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Lecture 6 - LECTURE 6 MULTIPLE REGRESSION MODEL Multiple...

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LECTURE 6: MULTIPLE REGRESSION MODEL Multiple variables affect the dependent variable Example: (Trivariate) Linear Population Regression Function (with Fixed Regressors): E(Y i |X) = β 0 + β 1 X i1 + β 2 X i2 Or Y i = β 0 + β 1 X i1 + β 2 X i2 + ε i Where E( ε i ) = 0 Note: E(Y|X) still gives the average value of Y for the fixed values of the X variables. Note: Still linear regression model (remember linear in parameters) What is different? β 1 , β 2 are partial regression coefficients β 1 measures the change in the mean value of Y per unit change of X 1 , holding X 2 constant. β 2 measures the change in the mean value of Y per unit change of X 2 , holding X 1 constant. GOAL: To find out what part of the change in the average value of Y can be directly attributed to X 1 and what part to X 2 Example: Returns to Education and Experience E(Y i |X) = 7 + .12X 1i + 0.09X 2i where Y = log (hourly wage) X 1 = education
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