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

• To: mathgroup at smc.vnet.net
• Subject: [mg70322] Re: Definition of SE (standard error) in LinearRegress and NonlinearRegress
• From: "Ray Koopman" <koopman at sfu.ca>
• Date: Fri, 13 Oct 2006 01:30:03 -0400 (EDT)
• References: <200609300913.FAA13235@smc.vnet.net><egl2ub\$4oi\$1@smc.vnet.net>

```Shouldn't both of those be multiplied by Sqrt[r.r/(n-p)],
where r is the vector of residuals at the minimum,
n is the number of data points,
and p is the number of parameters?

Darren Glosemeyer wrote:
> 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
> >
> >

```

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