Mathematica 9 is now available
Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
2006
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*November
*December
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 2006

[Date Index] [Thread Index] [Author Index]

Search the Archive

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
>>>
>>>
>>>       


  • Prev by Date: Re: How to extract numbers from list elements with text?
  • Next by Date: Re: RE:Beginner--[Please Help]How to get coefficient list issued from a Series Command
  • Previous by thread: Re: Definition of SE (standard error) in LinearRegress and NonlinearRegress
  • Next by thread: Re: convergence checking