Following the discussion here, I thought some scatterplots could be useful. I've put them below the fold so as not to bother those of you who are (justifiably, perhaps) tired of rehashing the 2008 election.
Here's the information in the second map of my earlier post, now expressed as scatterplots:
Each dot on the graphs is a county; the lines are lowess regressions. As you can see, my calculations were not perfect; in particular the formula says that Obama got less than 0% of the nonblack vote in some counties, which can't be right. Rather than correcting those points and putting them at zero, I've left them where they are as an indication of imperfection in the model.
Outside the South, Obama did best among nonblacks in counties with more blacks. Inside the South, he did best among nonblacks in counties with fewer blacks. This has got to be an urban-rural thing as much as anything else.
P.S. I like these scatterplots, but I think the maps are useful too, in particular for shooting down the story that whites in Appalachia were particularly anti-Obama.