Dear all
problem solved: !!
On 23 September 2016 at 10:13, Andrew Salmon <[log in to unmask]> wrote:
> 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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