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 > > > >

**Follow-Ups**:**Re: Re: Definition of SE (standard error) in LinearRegress and NonlinearRegress***From:*Darren Glosemeyer <darreng@wolfram.com>