lect14_2010

lect14_2010 - 1 / 16 Introduction to Econometrics Econ 322...

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Unformatted text preview: 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 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 = + 1 X 1 i + . . . + 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 { , 1 , . . . , k } ? square the intercept parameter ( ) has the same interpretation as before. That is, is the predicted value of y when all of the explanatory variables are set to 0. That is = 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 ( 1 , . . . , 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 X 1 = 0 X 2 = 0 . . . X j- 1 = 0 X j negationslash = 0 X j +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 5 / 16 square Then y = 1 X 1 + . . . + j- 1 X j- 1 + j X j + j +1 X j +1 + . . . + k X k , square Therefore y = j X j keeping all other explanatory variables constant square so that j = y X j keeping all other explanatory variables constant....
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This document was uploaded on 10/26/2011 for the course ECON 327 at Rutgers.

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lect14_2010 - 1 / 16 Introduction to Econometrics Econ 322...

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