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)



--
   O__  ---- Peter Dalgaard             Ă˜ster Farimagsgade 5, Entr.B
  c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
 (*) \(*) -- University of Copenhagen   Denmark      Ph:  (+45) 35327918
~~~~~~~~~~ - (p.dalga...@biostat.ku.dk)              FAX: (+45) 35327907

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