LECTURE 6: MULTIPLE REGRESSION MODEL •Multiple variables affect the dependent variable •Example: (Trivariate) Linear Population Regression Function (with Fixed Regressors): E(Yi|X) = β0+ β1Xi1+ β2Xi2Or Yi= β0+ β1Xi1+ β2Xi2+ εiWhere E(εi) = 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? •β1, β2are partialregression coefficients •β1measures the change in the mean value of Y per unit change of X1, holding X2constant. •β2measures the change in the mean value of Y per unit change of X2, holding X1constant. •GOAL: To find out what part of the change in the average value of Y can be directly attributed to X1and what part to X2Example: Returns to Education and ExperienceE(Yi|X) = 7 + .12X1i+ 0.09X2iwhere Y = log (hourly wage) X1= education
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