In econometrics, the Frisch–Waugh–Lovell (FWL) theorem is named after the econometricians Ragnar Frisch, Frederick V. Waugh, and Michael C. Lovell.
The Frisch–Waugh–Lovell theorem states that if the regression we are concerned with is:
where
where
known as the annihilator matrix, or orthogonal projection matrix. This result implies that all these secondary regressions are unnecessary: using projection matrices to make the explanatory variables orthogonal to each other will lead to the same results as running the regression with all non-orthogonal explanators included.