The Frisch–Waugh–Lovell theorem states that if the regression we are concerned with is:
where and are and respectively and where and are conformable, then the estimate of will be the same as the estimate of it from a modified regression of the form:
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.
- Frisch, Ragnar; Waugh, Frederick V. (1933). "Partial Time Regressions as Compared with Individual Trends". Econometrica 1 (4): 387–401. JSTOR 1907330.
- Lovell, M. (1963). "Seasonal Adjustment of Economic Time Series and Multiple Regression Analysis". Journal of the American Statistical Association 58 (304): 993–1010. doi:10.1080/01621459.1963.10480682.
- Mitchell, Douglas W. (1991). "Invariance of results under a common orthogonalization". Journal of Economics and Business 43 (2): 193–196. doi:10.1016/0148-6195(91)90018-R.
- Lovell, M. (2008). "A Simple Proof of the FWL Theorem". Journal of Economic Education 39 (1): 88–91. doi:10.3200/JECE.39.1.88-91.