Re: Re: Asking NonlinearRegression

*To*: mathgroup at smc.vnet.net*Subject*: [mg88817] Re: [mg88781] Re: Asking NonlinearRegression*From*: "Thomas Dowling" <thomasgdowling at gmail.com>*Date*: Sat, 17 May 2008 05:31:34 -0400 (EDT)*References*: <g0h4kd$la4$1@smc.vnet.net> <200805160933.FAA01135@smc.vnet.net>

Hello, I should have added to my previous post that the following is an example of a function that gives a reasonable fit, but perhaps it is not acceptable? fun2 = base + max/(1 + E^((xo - x)/r)); A fit may be obtained as follows: In[479]= rules2 = FindFit[Partition[d1, 2], fun2 , {{base, .2}, {max, 1}, {xo, 50}, {r, 8}}, x] Out[479]= {base -> -0.00839687, max -> 1.14459, xo -> 81.5014, r -> 10.5337} Plotting .... In[489]= plot2 = Plot[fun2 /. rules2, {x, 0, 105}]; In[487]= listplot = ListPlot[Partition[d1, 2], PlotRange -> {-.05, 1.1}, PlotStyle -> {Green, PointSize[Large]}]; In[490]= Show[plot2, listplot] Tom Dowling On Fri, May 16, 2008 at 4:18 PM, Thomas Dowling <thomasgdowling at gmail.com> wrote: > Hello, > > Are you sure about this? > > Proceeding as you outlined ... > > In[375]:= d1 = {1, 0.00, 2, 0.00, 3, 0.00, 4, 0.00, 5, 0.00, 6, 0.00, 7, > 0.00, > 8, 0.00, 9, 0.00, 10, 0.00, 11, 0.00, 12, 0.00, 13, 0.00, 14, 0.00, > 15, 0.00, 16, 0.00, 17, 0.00, 18, 0.00, 19, 0.00, 20, 0.00, 21, > 0.00, 22, 0.00, 23, 0.00, 24, 0.00, 25, 0.00, 26, 0.00, 27, 0.00, > 28, 0.00, 29, 0.00, 30, 0.00, 31, 0.00, 32, 0.00, 33, 0.00, 34, > 0.00, 35, 0.00, 36, 0.00, 37, 0.00, 38, 0.00, 39, 0.00, 40, 0.00, > 42, 0.00, 44, 0.00, 46, 0.00, 48, 0.00, 50, 0.00, 52, 0.04, 54, > 0.06, 56, 0.08, 58, 0.09, 60, 0.16, 65, 0.24, 70, 0.32, 75, 0.43, > 80, 0.49, 85, 0.58, 90, 0.80, 95, 0.91, 100, 1.00, 105, 1}; > > In[376]:= fun = Exp[(1 - Exp[a*(1 - Exp[-b*x])])*(Exp[-b*x])/(1 - > Exp[-b*x])]; > > In[412]:= paramrules = FindFit[d1, fun, {a, b}, x] > > Out[412]= {a -> 0.648266, b -> 1.02124} > > If I now plot the (partitioned) data and the fitted function, as follows: > > In[419]= plot = Plot[fun /. paramrules, {x, 0, 105}, AxesOrigin -> {0, > 0}]; > listplot = ListPlot[Partition[d1, 2], PlotRange -> {-.05, 1.1 > }, PlotStyle -> {Green, PointSize[Large]}]; > Show[plot, listplot] > > This does not seem to be a reasonable fit to me. > > Furthermore, the following gives an overflow error message. Are you sure > you > are trying to fit to an appropriate function? > > > In[422]= FindFit[Partition[d1, 2], fun, {a, b}, x] > > > IGeneral::ovfl: Overflow occurred in computation. >> > > General::ovfl: Overflow occurred in computation. >> > > General::ovfl: Overflow occurred in computation. >> > > General::stop: Further output of General::ovfl will be suppressed \ > during this calculation. >> > > FindFit::nrlnum: The function value <<1>> is not a list of real \ > numbers with dimensions {59} at {a,b} = {-1.80801,-5.23877}. > > Out[422]= {a -> -1.80801, b -> -5.23877} > > I have not been able to obtain a reasonable fit to your data even using > 'manual' values for 'a' and 'b' in 'fun'. Maybe fit to > a different function? > > Tom Dowling > > On Fri, May 16, 2008 at 10:33 AM, dh <dh at metrohm.ch> wrote: > >> >> >> Hi Navri, >> >> NonlinearRegression as well as FindFit (should be used instead of the >> >> older NonlinearFit) seem to work as expected: >> >> fun=Exp[(1-Exp[a*(1-Exp[-b*x])])*(Exp[-b*x])/(1-Exp[-b*x])]; >> >> >> d1={1,0.00,2,0.00,3,0.00,4,0.00,5,0.00,6,0.00,7,0.00,8,0.00,9,0.00,10,0.00,11,0.00,12,0.00,13,0.00,14,0.00,15,0.00,16,0.00,17,0.00,18,0.00,19,0.00,20,0.00,21,0.00,22,0.00,23,0.00,24,0.00,25,0.00,26,0.00,27,0.00,28,0.00,29,0.00,30,0.00,31,0.00,32,0.00,33,0.00,34,0.00,35,0.00,36,0.00,37,0.00,38,0.00,39,0.00,40,0.00,42,0.00,44,0.00,46,0.00,48,0.00,50,0.00,52,0.04,54,0.06,56,0.08,58,0.09,60,0.16,65,0.24,70,0.32,75,0.43,80,0.49,85,0.58,90,0.80,95,0.91,100,1.00,105,1}; >> >> FindFit[d1,fun,{a,b},x] >> >> NonlinearRegress[d1, fun, {a, b}, x] >> >> Could it bee that you had a syntax error? >> >> hope this helps, Daniel >> >> >> >> >> >> Navri Navri Bintang wrote: >> >> > Hi, >> >> > >> >> > I have a problem with nonlinear regression in Mathematica. I want to fit >> my data (below) to this following equation: >> >> > >> >> > y = Exp[(1-Exp[a*(1-Exp[-b*x])])*(Exp[-b*x])/(1-Exp[-b*x])] >> >> > >> >> > and I would like to find a and b values and also determined r-squared >> value. >> >> > >> >> > I try to use NonlinearRegression/NonlinearFit code, but its not working, >> I hope someone could help me >> >> > >> >> > Thanks a lot >> >> > >> >> > DATA: >> >> > x y >> >> > 1 0.00 >> >> > 2 0.00 >> >> > 3 0.00 >> >> > 4 0.00 >> >> > 5 0.00 >> >> > 6 0.00 >> >> > 7 0.00 >> >> > 8 0.00 >> >> > 9 0.00 >> >> > 10 0.00 >> >> > 11 0.00 >> >> > 12 0.00 >> >> > 13 0.00 >> >> > 14 0.00 >> >> > 15 0.00 >> >> > 16 0.00 >> >> > 17 0.00 >> >> > 18 0.00 >> >> > 19 0.00 >> >> > 20 0.00 >> >> > 21 0.00 >> >> > 22 0.00 >> >> > 23 0.00 >> >> > 24 0.00 >> >> > 25 0.00 >> >> > 26 0.00 >> >> > 27 0.00 >> >> > 28 0.00 >> >> > 29 0.00 >> >> > 30 0.00 >> >> > 31 0.00 >> >> > 32 0.00 >> >> > 33 0.00 >> >> > 34 0.00 >> >> > 35 0.00 >> >> > 36 0.00 >> >> > 37 0.00 >> >> > 38 0.00 >> >> > 39 0.00 >> >> > 40 0.00 >> >> > 42 0.00 >> >> > 44 0.00 >> >> > 46 0.00 >> >> > 48 0.00 >> >> > 50 0.00 >> >> > 52 0.04 >> >> > 54 0.06 >> >> > 56 0.08 >> >> > 58 0.09 >> >> > 60 0.16 >> >> > 65 0.24 >> >> > 70 0.32 >> >> > 75 0.43 >> >> > 80 0.49 >> >> > 85 0.58 >> >> > 90 0.80 >> >> > 95 0.91 >> >> > 100 1.00 >> >> > 105 1 >> >> > >> >> > >> >> > Rgds, >> >> > Navri >> >> > >> >> > >> >> > >> >> > >> >> > >> >> >> >> >

**References**:**Re: Asking NonlinearRegression***From:*dh <dh@metrohm.ch>

**Re: Re: Asking NonlinearRegression**

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**Re: Re: Asking NonlinearRegression**

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