TREND() does use the method of least squares.
The details of calculation (prior to Excel 2003) are that the
coefficients returned by LINEST() are calculated as
b = (X' * X)^-1 * X' * y
where y is the vector of known_y's, X is the matrix of known_x's
supplemented with a column of ones, unless const is specified as False,
X' is the transpose of X, ^-1 is matrix inversion, and all
multiplications are matrix multiplications.
TREND() then returns
Xn * b
where Xn is the matrix of new_x's, supplemented with a column of ones,
unless const is specified as False.
Excel 2003 uses singular value decomposition of X to permit calculation
of b with much less cancellation than is involved in forming
(X' * X)^-1 * X' * y
just as DEVSQ(data)/COUNT(data) is a numerically better way to calculate
than VARP(data) in versions prior to Excel 2003
http://groups.google.com/[email protected]
Jerry
