Peter N wrote:

....

"Jerry W. Lewis" wrote:


LINEST also returns #REF! when you exceed its hardcoded limit on
predictors. Empirically, that limit appears to be 17 predictors if no
constant is fitted, or 16 predictors and a fitted constant.

As a practical matter I would be very suspicious of the numerical
properties of LINEST solutions long before hitting that hard coded
limit. Perhaps that is why it is there, even though MINVERSE in theory
can invert a 52x52 X'X matrix.

Jerry
....
Is this hardcoded limit documented anywhere? Does Excel 2003 handle a
larger number of channels?


I have not seen it documented, unless you count
http://groups-beta.google.com/group/...daea364dd8957c

Excel 2003 has the same limit.


I have a limited understanding of matrix math, but I understand that the
"Normal Equations" involves inverting the [X'X] matrix. To minimize roundoff
errors in the computation, each vector in the X matrix should first be
shifted (centered about its mean). Hopefully LINEST performs this operation
automatically and transparently.


I do not believe that 2003 centers vectors.

I read the article http://support.microsoft.com/kb/828533#kb3 and Microsoft
acknowledges weakness in numerical methods with LINEST in Excel 2002 and
earlier. This article claims that LINEST has been improved in Excel 2003,
using QR decomposition (I'll have to read up to understand that) resulting in
more robust performance. They also advertise
€¢ Better numeric stability (generally smaller round off errors)
€¢ Analysis of collinearity issues


QR or SV (singular value) decomposition of X is definitely the most
accurate way to go, but there are issues with the 2003 implementation as
well

http://groups-beta.google.com/group/...57dccf7aa83b61

Jerry