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