Re: A Problem with the NonlinearFit?

*To*: mathgroup at smc.vnet.net*Subject*: [mg61765] Re: A Problem with the NonlinearFit?*From*: Antti Penttil <Antti.I.Penttila at helsinki.fi.removethis>*Date*: Sat, 29 Oct 2005 01:32:33 -0400 (EDT)*Organization*: University of Helsinki*References*: <djskuf$8p2$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Dear Axel, There's a different error that is minimized in nonlinear fit for cases A and B. For A, we minimize the sum of A) (y - a exp(-b x))^2 where as in B B) (ln(y) - ln(a exp(-b x)))^2 = (ln(y / (a exp(-b x)))^2 The idea of data conversions is to have errors that are homoskedastic and normally distributed, which is much more true with B. Yours, Antti Axel Ligon wrote: > Deas Sirs, > > concerning the NonlinearFit procedure I have a problem. I used the > following inputs: > > A) > *Raw datas {x, y}* > dat1={{0,319.9},{1,196.7},{3,140.2},{7,99.0},{14,56.1},{31,32.8},{90,1.9}} > FindFit[dat1,a*Exp[-b*x],{a,b},x] > > a ->280.376, b->0.175479 > > <<Statistics`NonlinearFit` > f=NonlinearFit[dat1,a*Exp[-b*x],x,{a,b}] > > 280.376 * Exp(-0.175479x) > > B) > *Convert datas {x, ln[y]}* > dat2={{0,5.7680},{1,5.2817},{3,4.9430},{7,4.5951},{14,4.0271},{31,3.4904},{90, 0.6419}} > FindFit[dat2,-b*x+a,{a,b},x] > > a->5.18756, b->0.0518199 > > <<Statistics`NonlinearFit` > f=NonlinearFit[dat2,-b*x+a,x,{a,b}] > > 5.18756 - 0.0518199 x > > The difference between A) and B) is only the conversion of y to ln[y] > and the equation y = a * exp(-b*x) to ln[y] = ln[a] - b*x. From this > it follows that a = exp[ln[a]]. > But I get in A) 280.376 / -0.175479 and in B) 179.031 / -0.05182 !! > Why do I get these error?? If I use Excel, I don't get these errors. > Is it an error in the programming of Mathematica, or not??? > > I'd be glad if you could help me. > > With best regards > > Axel Ligon > > -- Antti Penttilä Antti.I.Penttila at helsinki.fi.removethis Researcher Observatory tel. +358 50 5240968 00014 University of Helsinki