321_09_slides7

# 321_09_slides7 - Multiple Regression Chapter 3 Part II Econ...

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Multiple Regression Chapter 3 Part II Econ 321 Introduction to Econometrics Econ 321-Stéphanie Lluis 1

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Outline Multiple Regression Interpretation of the Results Omitting variables Adding Irrelevant variables Multicollinearity Properties of OLS in the k-variable Regression model Econ 321-Stéphanie Lluis 2 Chapter 3 part I Chapter 3 part II
Multicollinearity The relationship between the explanatory variable X and the dependent variable Y is not always accurately reflected in the coefficient of X. It depends on which other X ’s are included or not in the equation. Multicollinearity is the presence of very strong linear relationship between two or more explanatory variables and can lead the regression estimates to be unreliable.

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Example of Multicollinearity We want to explain a person’s height by means of foot length. The dependent variable is Height, and the explanatory variables are Right and Left, the length of the right foot and the left foot, respectively. What can occur when we regress Height on both Right and Left?
Example of Multicollinearity It is likely that there is a large correlation between height and foot size, so we would expect this regression equation to do a good job. The R 2 value will probably be large. But what about the coefficients of Right and Left?

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The coefficient we will get for Right indicates that the right foot’s effect on Height in addition to the effect of the left foot. But after the effect of Left on Height has already
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## This note was uploaded on 07/11/2011 for the course ECON 321 taught by Professor Louis during the Fall '09 term at Waterloo.

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321_09_slides7 - Multiple Regression Chapter 3 Part II Econ...

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