Problems with NonlinearRegress

• To: mathgroup at smc.vnet.net
• Subject: [mg32204] Problems with NonlinearRegress
• From: Martin Duemling <mduemlin at quasar.phys.vt.edu>
• Date: Sat, 5 Jan 2002 00:10:53 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,
I have the following problem:
I try to do a Lorentzian-fit with my data. It works very good if the datas are
simulated and very close to the ideal curve. But as soon as I use my real data
(they have still Lorentzian shape) I don't get any result which makes sense
(See example).

Maybe somebody can help, Thank you.
Martin

Input:

Clear["Global`*"]
Needs["Statistics`NonlinearFit`"]
data = ReadList["test4.txt", {Number, Number}];
fit2 = NonlinearRegress[data, \
Base + Amplitude/((1 + ((((freq - wo))/gamma))^2)),
freq, {{Base, 0.8}, {Amplitude, 1}, {wo, 9}, {gamma, 0.009}},
Weights -> Equal, MaxIterations -> 100, WorkingPrecision -> 16,
RegressionReport
-> {ParameterTable,  ANOVATable, EstimatedVariance},
AccuracyGoal -> 16, PrecisionGoal -> 16, ShowProgress -> True]

Output
Iteration:1 ChiSquared:37.193  Parameters:{0.8, 1., 9., 0.009}

Iteration:2 ChiSquared:37.5594  Parameters:{0.863029, 17.9184, 11.1608,
0.0648881}

Iteration:3 ChiSquared:38.099  Parameters:{0.878984, 46.7423, 16.506,
0.117541}

Iteration:4 ChiSquared:38.7406  Parameters:{0.900703, 29.929, 22.6742,
0.096431}

Iteration:5 ChiSquared:38.7053  Parameters:{0.901547, -25.3515, 44.1125,
0.0073759}
...
And than the values are staying approx constant

For comparison the correct values are (other fit program):
Base= 0.65
Amplitude= 1.31
wo= 8.82
gamma= 0.008

```

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