Re: NonlinearRegress and errors on parameter fit
- To: mathgroup at smc.vnet.net
- Subject: [mg78330] Re: NonlinearRegress and errors on parameter fit
- From: Bill Rowe <readnewsciv at sbcglobal.net>
- Date: Thu, 28 Jun 2007 04:31:56 -0400 (EDT)
On 6/27/07 at 5:41 AM, alan.zablocki at gmail.com wrote: >Could someone confirm whether EstimatedVariance is an error on the >value fitted to a parameter using NonlinearRegress? No, the estimated variance is not an error bound on the estimated parameters. When you do a regression analysis you assume the data is of the form model + error. The estimated variance is the estimate of the variance for the error term, that is the stuff left after you subtract out the model being fitted. >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 The model you are fitting in the example above is linear in both parameters a and b. When you are fitting a linear model, it is definitely better to use linear regression rather than non-linear regression. >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? Estimates for confidence bounds of the parameters are usually computed using Student's T statistics and the estimated variance. I don't recall the exact formula and I am not at my desk where I could easily look it up. My suggestion though would be to get a good text on regression analysis which will cover this and many other issues of importance when doing this kind of analysis. -- To reply via email subtract one hundred and four