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NonlinearModelFit and "ANOVATable" and "ParameterConfidenceIntervalTable"

• To: mathgroup at smc.vnet.net
• Subject: [mg121278] NonlinearModelFit and "ANOVATable" and "ParameterConfidenceIntervalTable"
• From: HansChristopf <hanschristopf at yahoo.de>
• Date: Wed, 7 Sep 2011 05:39:41 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

Dear friends,

I'm a Mathematica beginner and use in the course of a small project at my college in Germany. I'm using NonlinearModelFit in order to do fit a model to experimental data. I post the code in the following:

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In[1]:= data = {{1., 0.75}, {2., 0.89}, {3., 0.42}, {4., 0.99}, {5.,0.84}, {6., 0.34}, {7., 0.83}, {8., 0.93}, {9., 0.76}, {10.,0.11}};
nlm = NonlinearModelFit[data, {Exp[a + b x^2], b < -1/2}, {{a, 0}, {b, -1}}, x]

In[2]:= nlm[{"ANOVATable", "ParameterConfidenceIntervalTable"}]

During evaluation of In[9]:= FittedModel::constr: The property values {ANOVATable,ParameterConfidenceIntervalTable} assume an unconstrained model. The results for these properties may not be valid, particularly if the fitted parameters are near a constraint boundary. >>

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Now my questions to my problem:

I cannot interpret these results ?

1. Are the results from the ANOVATable the same as the results from the ANOVA (Analysis of Variance) ?
2. Which formulas uses Mathematica to obtain these results ? 
3. How Mathematica calculates the ANOVATable EXACTLY ???????


Greatings, Hans

• Follow-Ups:
  • Re: NonlinearModelFit and "ANOVATable" and "ParameterConfidenceIntervalTable"
    • From: Darren Glosemeyer <darreng@wolfram.com>