calculating mean prediction bands

*To*: mathgroup at smc.vnet.net*Subject*: [mg110513] calculating mean prediction bands*From*: "Thiesse, Matthew Dean" <matthew.thiesse at nist.gov>*Date*: Tue, 22 Jun 2010 07:00:34 -0400 (EDT)

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