Hi all --
Jon Cryer writes
correctly about the approach to Anthony's question. I've prepared a
more
specific reply (see way below at the end of this message) with
details of how to create the Regression Models to answer the
question.
But Jon
writes:
By the way, if you are
using Excel you are out of luck. I am told that
Excel is not
programmed
to do least squares with no intercept.
It really is possible
to use Excel with the "no intercept (or no constant) " if we understand
where
the ERROR EXISTS. If anyone wants a detailed example to show
where the ERROR IS IN EXCEL
when the no intercept is used, I will be glad
to send the example. The reason there is an ERROR is
due
to the programmer's knowing that IF HE HAS THE CORRECT TOTAL SUM OF
SQUARES, AND IF
HE HAS THE CORRECT ERROR SUM OF SQUARES, THEN THE CORRECT
REGRESSION SUM OF
SQUARES CAN BE COMPUTED FROM:
REGRESSION
SUM OF SQUARES = TOTAL SUM OF SQUARES MINUS ERROR SUM OF
SQUARES
HOWEVER, IN EXCEL, WHEN THE "NO INTERCEPT" OPTION IS
"CHECKED", THE WRONG TOTAL SUM OF SQUARES
IS USED, SO EVEN THOUGH THE
ERROR SUM OF SQUARES IS CORRECT, THE REGRESSION SUM OF SQUARES IS
WRONG. THE PROGRAMMER USED THE TOTAL SUM OF SQUARES FROM THE
"DEFAULT"
OPTION WHEN HE/SHE SHOULD HAVE USED THE TOTAL SUM OF SQUARES OF
THE DEPENDENT VARIABLE.
LET ME KNOW
IF YOU WANT THE EXAMPLE SENT AS AN EXCEL ATTACHMENT.
--JOE
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There are some secondary issues to be considered
here.
a. If the
regression is multi-variant, there may be some problems in the inversion of
the X'X matrix because of large size of the matrix and the correlation
matrix may have some error. This arises because the X matrix cannot be
centered with this type of regression, and (X"X)^-1 is prone to
numerical errors when there is a large offset. I have tested some data sets
on this regression, but have not been able to determine the extent of error
here. There is no StRD data set with 100 decimal digit accuracy available to
determine the extent of error.
b. Under normal LS regression both the sum
of squares of the residuals is minimized and the sum of the residuals are
set to be zero. Under LS regression through the origin, only the sum of
squares of the residuals is minimized, and the sum of the residuals is not
zero. This may be an important issue.
DAHeiser
