Re: Linearity of Independent varialbles in Multiple Regression.

yogi wrote:
> Hi Everybody,
> I am working on a multiple regression problem. I wanted to
> know is there any way to check the linearity of Independent variables
> using sas.

I have NOT used SAS for multiple regression since about the last
time I invited Jim Goodnight to an Interntional Symposium in 1978.
in which he presented a paper about SAS. :-) I don't think Jim had
the time to present any paper in ASA statistical meetings since.

If you used the multiple regression PROC in SAS, I would think that
if the program does not blow up, the linear independence had already
been checked and verified to be ok.

For any computer program one way to check for independence and
get plenty of additional information in return is to do an eigenvalue-
engenvector decomposition of the X'X matrix (including a column of
1s as one of the basis vectors for a model with an intercept, and the
other X's are the independent variable), then you not only checked
linear independence (eigenvalues all positive), but you would also
have obtained the Principal Components decomposition of the X's.

Otherwise, as Herman had already pointed out, the nonsingularity
of the X'X matrix is all that's required for linear independence of the
X's.

-- Bob.

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