Curve Fit Stats

["John Gastineau" <jgastin@imagixx.net>]

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. That tells you how well determined 
the slope is, for instance. The scatter standard deviation measures 
how far away from the fitted line, on average, the points are. That's 
useful too for comparison to the uncertainties of each y measurement. 


However, many graphing  packages, and all graphing calculators, only find 
r or r^2,  the correlation coefficient and coefficient of 
determination, respectively. Now, these two numbers are related to 
the probability that there is any correlation at all between the x and 
y columns.  Nothing more. That doesn't strike me as particularly 
useful, as I already know there is a correlation--that's why I  did 
the experiment. I want to know the details of the correlation. 

Does anyone out there actually use these r or r^2 numbers in curve 
fits? How do your students interpret them? 

What are the statistics that a good graphing package should give you? 

My list is the following:

For a single  column of numbers:

    min
    max
    mean
    std deviation
    number of points
         and optionally, std deviation of the mean

for a curve fit,  be it linear or otherwise:

    equation parameters (slope, intercept,  etc) 
    std errors of  parameters 
    scatter std deviation

The r and r^2 numbers don't play a role in any analysis that I
can think of in physics, so why bother  students with them? 

Again, my question:

Is  there a use for r or r^2 statistics in college or hs physics 
experiments? What? 

Is  there  use  of these commonly calculated values in chemistry or 
bio? 

JEG

John E. Gastineau
304 296 1966
Morgantown, WV 
http://www.imagixx.net/~jgastin
email: jgastin@imagixx.net