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
- References:
- A Problem with the NonlinearFit?
- From: "Axel Ligon" <ligonap@web.de>
- A Problem with the NonlinearFit?