"Together, these variables explain 43 percent of Mr. Trump’s gains over Mr. Romney, just edging out the 41 percent accounted for by the share of non-college whites" in a county, which has been widely cited as the best statistical predictor of a swing to Trump. "The two categories significantly overlap: counties with a large proportion of whites without a degree also tend to fare poorly when it comes to public health. However, even after controlling for race, education, age, sex, income, marital status, immigration and employment, these figures remain highly statistically significant. Holding all other factors constant—including the share of non-college whites—the better physical shape a county’s residents are in, the worse Mr. Trump did relative to Mr. Romney."
The correlation is indicated by the slope of a scatterplot of counties on a graph with health status as the X axis (across the bottom) and change in Republican margin from 2012 as the Y axis. The county dots were scaled by size and colored by region. The colors showed that the Midwest made the big difference for Trump.
The chart on the Economist website is interactive, with data for each county. Here's a screenshot with the cursor on Pike County, Kentucky, in the heart of the Central Appalachian coalfield: