       Re: 'NonlinearFit` confusion

• To: mathgroup at smc.vnet.net
• Subject: [mg49889] Re: [mg49844] 'NonlinearFit` confusion
• From: DrBob <drbob at bigfoot.com>
• Date: Thu, 5 Aug 2004 09:21:14 -0400 (EDT)
• References: <200408041446.KAA20105@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Fitting equations to data is always an inexact science. That's the only fundamental you're missing, I think.

Bobby

On Wed, 4 Aug 2004 10:46:20 -0400 (EDT), Klingot <klingot at yahoo.com> wrote:

> I'm trying to fit a sinusoidal function to my data using
> 'NonlinearFit' but it's exhibiting rather odd behaviour. Please see my
> examples below:
>
> EXAMPLE (1).
>**** As a test, I created a list of data from a function of the form y
> = 6 + 2Sin[3 + x] with:
>
> datay = Table [6 + 2Sin[3 + x], {x, -10Pi, 10Pi, 0.05}];
> datax = Table [x, {x, -10Pi, 10Pi, 0.05}];
> data = Table[{datax[[i]], datay[[i]]}, {i, 1, Length[datay]}];
>
> **** Then tested to see whether NonlinearFit would correctly deduce
> the equations parameters with:
>
> NonlinearFit[data, c + a Sin[d + e x], x, {a, c, d,e}]
>
> **** As expected, it gave me '6.+ 2. Sin[3. + 1. x]' ... exactly as
> one would expect :)
>
>
> EXAMPLE (2).
>
> **** Second test, I modified the equation by multiplying x by 5, ie.
> y = 6 + 2Sin[3 + 5x]:
>
> datay = Table [6 + 2Sin[3 + 5 x], {x, -10Pi, 10Pi, 0.05}];
> datax = Table [x, {x, -10Pi, 10Pi, 0.05}];
> data = Table[{datax[[i]], datay[[i]]}, {i, 1, Length[datay]}];
>
> ***** and applied the NonlinearFit as before:
>
> NonlinearFit[data, c + a Sin[d + e x], x, {a, c, d,e}]
>
> ***** but this time I get a wildly innacurate result:    6.000165 +
> 0.025086 Sin[0.0080308 - 0.247967 x]
>
> Specifically, the parameters 'a', 'd' and 'e' are all completely in
> error by orders of magnitude.
>
> I tried extending the range of the data to include more cycles of the
> sinusoid, thereby making it more continuous/monotonic but that made no
> difference.
>
> Am I missing something fundamental here?
>
> Any assistance would be greatly appreciated.
>
> PS: I'm using Mathematica 5.0 on a MAC.
>
>
>

--
DrBob at bigfoot.com
www.eclecticdreams.net

```

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