Needs["NonlinearRegression`"]

data={{1.0,1.0,0.126},{2.0,1.0,0.219},{1.0,2.0,0.076},{2.0,2.0,0.126},{0.1,0.0,0.186}};

NonlinearRegress[data,theta1*theta3*x1/(1+theta1*x1+theta2*x2),{theta1,theta2,theta3},{x1,x2}]

OK ... This reproduces very well the tutorial available on the Wolfram web site. Now, let's try to reproduce some of the results of Gritti et al. (2006).

data2={{5,35},{10,65},{20,90},{40,125},{60,145},{80,165},{100,180},{120,195},{140,207},{160,217}}

result2=NonlinearRegress[data2,qS1*b1*conc/(1+b1*conc)+qS2*b2*conc/(1+b2*conc)+qS3*b3*conc/(1+b3*conc),{qS1,qS2,qS3,b1,b2,b3},conc,Method->QuasiNewton,MaxIterations->200]

qS1N=result2[[1,2,1,2]](*g/L*)
qS2N=result2[[1,2,2,2]]
qS3N=result2[[1,2,3,2]]
b1N=result2[[1,2,4,2]](*L/g*)
b2N=result2[[1,2,5,2]]
b3N=result2[[1,2,6,2]]
qS1N1=qS1N/(6*12+6+16)
qS2N1=qS2N/(6*12+6+16)
qS3N1=qS3N/(6*12+6+16)
b1N1=b1N*(6*12+6+16)
b2N1=b2N*(6*12+6+16)
b3N1=b3N*(6*12+6+16)

Compare these results with qS1 = 3.88, qS2 = 0.95, qS3 = 14.3, b1 = 0.339, b2 = 14.0 and b3 = 0.109, and comment! For example, how sensitive are the results to the method used for nonlinear regression?

lrr3@psu.edu