Econ 399 Chapter4a - 4 Multiple Regression Analysis...

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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
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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
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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
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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:
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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 : ) , 0 ( ~ 2 N u
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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 assumptions plus a normally distributed error
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4.1 CLM Assumptions
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