3210_08_MultReg3-2 - MULTIPLE REGRESSION ANALYSIS STATISTICAL INFERENCE PART I Introductory Econometrics A Modern Approach 5e South-Western Cengage

# 3210_08_MultReg3-2 - MULTIPLE REGRESSION ANALYSIS...

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MULTIPLE REGRESSION ANALYSIS: STATISTICAL INFERENCE, PART I Introductory Econometrics: A Modern Approach, 5e South-Western, Cengage Learning Jeffrey M. Wooldridge 1. Sampling Distributions of the OLS Estimators 2. Testing Hypotheses About a Single Population Parameter 3. Confidence Intervals 4. Testing Single Linear Restrictions 1 1 Recap So far, what do we know how to do with the population modely=β0+β1x1+...+βkxk+u? 2 3 2. Unbiasedness of OLS under MLR.1 to MRL.4. Obtain bias (or at least thedirection) when MLR.4 fails due to an omitted variable.3. Obtain the variances,V ar(ˆβj), under MLR.1 to MLR.5. 4 2 Sampling Distributions of the OLS Estima- tors We now want to test hypotheses about the β j . This means we hypothesize that a population parameter is a certain value, then use the data to determine whether the hypothesis is likely to be false. EXAMPLE: (Motivated by ATTEND.DTA) final = β 0 + β 1 missed + β 2 priGPA + β 3 ACT + u where ACT is the achievement test score. The null hypothesis, that missing lecture has no effect on final exam performance (after accounting for prior MSU GPA and ACT score), is H 0 : β 1 = 0 5 6 7 8 The important part of MLR.6 is that we have now made a very specific distributional assumption for u : the familiar bell-shaped curve: The important part of MLR.6 is that we have now made a very ecific distributional assumption for u : the familiar bell-shaped curve: 0 .1 .2 .3 .4 f(u) 0 u 9 9   • • • 