A Pearson's R of 0.8 is actually *really* tight. With the kind of N that we're looking at here, you don't need to have anywhere near 0.8 to prove that a correlation exists (i.e. that the linear regression line has a slope significantly different from 0). There are at least 200 data points there, and a quick calculation with that R of 0.46 gives a p-value < 1e-6 (less than 1 chance in 1,000,000 that the correlation isn't real). I'm pretty sure I could make that stand up in court.

The corollary suggestion (raised, though certainly hedged, by twslam) that improving FT% (without working on three-point shooting) might have some sort of "halo effect" on three-point shooting seems

*very* questionable to me, however, and certainly this data can't speak to it. You could design a test for that sort of thing in a controlled setting, but I think you'd find it extremely hard to glean box score data to find evidence for that sort of effect.