Hello all, can help clarify something? According to R's lm() doc:
Non-NULL weights can be used to indicate that different observations have different variances (with the values in weights being inversely *proportional* to the variances); or equivalently, when the elements of weights are positive integers w_i, that each response y_i is the mean of w_i unit-weight observations (including the case that there are w_i observations equal to y_i and the data have been summarized).
Since the idea here is *proportion*, not equality, shouldn't the vectors of weights x, 2*x give the same result? And yet they don't, standard errors differs:
> summary(lm(c(1,2,3,1,2,3)~c(1,2.1,2.9,1.1,2,3),weight=rep(1,6)))$sigma [1] 0.07108323 > summary(lm(c(1,2,3,1,2,3)~c(1,2.1,2.9,1.1,2,3),weight=rep(2,6)))$sigma [1] 0.1005269
So what if I know a-priori, observation A has variance 2 times bigger than observation B? Both weights=c(1,2) and weights=c(2,4) (and so on) represent very well this knowledge, but we get different regression (since sigma is different).
Also, if we do the same thing with a glm() model, than we get a lot of other differences like in the deviance.
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