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MathGroup Archive 2005

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Re: A Problem with the NonlinearFit?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg61792] Re: [mg61757] A Problem with the NonlinearFit?
  • From: Chris Chiasson <chris.chiasson at gmail.com>
  • Date: Sun, 30 Oct 2005 00:43:21 -0400 (EDT)
  • References: <200510280725.DAA08743@smc.vnet.net> <acbec1a40510280710j15cef80aqda039e50d9f4541@mail.gmail.com> <002201c5dc57$305094e0$0100a8c0@Axel>
  • Sender: owner-wri-mathgroup at wolfram.com

Well Axel,

Fooling around with ridiculous curve fitting ideas like setting the model to be:
a*c^(b*x)=y
and trying a fit both in "c space" and in regular space did not result
in a better model, as I hoped. In c space, the total error is
minimized near c = 1, because the locations of the data points are not
very dependant on x (the y values are semi-infinite). This yields a
bad fit. In normal space, the fit gives results analogous the the
exponential fit because allowing a variable base (c) doesn't really
add more independent degrees of freedom to the model.

Thinking back to a problem I had in an Automotive Powertrain class,
where we needed to back out the coefficient of (form) drag from a
vehicle coast down test, I realized the problems that many people were
having with their fits resulted from ignoring the physics of the
problem. So, with Mathematica, I solved the differential equation of
the vehicle free body being decelerated by the wind force (which was
dependant on the square of the vehicle speed). It was a difficult
equation to solve and the solution looked ugly, but Mathematica
handled it. Afterwards, NonlinearRegress easily stitched a curve that
really followed the data and told me what the coefficient of drag was.

What I am trying to say is that your model should reflect the physics
of your problem very well. After that, regression can possibly tell
you what the values and confidence intervals are for the constants in
your system.

So, what kind of system are you modeling, etc?

<snip>

--
http://chrischiasson.com/contact/chris_chiasson


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