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

*To*: mathgroup at smc.vnet.net*Subject*: [mg70355] Re: [mg70322] Re: Definition of SE (standard error) in LinearRegress and NonlinearRegress*From*: Darren Glosemeyer <darreng at wolfram.com>*Date*: Sat, 14 Oct 2006 03:06:50 -0400 (EDT)*References*: <200609300913.FAA13235@smc.vnet.net><egl2ub$4oi$1@smc.vnet.net> <200610130530.BAA01084@smc.vnet.net>

Yes, I left out the variance estimates in the covariance matrix formulas. Thanks for catching this. The covariance formulas should have been r.r/(n-p) Inverse[Transpose[X].X] and r.r/(n-p) Inverse[Transpose[approxX].approxX] Darren Glosemeyer Wolfram Research Ray Koopman wrote: > 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 >>> >>> >>>

**References**:**Re: Definition of SE (standard error) in LinearRegress and NonlinearRegress***From:*"Ray Koopman" <koopman@sfu.ca>