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MathGroup Archive 2007

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Re: NonlinearRegress and errors on parameter fit

  • To: mathgroup at smc.vnet.net
  • Subject: [mg78333] Re: [mg78293] NonlinearRegress and errors on parameter fit
  • From: Darren Glosemeyer <darreng at wolfram.com>
  • Date: Thu, 28 Jun 2007 04:33:28 -0400 (EDT)
  • References: <200706270941.FAA01898@smc.vnet.net>

alan.zablocki at gmail.com wrote:
> Dear All
>
> Could someone confirm whether EstimatedVariance is an error on the
> value fitted to a parameter using NonlinearRegress? Example:
>
> In[20]:= << NonLinearRegression`
>
> In[26]:= data = {{0, -1}, {2, 0}, {4, 1}}
>
> Out[26]= {{0, -1}, {2, 0}, {4, 1}}
>
> In[27]:= NonlinearRegress[data, a x + b, {a, b}, x]
>
> Out[27]= {BestFitParameters -> {a -> 0.5, b -> -1.},
>
>
>  EstimatedVariance -> 1.35585*10^-31
>
> I have shown all the working and results. Lastly why only one error on
> both a and b?
>
> If this is not the error on a and b, how can I obtain it?
>
> Alan
>
>   

The parameter errors are the Asymptotic SE values given in the 
ParameterCITable and ParameterTable RegressionReport values. The square 
root of EstimatedVariance is a component of these standard errors. Here 
is one way to obtain the values.

In[1]:= << NonlinearRegression`

In[2]:= data = {{0, -1}, {2, 0}, {4, 1}};

In[3]:= tab = NonlinearRegress[data, a x + b, {a, b}, x,
          RegressionReport -> ParameterCITable]

Out[3]= {ParameterCITable ->     Estimate   Asymptotic SE   CI        }
                                                      -16
                             a   0.5        1.30185 10      {0.5, 0.5}

                                                      -16
                             b   -1.        3.36137 10      {-1., -1.}

In[4]:= (ParameterCITable /. tab)[[1, All, 2]]

                   -16            -16
Out[4]= {1.30185 10   , 3.36137 10   }

Of course, in this particular example the data would fit the function 
exactly and the non-zero errors are just due to numerical error.


Darren Glosemeyer
Wolfram Research


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