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- Path: sparky!uunet!munnari.oz.au!bunyip.cc.uq.oz.au!topaz.ucq.edu.au!bakera
- From: bakera@topaz.ucq.edu.au (Alan Baker)
- Newsgroups: sci.math.stat
- Subject: Regression - Partition Inverse Problem
- Message-ID: <1992Sep14.111943.12371@topaz.ucq.edu.au>
- Date: 14 Sep 92 11:19:42 AET
- Organization: University of Central Queensland, Australia
- Lines: 27
-
- Hi,
- I have a problem that I have not been able to sort out and would
- certainly appreciate some help.
-
- In the regression model y = X*B + e
- by writing y = x*B1 + Xs*Bs + e
- where x is a T-vector, B1 a scalar, Xs a T*(K-1) matrix and Bs is
- a (K-1) vector.
-
- The result var(B1) = sigma^2 / summation(x - xbar)^2(1-R^2)
- can be derived (but how it is derived is the problem I cannot solve)
- by applying partitioned inversion to X'X
- which comes from
- var-cov(b) = sigma^2(X'X)^-1
-
- R^2 is the coefficient of determination obtained by regressing x on
- Xs.
-
-
- This is a problem that has annoyed me for some days and if any one can
- shed some light on the matter I would certainly appreciate their help.
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- Alan Baker AARNET: BAKER@COVAX.COMMERCE.UQ.OZ.AU
- Department of Commerce TELEPHONE: Work 07 365 6686
- University of Queensland, QLD 4072 International +617 365 6686
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