Re: Re: Re: regress versus fit - force throughzero/forceconstant term to zero

• To: mathgroup at smc.vnet.net
• Subject: [mg61734] Re: [mg61613] Re: [mg61574] Re: [mg61493] regress versus fit - force throughzero/forceconstant term to zero
• From: ggroup at sarj.ca
• Date: Thu, 27 Oct 2005 05:54:28 -0400 (EDT)
• References: <acbec1a40510192358g44579892k5d78ab545b45e151@mail.gmail.com> <002901c5d556\$c37f97f0\$0401a8c0@achirana> <200510220911.FAA14997@smc.vnet.net> <200510230946.FAA10837@smc.vnet.net> <1154551111.20051027002059@aggarwal.ca>
• Reply-to: ggroup at sarj.ca
• Sender: owner-wri-mathgroup at wolfram.com

```It was Thursday, October 27, 2005 at 12:20 AM, when I wrote:

> On Sunday, October 23, 2005 at 05:46 GMT -0400, Chris Chiasson wrote:
<snip>
>> What is the best way to take into account the variance in the best fit
>> parameters due to the fact that the model might be not 100% correct
>> **and** the fact that each data point is probably not infinitely
>> precise?
<snip>

Sorry, I didn't really answer the question.

The regression is taking the into account all sources of variation in
it's parameter error estimates. If you want to *separate* the
contributions from various sources (ie how much of that variation is
due to an inaccurate model vs noisy data), then your best bet is to
model the noise and the expected form of the inaccuracy (for example
DC offsets). You have to be careful that you don't add so many
parameters that your model can fit any data set. A Bayesian analysis
can help you quantify a model complexity parameter.

If you have an estimate of the error bars (non-uniform) for your data
points, you can also use the Weights option to modify the initial
relative importance given to each data point while performing the
regression.

```

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