> On 27 Nov 1999 18:44:33 -0800, [EMAIL PROTECTED] wrote:
>
> > Obviously the sets are not related in a linear fashion.
> >
> > I would suggest that a 4th degree polynomial equation best fits the data.
>
> Oh! that should have been obvious....
> Rich Ulrich, [EMAIL PROTECTED]
> http://www.pitt.edu/~wpilib/index.html
I was hoping someone else would respond to the polynomial problem.
Rich did, but I fear his point and his humor may be lost on those who
need it most.
Higher order polynomial fits are problematic in many ways. It would
be VERY unusual for a polynomial of degree higher than two to be a
reasonable model (outside of cases where prior theory specifically
predicts a higher order polynomial). A software package that
recommends fitting a slew of higher order polynomials and then
choosing among them is of dubious statistical quality. To know what
to do instead you would need to know more about the context and
meaning of the data. For example, in my current regression class we
had data on electrical consumption of condominium units of different
sizes. A parabola gave a considerably better fit than a straight line
-- but it also predicted that costs would peak out at a size within
the range of the data and then drop off for larger sizes. This is not
very sensible. My choice was to transform size into 1/size^2. This
was not perfect but it was reasonable for the range of sizes studied
and did not do bizzare things just beyond that range. It gave a model
that rose more slowly for large sizes but never went down with
increasing size.
PS I learned about the dangers of fitting higher order polynomials as
part of a final programming assignment in a Forttran course I took as
an undergraduate at MIT in about 1970. If you have n data points with
distinct x-values, a polynomial of degree n-1 gives a PERFECT fit in
the sense of going right through each point. However, for n more than
a few, it wiggles wildly between points and the matrix algebra croaked
all the canned pckages we had at the time because of multicollinearity
problems. The point of the assignment: having a computer is no
substitute for knowing what you're doing.
_
| | Robert W. Hayden
| | Department of Mathematics
/ | Plymouth State College MSC#29
| | Plymouth, New Hampshire 03264 USA
| * | Rural Route 1, Box 10
/ | Ashland, NH 03217-9702
| ) (603) 968-9914 (home)
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