Frisch–Waugh–Lovell theorem
E143681
The Frisch–Waugh–Lovell theorem is a fundamental result in econometrics that shows how the coefficients of a multiple linear regression can be obtained by first partialling out (regressing out) other explanatory variables.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Frisch–Waugh theorem | 1 |
| Frisch–Waugh–Lovell theorem canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1252897 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Frisch–Waugh–Lovell theorem Context triple: [Ragnar Frisch, knownFor, Frisch–Waugh–Lovell theorem]
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A.
Gauss–Markov theorem
The Gauss–Markov theorem is a fundamental result in statistics stating that, under certain conditions, the ordinary least squares estimator is the best linear unbiased estimator (BLUE) of the coefficients in a linear regression model.
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B.
The Probability Approach in Econometrics
The Probability Approach in Econometrics is Trygve Haavelmo’s landmark work that founded modern econometrics by rigorously formulating economic relationships within a probabilistic, statistical framework.
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C.
Lucas critique
The Lucas critique is an influential argument in macroeconomics asserting that policy evaluations based on historical correlations are unreliable because people’s expectations and behavior change systematically when policy rules change.
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D.
William O. Wooldridge
William O. Wooldridge was a United States Army noncommissioned officer who became the first Sergeant Major of the Army, serving as the senior enlisted advisor to the Army’s leadership.
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E.
Berry–Esseen theorem
The Berry–Esseen theorem is a quantitative refinement of the central limit theorem that provides explicit bounds on the rate of convergence of normalized sums of independent random variables to the normal distribution.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Frisch–Waugh–Lovell theorem Target entity description: The Frisch–Waugh–Lovell theorem is a fundamental result in econometrics that shows how the coefficients of a multiple linear regression can be obtained by first partialling out (regressing out) other explanatory variables.
-
A.
Gauss–Markov theorem
The Gauss–Markov theorem is a fundamental result in statistics stating that, under certain conditions, the ordinary least squares estimator is the best linear unbiased estimator (BLUE) of the coefficients in a linear regression model.
-
B.
The Probability Approach in Econometrics
The Probability Approach in Econometrics is Trygve Haavelmo’s landmark work that founded modern econometrics by rigorously formulating economic relationships within a probabilistic, statistical framework.
-
C.
Lucas critique
The Lucas critique is an influential argument in macroeconomics asserting that policy evaluations based on historical correlations are unreliable because people’s expectations and behavior change systematically when policy rules change.
-
D.
William O. Wooldridge
William O. Wooldridge was a United States Army noncommissioned officer who became the first Sergeant Major of the Army, serving as the senior enlisted advisor to the Army’s leadership.
-
E.
Berry–Esseen theorem
The Berry–Esseen theorem is a quantitative refinement of the central limit theorem that provides explicit bounds on the rate of convergence of normalized sums of independent random variables to the normal distribution.
- F. None of above. chosen
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
result in econometrics
ⓘ
theorem ⓘ |
| alsoKnownAs |
Frisch–Waugh–Lovell theorem
ⓘ
surface form:
Frisch–Waugh theorem
|
| appliesTo |
multiple linear regression
ⓘ
ordinary least squares regression ⓘ |
| assumes |
full column rank of regressor matrix
ⓘ
linear regression model ⓘ standard OLS conditions for existence of coefficients ⓘ |
| category |
econometric theorems
ⓘ
linear regression theory ⓘ |
| clarifies |
interpretation of coefficients as effects holding other variables constant
ⓘ
role of control variables in regression ⓘ |
| concerns |
coefficient estimation
ⓘ
partialling out regressors ⓘ regression residuals ⓘ |
| field |
econometrics
ⓘ
statistics ⓘ |
| hasConsequence |
coefficients on a subset of regressors are unaffected by linear transformations of other regressors
ⓘ
enables stepwise computation of OLS estimates ⓘ facilitates graphical partial regression plots ⓘ |
| implies |
equivalence between full OLS and regression on residuals for a subset of variables
ⓘ
invariance of partial regression coefficients to inclusion order of regressors ⓘ |
| mathematicalForm |
Y = X1β1 + X2β2 + u with partitioned regressors
ⓘ
partitioned regression formula ⓘ |
| namedAfter |
Frederick V. Waugh
ⓘ
Michael C. Lovell ⓘ Ragnar Frisch ⓘ |
| relatedTo |
Gauss–Markov theorem
ⓘ
orthogonal projections in Euclidean space ⓘ partial regression ⓘ projection matrix ⓘ residual maker matrix ⓘ |
| shows |
OLS coefficients on a subset of regressors can be obtained after partialling out other regressors
ⓘ
orthogonality of residuals to the space spanned by partialled-out regressors ⓘ regressing residuals of the dependent variable on residuals of regressors yields same coefficients as full regression ⓘ |
| states | β2 from full regression equals OLS of M1Y on M1X2 where M1 is residual maker for X1 ⓘ |
| usedFor |
computational simplification of OLS
ⓘ
derivation of fixed effects estimators ⓘ derivation of within estimators in panel data ⓘ interpretation of partial regression coefficients ⓘ projection of variables onto subspaces ⓘ understanding omitted variable bias ⓘ |
| usedIn |
applied microeconometrics
ⓘ
econometric pedagogy ⓘ panel data analysis ⓘ time series econometrics ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Frisch–Waugh–Lovell theorem Description of subject: The Frisch–Waugh–Lovell theorem is a fundamental result in econometrics that shows how the coefficients of a multiple linear regression can be obtained by first partialling out (regressing out) other explanatory variables.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Frisch–Waugh theorem