[R] ANOVA with Weighted LM

[VBMorozov@lbl.gov]

Dear All
I have data in the following format: three columns with X_i, Y_i and SE
(Y_i), for i from 1 to 1000. X is independent variable, Y is explained 
variable (a measurement of some sort) and SE(Y) is standard error of 
measurement of Y, it's different for each Y_i. I'm stuck with the 
following statistics questions on using R and on statistics in general:

I can do anova(lm(Y~X)) to get an estimate of how much variability in Y 
is explained by X and how much is in the residuals. 
But now I want to do weighted linear fit MyLm<-lm(Y~X, weights=1/SE(Y)
^2 ). I think this is a right thing to do, because my Y_i have errors 
on them, and the errors vary greatly for different Y_i. So, if I do 
that, how do I get a "fair" estimate of explained and unexplained 
variability? Since ANOVA doesn't know about weights (or does it?) what 
should I use?

Thank you,
Vlad.


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