Re: Curve Fit Stats

["Richard L. Bowman" <rbowman@bridgewater.edu>]

On Thu, 12 Sep 1996, John Gastineau wrote:

> A question for both HS and college instructors. I've been looking at 
> some graphing and curve fitting packages,  trying to figure out just 
> what statistics should be provided by the software when performing a 
> least-squares fit. 
>
> > From my background, what's useful is the uncertainties on the fitted
> parameters, ie,  the standard error of the slope and intercept, or
> whatever the parameters may be. ....

This raises an interesting point for most of us physicists without a
complicated background in statistics.  I use _Mathematica_ for curve
fitting with our upper-level undergraduate physics majors.  Using the
Regress[] function, one can get a lot of statistical information.
Invariably I find myself going to one of our math profs and asking for
some interpretation of the output.

Directly related to your suggestion for the standard deviation of the
slope and y-intercept, these sound like good things to know, but how does
one calculate them?  It cannot be simply the sum of the square of the
errors divided by one less than the number of data points (as one would do
with a simple list of single values for different trials).  The degrees of
freedom need to be included, too.  Plus what happens when one does
non-linear fits such as log-log and semi-log plots or exponential fits?

I think we probably need R^2 and much more, PLUS a good reference on how
to interpret the whole thing!!

Richard
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Dr. Richard L. Bowman
Dept. of Physics                         e-mail:  rbowman@bridgewater.edu
Bridgewater College                                  phone:  540-828-5441
Bridgewater, VA  22812                                 FAX:  540-828-5479
  "http://www.bridgewater.edu/departments/physics/physics.html";
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