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Unformatted text preview: 4. Multiple Regression Analysis: EstimationMost econometric regressions are motivated by a questionie: 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 questionTo do this, we assume that the error is normally distributedHypothesis 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 OLSIn chapter 3, we formed assumptions that make OLS unbiased and covered the issue of omitted variable biasIn chapter 3 we also obtained estimates for OLS variance and showed it was smallest of all linear unbiased estimatorsExpected 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 OLSFrom our OLS estimate formulas, the sample distributions of OLS estimators depends on the underlying distribution of the errorsIn order to conduct hypothesis tests, we assume that the error is normally distributed in the populationThis 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(uX)=E(u)=0 MLR. 5: Var(uX)=Var(u)= σ 2 Assumptions MLR. 1 through MRL. 6 are the CLASSICAL LINEAR MODEL (CLM) ASSUMPTIONS used to produce the CLASSICAL LINEAR MODELCLM assumptions are all the GaussMarkov 4.1 CLM Assumptions4....
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 Spring '09
 Priemaza
 Econometrics, Normal Distribution, Regression Analysis, Errors and residuals in statistics, OLS estimators, Bjhat

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