My first thought was to compute a pseudo $R^2$ measure as follows:
ss.dist <- sum(scale(cars$dist, scale=FALSE)^2)
ss.resid <- sum(resid(cars.lo)^2)
Here, we get a value of 0.6814984 ($\approx$
cor(cars$dist, predict(cars.lo))^2), close to what would be obtained from a GAM:
summary(gam(dist ~ speed, data=cars))
This also seems to be in agreement with what S
loess function would return (I don't have S so I can't check by myself) as
Multiple R-squared. For example, using the
airquality R dataset, which looks like the
air data Chambers and Hastie used in the 'white book' (the one that is being referenced in the on-line help for
loess; but that's not the exact same dataset), I got an $R^2$ of 0.8101377 using the above formula. That's pretty in agreement with what Chambers and Hastie reported.
I should note that I didn't find any paper dealing specifically with that (ok, that was just a quick googling), and William Cleveland doesn't speak about $R^2$-like measure in his paper.
However, I wonder if the liberty with which you can choose the degree of smoothing (or window
span) does not preclude any use of $R^2$-based measure.