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 )
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
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
1. Direct Computation Method

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

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