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MathGroup Archive 2006

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Re: standard errors and confidence intervals in NonlinearRegress

  • To: mathgroup at smc.vnet.net
  • Subject: [mg67331] Re: standard errors and confidence intervals in NonlinearRegress
  • From: "Jason Quinn" <jason.lee.quinn at gmail.com>
  • Date: Sun, 18 Jun 2006 05:13:33 -0400 (EDT)
  • References: <e70f49$rg4$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Darren Glosemeyer wrote:
> The standard errors and confidence intervals in nonlinear regression are
> based on asymptotic normality.

     While the topic is up, I have a similar question about the
standard error (SE), covariance matrix, and correlation matrix reported
by Regress. Do you know how are they calculated? I've been using
Bevington and Robertson's "Data Reduction and Error Analysis for the
Physical Sciences" to calculate them and I cannot reproduce any of the
values given by Mathematica (with or without weighting). For instance,
Bevington says that the error on the fitting parameters for linear
regression are the square roots of the entries in the inverse of the
following matrix (the curvature matrix):

A_jk= Sum[w_i * f_j(x_i) * f_k(x_i)].

Here w_i is the weight of the i-th datum, f_k is the k-th basis
function, and the i-th measurement of the independent variables are
collectively called x_i. The "errors" generated using this formula do
not agree with the SE values reported by Regress (ignoring me doing
something totally stupid, of course). Simiarly with what he calls the
covariance matrix. I've tried working in factors of Sqrt(N), etc.,
thinking is some parent vs sample problem but to no avail. I just don't
know what is being reported by Regress and the documentation doesn't
specify in detail.

Thanks for any insight anybody can give,
Jason Quinn


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