My reply is at the bottom.
Jerry W. Lewis said:
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
My *EXACT* formula is =LINEST(Y14:Y50,A14:Q50,1,1)
Is this hardcoded limit documented anywhere? Does Excel 2003 handle a
larger number of channels?
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 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
In what form is the result of this "Analysis of collinearity" presented to
the Excel user? What statistic in the matrix returned by LINEST should I look
at to know that the X matrix is "nearing" collinearity.
If the predictors exhibit near collinearity, the solution is to remove
predictors from the group of predictors that are nearly collinear. Is there
an easy way to identify which predictors form a group that is nearly
collinear?