calculating mean prediction bands
in [Mathematica]
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From: Thiesse, Matthew Dean on 22 Jun 2010 07:00 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
From: Darren Glosemeyer on 23 Jun 2010 01:54 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 http://reference.wolfram.com/mathematica/tutorial/StatisticalModelAnalysis.html "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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