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MathGroup Archive 2005

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Re: Correct errors on fit parameter ?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg55445] Re: Correct errors on fit parameter ?
  • From: Antti Penttilä@smc.vnet.net
  • Date: Wed, 23 Mar 2005 05:35:00 -0500 (EST)
  • Organization: University of Helsinki
  • References: <d1omp4$na4$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Bruyndonckx P wrote:
> Is there an easy way to obtain the correct statistical error on fitted parameters ?
> 
> I tried the following simple example :
> 
> x=Range[5];
> y=x^2;
> yerror={10,10,10,10,10}
> 
> NonlinearRegress[Transpose[{x, y}], a + b*xx + c*xx^2, {xx}, {a, b, c}, Weights -> 1/yerror^2, RegressionReport -> {ParameterCITable}]
> 
> 
> The asymptotic error and confidence intervals are of the order of 10^-15 !!!!.   Obviously the weights (errors or uncertainty on the data) are not taken 
> into account when computing the error on the parameter.  It seems that the SE is only based on the residuals, which are nearly 0 is this case because the 
> fit is 
> perfect.  Changing the value of the errors has no impact on the standard errors of the fit parameters.

The weigths are not "errors or uncertainty on the data" as you say it. The only say about the weight or influence that the residual matching the weight should have. All the residuals are zero, so there is no error in your data.


-- 
   Antti Penttilä       Antti.I.Penttila at helsinki.fi.removethis
     Researcher                     Observatory
tel. +358 50 5240968        00014 University of Helsinki


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