Why would one wish to avoid multiple linear regression, which is so much
more convenient than the sequence of simple linear regressions alluded to
below? Two possible reasons occur to mind:
(1) for the challenge of finding out how to do it (in which case I
wouldn't want to spoil your fun!);
(2) this is an assigned homework problem (in which case it would be a
shame to spoil your instructor's intent).
On Sat, 12 Feb 2000 [EMAIL PROTECTED] wrote:
> I am told that I can solve for these three unknowns (B1, B2 and B3) by
> doing simple linear regression to obtain "residuals"; from the
> residuals come the unknowns. For example, I know that with just two
> unknowns (B1 and B2) in:
>
> y = B0 + B1 * x1 + B2 * x2 + e [1]
>
> I can obtain B1 after the following schedule of calculations:
>
> regress y on x2 which yields R1 (residual one)
> regress x1 on x2 which yields R2
> regress R1 on R2 which leads to a slope value that is B1
>
> Now the pitiful questions: how do I get B2?
Same way you got B1.
> When I have three unknowns how do I get B3?
I take it you refer to a model like [2]:
y = B0 + B1*x1 + B2*x2 + B3*x3 + e [2]
A straightforward extension of the schedule above applies.
Presumably you are aware that B1 and B2 in [2] are in general not equal
to B1 and B2 in [1]. Your schedule shows one way of partialling out x2
in [1] to estimate B1; in [2] you will partial out both x2 and x3 in
estimating B1, etc.
> Please format your excellent answer using my little "schedule" jargon.
------------------------------------------------------------------------
Donald F. Burrill [EMAIL PROTECTED]
348 Hyde Hall, Plymouth State College, [EMAIL PROTECTED]
MSC #29, Plymouth, NH 03264 603-535-2597
184 Nashua Road, Bedford, NH 03110 603-471-7128
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