Higher Gas Prices and Thinner Americans Linked?

Now this would be interesting if it were true.

The report, written by Charles Courtemanche for his doctoral dissertation in health economics, found that the 13 percent rise in obesity between 1979 and 2004 can be attributed to falling pump prices.

I wonder if gas prices and stocks like NutriSystem Inc. (NTRI) negatively correlated? Gas prices already affect casual dining restaurants in a negative way. If you pay more for gas you end up eating less at Ruby Tuesdays (RT) or other casual dining restaurants