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lect14_2010

# lect14_2010 - Introduction to Econometrics Econ 322 Fall...

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1 / 16 Introduction to Econometrics Econ 322 Fall, 2010 Lecture 14: Multiple Regression October 20, 2010
Topics Covered triangleright Topics Covered The General Linear Regression Model The Least Squares Estimator for the GLRM The GLRM in matrix notation Assumptions of the GLRM Assumption 1 Assumptions 2 and 3 Assumption 4: No perfect multicollinearity Returns to Schooling Example 2 / 16 1. The multiple regression estimator 2. assumptions of the multiple regression model

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The General Linear Regression Model Topics Covered triangleright The General Linear Regression Model The Least Squares Estimator for the GLRM The GLRM in matrix notation Assumptions of the GLRM Assumption 1 Assumptions 2 and 3 Assumption 4: No perfect multicollinearity Returns to Schooling Example 3 / 16 square The GLRM is y i = β 0 + β 1 X 1 i + . . . + β k X ki + epsilon1 i . square Here there are k independent (or explanatory) regressors { X 1 , . . . , X k } that are included in the model in order to try and explain the dependent variable, y . square In this extended version of the linear regression model, how do we interpret the coefficients { β 0 , β 1 , . . . , β k } ? square the “intercept” parameter ( β 0 ) has the same interpretation as before. That is, β 0 is the predicted value of y when all of the explanatory variables are “set to 0”. That is β 0 = E ( y | X 1 = 0 , . . . , X k = 0) .
The GLRM (Cont) Topics Covered triangleright The General Linear Regression Model The Least Squares Estimator for the GLRM The GLRM in matrix notation Assumptions of the GLRM Assumption 1 Assumptions 2 and 3 Assumption 4: No perfect multicollinearity Returns to Schooling Example 4 / 16 square the interpretation of the “slope” ( β 1 , . . . , β k ) parameters are slightly different. Consider the case of a change in X j keeping all other values of the explanatory variables constant. That is, suppose Δ X 1 = 0 Δ X 2 = 0 . . . Δ X j - 1 = 0 Δ X j negationslash = 0 Δ X j +1 = 0 . . . Δ X k = 0

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The GLRM (cont) Topics Covered triangleright The General Linear Regression Model The Least Squares Estimator for the GLRM The GLRM in matrix notation Assumptions of the GLRM Assumption 1 Assumptions 2 and 3 Assumption 4: No perfect multicollinearity Returns to Schooling Example 5 / 16 square Then Δ y = β 1 Δ X 1 + . . . + β j - 1 Δ X j - 1 + β j Δ X j + β j +1 Δ X j +1 + . . . + β k Δ X k , square Therefore Δ y = β j Δ X j keeping all other explanatory variables constant square so that β j = Δ y Δ X j keeping all other explanatory variables constant. square thus we can interpret the slope parameter as a partial regression coefficient square this is very similar to the interpretation of a partial derivative. i.e. the change in y caused by a change in X j keeping all other variables constant
The Least Squares Estimator for the GLRM Topics Covered

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