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Re: calculating mean prediction bands

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  • Subject: [mg110528] Re: calculating mean prediction bands
  • From: Darren Glosemeyer <darreng at>
  • Date: Wed, 23 Jun 2010 01:53:32 -0400 (EDT)

Thiesse, Matthew Dean wrote:
> I have a 3 dimensional grid of data points that I am fitting to a 2 dimensional (second order) polynomial model. I wanted to use the Levenburg-Marquardt method so I used the NonlinearModelFit function with the appropriate options selected. But what I am really interested in is the mean prediction bands associated with the fit. What is the method that Mathematica uses to calculate these prediction bands? Is it an exact or approximate method? Is the method for the 3 dimensional case different from the method for the 2 dimensional case? Are there any other methods available for calculating prediction bands (or confidence bands)?
> Thank you

The method used is very briefly described near the end of

"Tabular results for confidence intervals are given by 
"MeanPredictionConfidenceIntervalTable" and 
"SinglePredictionConfidenceIntervalTable". These results are analogous 
to those for linear models obtained via LinearModelFit, again with 
first-order approximations used for the design matrix.

"MeanPredictionBands" and "SinglePredictionBands" give functions of the 
predictor variables."

The bands use the same formulas as the confidence intervals. The method 
is the same for 2, 3, or more parameters.

Darren Glosemeyer
Wolfram Research

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