo,β1, and θ . The likelihood for the non-linear regression model is maximized when residual sum of squares is minimized .
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Non-Linear Regression Methods 1 . "Direct Computation" Method: y = β o + β 1 *2 -t/θ 1. "Derivative" Method: η(β) ≈ ω (0) + Z (0) β 1. Self-Starting Method: y = β o + β 1 exp(-x/θ) + ε
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1. Direct Computation Method
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This note was uploaded on 04/11/2011 for the course ECE 357 taught by Professor Subjolly during the Spring '11 term at National University of Ireland, Galway.

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Non-Linear Regression Models B - Fitting Non-Linear...

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