[R] naive "collinear" weighted linear regression

[Peter Dalgaard]

Mauricio O Calvao wrote:

> Unfortunately you eschewed answering objectively any of my questions; I insist
> they do make sense. Don't mention the data are perfect; this does not help to
> make any progress in understanding the choice of convenient summary info the lm
> method provides, as compared to what, in my humble opinion and in this specific
> particular case, it should provide: the covariance matrix of the estimated
> coefficients...

The point is that R (as well as almost all other mainstream statistical 
software) assumes that a "weight" means that the variance of the 
corresponding observation is the general variance divided by the weight 
factor. The general variance is still determined from the residuals, and 
if they are zero to machine precision, well, there you go. I suspect you 
  get closer to the mark with glm, which allows you to assume that the 
dispersion is known:

 > summary(glm(y~x,family="gaussian"),dispersion=0.3^2)

or

 > summary(glm(y~x,family="gaussian",weights=1/error^2),dispersion=1)



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