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### Transcript of ECONOMETRICS I CHAPTER 8 MULTIPLE REGRESSION ANALYSIS: THE PROBLEM OF INFERENCE Textbook: Damodar N....

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• ECONOMETRICS I CHAPTER 8 MULTIPLE REGRESSION ANALYSIS: THE PROBLEM OF INFERENCE Textbook: Damodar N. Gujarati (2004) Basic Econometrics, 4th edition, The McGraw-Hill Companies
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• 8.1 THE NORMALITY ASSUMPTION ONCE AGAIN We continue to assume that the u i follow the normal distribution with zero mean and constant variance 2. With normality assumption we find that the OLS estimators of the partial regression coefficients are best linear unbiased estimators (BLUE).
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• 8.1 THE NORMALITY ASSUMPTION ONCE AGAIN
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• 8.2 EXAMPLE 8.1: CHILD MORTALITY EXAMPLE REVISITED
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• 8.3 HYPOTHESIS TESTING IN MULTIPLE REGRESSION: GENERAL COMMENTS
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• 8.4 HYPOTHESIS TESTING ABOUT INDIVIDUAL REGRESSION COEFFICIENTS
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• 8.5 TESTING THE OVERALL SIGNIFICANCE OF THE SAMPLE REGRESSION
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• The Analysis of Variance Approach to Testing the Overall Significance of an Observed Multiple Regression: The F Test
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• Testing the Overall Significance of a Multiple Regression: The F Test
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• An Important Relationship between R 2 and F
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• where use is made of the definition R 2 = ESS/TSS. Equation on the left shows how F and R 2 are related. These two vary directly. When R 2 = 0, F is zero ipso facto. The larger the R 2, the greater the F value. In the limit, when R 2 = 1, F is infinite. Thus the F test, which is a measure of the overall significance of the estimated regression, is also a test of significance of R 2. In other words, testing the null hypothesis (8.5.9) is equivalent to testing the null hypothesis that (the population) R 2 is zero.
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• An Important Relationship between R 2 and F
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• Testing the Overall Significance of a Multiple Regression in Terms of R 2
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• The Incremental or Marginal Contribution of an Explanatory Variable
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• This F value is highly significant, as the computed p value is 0.0008.
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• The Incremental or Marginal Contribution of an Explanatory Variable
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• This F value is highly significant, suggesting that addition of FLR to the model significantly increases ESS and hence the R 2 value. Therefore, FLR should be added to the model. Again, note that if you square the t value of the FLR coefficient in the multiple regression (8.2.1), which is (10.6293) 2, you will obtain the F value of (8.5.17).
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• The Incremental or Marginal Contribution of an Explanatory Variable
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• 8.6 TESTING THE EQUALITY OF TWO REGRESSION COEFFICIENTS
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• 8.7 RESTRICTED LEAST SQUARES: TESTING LINEAR EQUALITY RESTRICTIONS
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• General F Testing
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• 8.8 TESTING FOR STRUCTURAL OR PARAMETER STABILITY OF REGRESSION MODELS: THE CHOW TEST
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