[R] R.squared in Weighted Least Square using the Lm Function

[Prof Brian Ripley]

On Fri, 25 Aug 2006, Charles wrote:

> Hello all,
> I am using the function lm to do my weighted least
> square regression.
> 
> model<-lm(Y~X1+X2, weight=w)
> 
> What I am confused is the r.squared.

What r.squared?  There is no r.squared in that object, but it is 
calculated by the summary method.

> It does not seem that the r.squared for the weighted
> case is an ordinary 1-RSS/TSS.
> What is that precisely?

Precisely that, with weights in the SS.  The code is

    r <- z$residuals
    f <- z$fitted
    w <- z$weights
    if (is.null(w)) {
        mss <- if (attr(z$terms, "intercept"))
            sum((f - mean(f))^2)
        else sum(f^2)
        rss <- sum(r^2)
    } else {
        mss <- if (attr(z$terms, "intercept")) {
            m <- sum(w * f/sum(w))
            sum(w * (f - m)^2)
        }
        else sum(w * f^2)
        rss <- sum(w * r^2)
        r <- sqrt(w) * r
    }
    ans$r.squared <- mss/(mss + rss)

That's the great thing about R: you can answer your own question by 
reading the code for yourself.

> Is the r.squared measure comparable to that obtained
> by the ordinary least square?
> 
> <I also notice that
> model$res is the unweighted residual while
> summary(model)$res  is the weighted residual>

Yes, as documented with added emphasis in ?summary.lm .

-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
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