Econ 399 Chapter4a - 4 Multiple Regression Analysis...

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Unformatted text preview: 4. Multiple Regression Analysis: Estimation-Most econometric regressions are motivated by a question-ie: Do Canadian Heritage commercials have a positive impact on Canadian identity?-Once a regression has been run, hypothesis tests work to both refine the regression and answer the question-To do this, we assume that the error is normally distributed-Hypothesis tests also assume no statistical issues in the regression 4. Multiple Regression Analysis: Inference 4.1 Sampling Distributions of the OLS Estimators 4.2 Testing Hypotheses about a Single Population Parameter: The t test 4.3 Confidence Intervals 4.4 Testing Hypothesis about a Single Linear Combination of the Parameters 4.5 Testing Multiple Linear Restrictions: The F test 4.6 Reporting Regression Results 4.1 Sampling Distributions of OLS-In chapter 3, we formed assumptions that make OLS unbiased and covered the issue of omitted variable bias-In chapter 3 we also obtained estimates for OLS variance and showed it was smallest of all linear unbiased estimators-Expected value and variance are just the first two moments of B j hat, its distribution can still have any shape 4.1 Sampling Distributions of OLS-From our OLS estimate formulas, the sample distributions of OLS estimators depends on the underlying distribution of the errors-In order to conduct hypothesis tests, we assume that the error is normally distributed in the population-This is the NORMALITY ASSUMPTION: Assumption MLR. 6 (Normality) The population error u is independent of the explanatory variables x 1 , x 2 ,…,x k and is normally distributed with zero mean and variance σ 2 : ) , ( ~ 2 σ N u Assumption MLR. 6 Notes MLR. 6 is much stronger than any of our previous assumptions as it implies: MLR. 4: E(u|X)=E(u)=0 MLR. 5: Var(u|X)=Var(u)= σ 2 Assumptions MLR. 1 through MRL. 6 are the CLASSICAL LINEAR MODEL (CLM) ASSUMPTIONS used to produce the CLASSICAL LINEAR MODEL-CLM assumptions are all the Gauss-Markov 4.1 CLM Assumptions4....
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This note was uploaded on 03/14/2009 for the course ECON ECON 399 taught by Professor Priemaza during the Spring '09 term at University of Alberta.

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Econ 399 Chapter4a - 4 Multiple Regression Analysis...

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