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Re: standard errors and confidence intervals in NonlinearRegress

• To: mathgroup at smc.vnet.net
• Subject: [mg67302] Re: [mg67112] standard errors and confidence intervals in NonlinearRegress
• From: Darren Glosemeyer <darreng at wolfram.com>
• Date: Sat, 17 Jun 2006 04:36:19 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

At 01:09 AM 6/9/2006 -0400, dantimatter wrote:

>hello all,
>
>I'm trying to figure out the relationship between the aymptotic
>standard error and the confidence interval spit out by
>NonlinearRegress.  They seem to be related by a constant, but I don't
>understand the significance of it.  Is there a simple interpretation to
>the aymptotic standard error?
>
>Thanks,
>Dan


The standard errors and confidence intervals in nonlinear regression are 
based on asymptotic normality, so the parameter estimates follow 
StudentTDistribution. With a confidence level of c, a model with p 
parameters and a data set with n data points, the confidence interval is

Estimate +/- Quantile[StudentTDistribution[n - p], 1-(1-c)/2]*AsymptoticSE


The default value of c is .95, so the constant is 
Quantile[StudentTDistribution[n - p], .975].


Darren Glosemeyer
Wolfram Research