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Econ 399 Chapter3a - 3 Multiple Regression Analysis...

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3. Multiple Regression Analysis: Estimation -Although bivariate linear regressions are sometimes useful, they are often unrealistic -SLR.4, that all factors affecting y are uncorrelated with x, is often violated -MULTIPLE REGRESSION ANALYSIS allows us to explicitly control factors to obtain a Ceteris Paribus situation -this allows us to infer causality better than a bivariate regression
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3. Multiple Regression Analysis: Estimation -multiple regression analysis includes more variables, therefore explaining more of the variation in y -multiple regression analysis can also “incorporate fairly general functional form relationships -it’s more flexible
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3. Multiple Regression Analysis: Estimation 3.1 Motivation for Multiple Regression 3.2 Mechanics and Interpretation of Ordinary Least Squares 3.3 The Expected value of the OLS Estimators 3.4 The Variance of the OLS Estimators 3.5 Efficiency of OLS: The Gauss-Markov Theorem
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3.1 Motivation for Multiple Regression Take the bivariate regression: (ie) u P 1 0 lot ty Moviequali -where u takes into other factors affecting movie quality, such as the characters -for this regression to be valid, we have to assume that characters are uncorrelated with the plot – a poor assumption -since u affects Plot, this estimate is biased and we can’t isolate the Ceteris Paribus effect of plot on movie quality
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3.1 Motivation for Multiple Regression Take the multiple variable regression: (ie) u P 2 1 0 Character lot ty Moviequali -we still need to be concerned of u’s effect on character and plot BUT… -by including Character in the regression we ensure we can examine Plot’s effect with Character held constant (B 1 ) -We can also analyze Character’s effect on movie quality with Plot held constant (B 2 )
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3.1 Motivation for Multiple Regression -”Multiple regression analysis is also useful for generalizing functional relationships between variables”: (ie) u 2 2 1 0 Study Study Exammark -here study time can impact exam mark in a direct and/or quadratic fashion -this quadratic equation effects how the parameters are interpreted -you cannot examine study’s effect on exammark by holding study 2 constant
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3.1 Motivation for Multiple Regression -the change in exammark due to an extra hour of studying therefore becomes: (ie) 2 2 1 Study Study Exammark -the impact is no longer a constant (B 1 ).
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