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Re: Definition of SE (standard error) in LinearRegress and NonlinearRegress

• To: mathgroup at smc.vnet.net
• Subject: [mg70296] Re: [mg70029] Definition of SE (standard error) in LinearRegress and NonlinearRegress
• From: Darren Glosemeyer <darreng at wolfram.com>
• Date: Thu, 12 Oct 2006 05:37:01 -0400 (EDT)
• References: <200609300913.FAA13235@smc.vnet.net>

The standard errors for parameter estimates in linear regression are the 
square roots of the diagonal elements of the parameter covariance matrix

Inverse[Transpose[X].X]

where X is the design matrix for the regression.  The ith row of the 
design matrix contains the values of the basis functions evaluated at 
the ith data point.

The standard errors for parameter estimates in nonlinear regression are 
the square roots of the diagonal elements of the asymptotic parameter 
covariance matrix

Inverse[Transpose[approxX].approxX]

where approxX is an approximate design matrix for the nonlinear model. 
The ith row of the approximate design matrix contains the values of the 
first derivatives of the model function with respect to each of the 
parameters evaluated at the ith data point.


Darren Glosemeyer
Wolfram Research


Seo Ho Youn wrote:
> Hello, all.
>
>  
>
> Can I ask how SE (standard error) in LinearRegress and NonlinearRegress is
> defined or calculated in Mathematica for a multi-parameter least-square fit?
> Or, does anybody know about document (or definition) on SE in Mathematica? I
> haven't been able to find any about how it is calculated in Mathematica.
>
>  
>
> Thank you for your help and have a good day.
>
>  
>
> Seo Ho
>
>