You may be abusing R-squared. A polynomial of degree n-1 will perfectly fit
(R^2=1) n data points, but will typically be useless for any descriptive
purpose, especially for interpolation and extrapolation. To avoid
over-fitting of this type, the quality of the fit is typically measured by
adjusted R-squared, when the polynomial order is not known a-priori. For a
polynomial of order k, the adjusted R-squared is
=1-(1-Rsq)*(1+k/dfe).

Assuming that a 6th order polynomial does describe the data in some
meaningful way, then there is the question of whether the coefficients can be
computed with sufficient accuracy to be meaningful.
http://groups.google.com/group/micro...9a2bb33e6cdbb8
gives 6th degree polynomial problem that looks innocuous, yet is so
numerically difficult, that LINEST in Excel versions prior to 2003 could not
give even single figure accuracy for any coefficient! The higher the order
of the polynomial, the more likely it is that you will have this kind of
numerical difficulty.

Not sure why less than half of the posts in this thread are making it into
the MS Discussion Groups portal.

Jerry

"jnewby72" wrote:

a sixth-order polynomial usually overfits the data

I've used the linest function in the worksheets on multiple sets of
data. I found that I consistently obtained an R² value that was greater
than .99 when I used the sixth order. I understand that the R² value is
a "rating" of how well the function fits the actual data and a rating
of 1 is best.

Some data sets fit fine with a third degree and some required higher
order fitting. I agree that it is probably overkill in some of the data
sets, but I need the precision at times. Thanks for the advice.