In article <[EMAIL PROTECTED]>,
Kenmlin <[EMAIL PROTECTED]> wrote:
>Whoever told you how to do this is completely wrong. For multiple regression,
>you must find all parameters simultaneously. This is because X1, X2, and X3
>are NOT independent.
This is incorrect. In fact, the standard Gaussian elimination
or Cholesky approach to solving the normal equations in fact
regresses y and x2, ..., xk on x1, regresses the residuals on
x2.1, then on x3.12, ..., until the coefficient of y on xk is
obtained. Then one substitutes back.
The lack of independence is that one needs to use the regression
of the penultimate xk on the last x(k-1) to correct the value
given for the coefficient of x(k-1).
In the simpler example below, one obtains a regression
coefficient c2 of y on x2 and a regression r12 of x1 on
x2. This means that R2 = x1 - r12*x2. So the equation
is, apart from constant terms,
y = B1*(x1-r12*x2) + c2*x2,
or
y = B1*x1 + (c2-B1*r12)*x2.
>Ken
>>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
>>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? When I have three unknowns
>>how do I get B3? Please format your excellent answer using my
>>little "schedule" jargon.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
[EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558
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