Ecological regression

Ecological regression is a statistical technique used especially in political science and history to estimate group voting behavior from aggregate data. For example, if counties have a known Democratic vote (in percentage) D, and a known percentage of Catholics, C, then run the linear regression of dependent variable D against independent variable C. This gives D = a + bC. When C = 1 (100% Catholic) this gives the estimated Democratic vote as a+b. When C = 0 (0% Catholic), this gives the estimated non-Catholic vote as a. For example, if the regression gives D = .22 + .45C, then the estimated Catholic vote is 67% Democratic and the non-Catholic vote is 22% Democratic. The technique has been often used in litigation brought under the Voting Rights Act of 1965 to see how blacks and whites voted.