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MathGroup Archive 2005

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Re: Correct errors on fit parameter ?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg55424] Re: Correct errors on fit parameter ?
  • From: dh <dh at metrohm.ch>
  • Date: Wed, 23 Mar 2005 05:34:36 -0500 (EST)
  • References: <d1omp4$na4$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,
It seems to me that you and "NonlinearRegress" are trying to solve two 
different problems.

A) Given points about which nothing more is known.
B) Given points with known values of errors.

Then try to fit paramters of some function and try to guess the errors 
of the parameters.

The fact that "NonlinearRegress" can make a weighted fit and that it is 
statistically  correct to take 1/variance as the weight, does not would 
allow you to input errors.

By the way, what do you want to do with the errors of the parameters? If 
you intend to use the fitted function for further calculations I hope 
you are aware that you will not only need the variances but also the 
covarinaces, what does not exactly simplify the subsequent calculations.

Daniel

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.
> 
> Using the Regress command makes no difference.
> 
> Through other examples I have found that the errors are taking into account correctly to find the correct value of the fit parameters but NOT to compute 
> the statistical error on the fit parameter.
> 
> I presume other experimental scientist must have faced this problem when analyzing data.
> 
> Any suggestions ?
> 
> Thanks,
> 
> Peter
> 


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