The algorithm that LINEST uses (in pre-2003 versions) to calculate
regression coefficients is
=MMULT(MINVERSE(MMULT(TRANSPOSE(x),x)),MMULT(TRANSPOSE(x),y))
where x is the x matrix. Note that the above formula would return
coefficients in the same order as the columns of the x matrix (reverse
of the order of coefficients returned by LINEST). Also note that the x
matrix needs a column of ones to fit an intercept.
The above formula is mathematically exact, but numerically unstable.
With 16+ columns, you may frequently get nonsense because of numerical
problems. Algorithms 75 and 274 from
http://lib.stat.cmu.edu/apstat/
are numerically superior to to the above formula.
Another question to consider is whether you would get anything
meaningful from a regression on 16+ variables even if you had unlimited
numerical accuracy. In typical data situations that I have encountered,
this would grossly overfit the data. You might get more meaningful
information from a stepwise regression or a principal components
analysis to identify primary predictors.
Jerry
