Hi all
I am trying to put together a linear regression introduction for
people who are not STATs package users. I have from my notes that the
variance covariance matrix of the parameter estimates is given by
b =sigma^2*( inverse of (X'X))
I have generated 100 random observations in STATA on one output
(systolic bp) and 3 covariates age height and weight.
I now have the information matrix G ( = X'X)
= 100 16000 8499 6502
16000 2599528 1362556 1044625
8499 1362556 727177 555648
6502 1044625 555648 434728
(where the 100 is clearly from the column of 1s)
and it's inverse (approximately correct when I checked)
1.83414 -0.00293 -0.01564 -0.00040
-0.00293 0.00003 -0.00001 -0.00001
-0.01564 -0.00001 0.00025 -0.00006
-0.00040 -0.00001 -0.00006 0.00010
and finally half of the variance covariance matrix obtained from STATA
after fitting the 3 parameter model
e(V) height weight age cons
height 0.00102812
weight -0.00040925 0.0095863
age -0.00255601 -0.00229 0.0038852
_cons -0.71278521 -0.600348 -0.015442 70.4014
At this stage, i would expect the entries of matrices 2 and 3 to be
related by a constant, which I would expect to be the MSE (about 6.1).
It clearly isn't that, or any other constant value. Can anyone please
tell me how to get from 2 to 3 freehand?
thanks
Andy
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