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
- References:
- NonlinearRegress and errors on parameter fit
- From: alan.zablocki@gmail.com
- NonlinearRegress and errors on parameter fit