FWL theorem Meaning Concept and Practical Explanation in STATA

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Frisch – Waugh Theorem states that the coefficient of one of the variables in the multiple linear regression model can be obtained by netting off the effect of other variables in the regression model from both dependent and independent variables. • 𝒀=𝒂+𝒃_𝟏 𝑿_𝟏+𝒃_𝟐 𝑿_𝟐+𝒃_𝟑 𝑿_𝟑+𝒆 • The value of 𝑏_1 can be obtained by • Netting off the effect of 𝑋_2 𝑎𝑛𝑑 𝑋_3 from Y • 𝒀=𝒂+𝒃_𝟐 𝑿_𝟐+𝒃_𝟑 𝑿_𝟑+𝒗_𝟏 • Netting off the effect of 𝑋_2 𝑎𝑛𝑑 𝑋_3 from 𝑋_1 • 𝑿_𝟏=𝒂+𝒃_𝟐 𝑿_𝟐+𝒃_𝟑 𝑿_𝟑+𝒗_𝟐 • Now, • 𝒗_𝟏=𝒂′+𝒌𝒗_𝟐+𝒆 • Here, 𝒌 𝒉𝒂𝒕=𝒃_𝟏 𝒉𝒂𝒕 • Time • 0:00 Meaning and Concept • 3:49 STATA practical

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