Frisch–Waugh–Lovell theorem
Theorem in statistics and econometrics
Frisch–Waugh–Lovell theorem
In statistics and econometrics, the Frisch–Waugh–Lovell (FWL) theorem is a property of ordinary least squares estimators. Named for econometricians Ragnar Frisch, Frederick V. Waugh, and Michael C. Lovell, the theorem states that estimates of multiple regression coefficients depend only on the unique variation of each explanatory variable. Ordinary least squares is a method of estimating coefficients in a linear regression where a single dependent variable is modeled as a linear function of one or more explanatory variables. The Frisch–Waugh–Lovell theorem states that, in a linear regression fitted by least squares, each explanatory variable's coefficient reflects the relationship between the dependent variable and the part of that explanatory variable which is not linearly related to the other explanatory variables. Specifically, each explanatory variable can be decomposed into two parts: the part linearly related to the other explanatory variables, and a residual component. Then, that...
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