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Lecture+5+Regression+with+dummy+variables

# Lecture+5+Regression+with+dummy+variables - DummyVariables...

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1 Lecture 5 Regression with dummy variables Dummy Variables A dummy variable is a variable that equals either 1 or 0, representing two groups/categories. Examples : male (= 1 if are male, 0 otherwise), urban (= 1 if in urban area, 0 otherwise), etc. Dummy variables are also called binary variables, for obvious reasons. A Dummy Independent Variable A simple model with one dummy ( d ) independent variable: 0 Y d u α δ = + + If d = 0, then Y= , and hence ( ) u E Y α α + = , If d = 1, then 0 0 ( ) , and hence ( ) Y u E Y α δ α δ = + + = + . The case of d = 0 is the base group, and α is the intercept for the base group; 0 δ is the mean difference in the outcome between the represented group ( d =1) and the base group. Testing the significance of 0 δ tells whether the mean Y’s are significantly different between the two groups. Example : In a study of wage differences between male and female workers of similar age and education, the following equation is estimated using OLS: = + + , W F u α β where W is wage in dollars and F is a dummy that equals 1 if a worker is female and 0 if male, and u is an error term. In the data, the average wage for male W f , and for male is W m . (i) How would you interpret the intercept and slope α β (ii) Based on your interpretation, ˆ ˆ ? and ? α β = = When there is an intercept in the model, the coefficient of a dummy variable always represents the mean difference between the dummy represented group and the based group.

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