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Unformatted text preview: 3. Multiple Regression Analysis: EstimationAlthough bivariate linear regressions are sometimes useful, they are often unrealisticSLR.4, that all factors affecting y are uncorrelated with x, is often violatedMULTIPLE REGRESSION ANALYSIS allows us to explicitly control factors to obtain a Ceteris Paribus situationthis allows us to infer causality better than a bivariate regression 3. Multiple Regression Analysis: Estimationmultiple regression analysis includes more variables, therefore explaining more of the variation in ymultiple regression analysis can also “incorporate fairly general functional form relationshipsit’s more flexible 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 GaussMarkov Theorem 3.1 Motivation for Multiple Regression Take the bivariate regression: (ie) u P 1 + + = lot ty Moviequali β βwhere u takes into other factors affecting movie quality, such as the charactersfor this regression to be valid, we have to assume that characters are uncorrelated with the plot – a poor assumptionsince u affects Plot, this estimate is biased and we can’t isolate the Ceteris Paribus effect of plot on movie quality 3.1 Motivation for Multiple Regression Take the multiple variable regression: (ie) u P 2 1 + + + = Character lot ty Moviequali β β βwe 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 ) 3.1 Motivation for Multiple Regression”Multiple regression analysis is also useful for generalizing functional relationships between variables”: (ie) u 2 2 1 + + + = Study Study Exammark β β βhere study time can impact exam mark in a direct and/or quadratic fashionthis quadratic equation effects how the parameters are interpretedyou cannot examine study’s effect on exammark by holding study 2 constant 3.1 Motivation for Multiple Regressionthe change in exammark due to an extra hour of studying therefore becomes: (ie) 2 2 1 Study Study Exammark β β + = ∆ ∆the impact is no longer a constant (B 1 )....
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 Spring '09
 Priemaza
 Econometrics, Linear Regression, Regression Analysis, independent variables, Ordinary least squares, Moviequality

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