Charlie Gardner at Old Urbanist has done the tedious but very useful work of collecting a bunch of metropolitan area statistics, running pairwise regressions, and then publishing the correlation coefficients in an elegant little chart. If you are looking for the correlation between, say, 2010 metropolitan area population and 2010 weighted density (spoiler: it's 0.793.), or the correlation between weighted density and median home value (0.582.), there you go.
He's also got some provocate thoughts on the relationship between weighted density, productivity and affordability.