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MathGroup Archive 2000

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Re: How to use BestFitParameters?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg24297] Re: How to use BestFitParameters?
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Fri, 7 Jul 2000 00:11:37 -0400 (EDT)
  • Organization: Universitaet Leipzig
  • References: <8k0v83$q8s@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

I assume your data named p, and I will user formfun as function.

formfun = a/Sqrt[d^2 + (x1 - w0)^2];

fitres=BestFitParameters /. NonlinearRegress[
                              p, formfun, {x1}, {a, d, w0},
                              MaxIterations -> 200, 
                              RegressionReport -> BestFitParameters
                             ];

Now you can use the results in a plot
by

Plot[
  Evaluate[formfun/. fitres],
  {x1,First[p][[1]],Last[p][[1]]},
   Epilog-> Point /@ p
  ]

I have assumed that your p data are ordered.

Regards
  Jens


rob wrote:
> 
> p is a list of data pairs { {x1,y1}, {x2,y2}, ....} and when I fit
> this data to a function Mathematica does a pretty good job of doing the fit:
> 
> NonlinearRegress[p, a/Sqrt[d^2 + (x1 - w0)^2], {x1}, {a, d, w0},
>   MaxIterations -> 200, RegressionReport -> BestFitParameters]
> 
> gives this as an output:
> {BestFitParameters -> {a -> 1.07061, d -> 0.300272, w0 -> 28.8068}}
> 
> I know it is pretty a pretty good fit to the data because I can use
> another program like Excel to plot the curve using these parameters
> and display it next to the data.  It sure would be nice to do this in
> Mathematica without going to an outside program.  I've tried things but I
> can't seem to be able to get to the parameters a, d and w0.  I can't
> even list them.  For example,  I'd like to display the number
> d/Sqrt[w0^2-d^2]. So I tried this:
> 
> d/Sqrt[w0^2-d^2] /. %
> 
> All I get is the formula in symbolic form.
> 
> Can someone here provide some relief?
> 
> Thanks, Rob


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