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ECONOMETRICS I

ECONOMETRICS I. CHAPTER 8 MULTIPLE REGRESSION ANALYSIS: THE PROBLEM OF INFERENCE. Textbook: Damodar N. Gujarati (2004)  Basic Econometrics , 4th edition, The McGraw-Hill Companies. 8.1 THE NORMALITY ASSUMPTION ONCE AGAIN.

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ECONOMETRICS I

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  1. ECONOMETRICS I CHAPTER 8 MULTIPLE REGRESSIONANALYSIS: THE PROBLEMOF INFERENCE • Textbook: Damodar N. Gujarati (2004) Basic Econometrics, 4th edition, The McGraw-Hill Companies

  2. 8.1 THE NORMALITY ASSUMPTION ONCE AGAIN • We continue to assume that the ui follow thenormal distribution with zero mean and constant variance σ2. • With normality assumption we findthat the OLS estimators of the partial regression coefficients are best linear unbiasedestimators (BLUE).

  3. 8.1 THE NORMALITY ASSUMPTION ONCE AGAIN

  4. 8.1 THE NORMALITY ASSUMPTION ONCE AGAIN

  5. 8.2 EXAMPLE 8.1: CHILD MORTALITY EXAMPLE REVISITED

  6. 8.2 EXAMPLE 8.1: CHILD MORTALITY EXAMPLE REVISITED

  7. 8.3 HYPOTHESIS TESTING IN MULTIPLE REGRESSION: GENERAL COMMENTS

  8. 8.4 HYPOTHESIS TESTING ABOUTINDIVIDUAL REGRESSION COEFFICIENTS

  9. 8.4 HYPOTHESIS TESTING ABOUTINDIVIDUAL REGRESSION COEFFICIENTS

  10. 8.4 HYPOTHESIS TESTING ABOUTINDIVIDUAL REGRESSION COEFFICIENTS

  11. 8.4 HYPOTHESIS TESTING ABOUTINDIVIDUAL REGRESSION COEFFICIENTS

  12. 8.4 HYPOTHESIS TESTING ABOUTINDIVIDUAL REGRESSION COEFFICIENTS

  13. 8.4 HYPOTHESIS TESTING ABOUTINDIVIDUAL REGRESSION COEFFICIENTS

  14. 8.5 TESTING THE OVERALL SIGNIFICANCEOF THE SAMPLE REGRESSION

  15. The Analysis of Variance Approach to Testing the Overall Significance of an Observed Multiple Regression: The F Test

  16. The Analysis of Variance Approach to Testing the Overall Significance of an Observed Multiple Regression: The F Test

  17. The Analysis of Variance Approach to Testing the Overall Significance of an Observed Multiple Regression: The F Test

  18. The Analysis of Variance Approach to Testing the Overall Significance of an Observed Multiple Regression: The F Test

  19. Testing the Overall Significance of a Multiple Regression: The F Test

  20. Testing the Overall Significance of a Multiple Regression: The F Test

  21. An Important Relationship between R2 and F

  22. An Important Relationship between R2 and F

  23. An Important Relationship between R2 and F where use is made of the definition R2 = ESS/TSS. Equation on the left shows how F and R2 are related. These two vary directly. When R2 = 0, F is zero ipso facto. The larger the R2, the greater the F value. In the limit, when R2 = 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 R2. In other words, testing the null hypothesis (8.5.9) is equivalent to testing the null hypothesis that (the population) R2 is zero.

  24. An Important Relationship between R2 and F

  25. Testing the Overall Significance of a MultipleRegressionin Terms of R2

  26. The “Incremental” or “Marginal” Contribution of an Explanatory Variable

  27. The “Incremental” or “Marginal” Contribution of an Explanatory Variable

  28. The “Incremental” or “Marginal” Contribution of an Explanatory Variable

  29. The “Incremental” or “Marginal” Contribution of an Explanatory Variable This F value is highly significant, as the computed p value is 0.0008.

  30. The “Incremental” or “Marginal” Contribution of an Explanatory Variable

  31. The “Incremental” or “Marginal” Contribution of an Explanatory Variable

  32. The “Incremental” or “Marginal” Contribution of an Explanatory Variable

  33. The “Incremental” or “Marginal” Contribution of an Explanatory Variable

  34. The “Incremental” or “Marginal” Contribution of an Explanatory Variable

  35. The “Incremental” or “Marginal” Contribution of an Explanatory Variable This F value is highly significant,suggesting that addition of FLR to the model significantly increases ESSand hence the R2 value.Therefore, FLR should be added to the model. Again, note that if you square the tvalue 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).

  36. The “Incremental” or “Marginal” Contribution of an Explanatory Variable

  37. The “Incremental” or “Marginal” Contribution of an Explanatory Variable

  38. The “Incremental” or “Marginal” Contribution of an Explanatory Variable

  39. The “Incremental” or “Marginal” Contribution of an Explanatory Variable

  40. 8.6 TESTING THE EQUALITY OF TWO REGRESSION COEFFICIENTS

  41. 8.6 TESTING THE EQUALITY OF TWO REGRESSION COEFFICIENTS

  42. 8.6 TESTING THE EQUALITY OF TWO REGRESSION COEFFICIENTS

  43. 8.6 TESTING THE EQUALITY OF TWO REGRESSION COEFFICIENTS

  44. 8.6 TESTING THE EQUALITY OF TWO REGRESSION COEFFICIENTS

  45. 8.7 RESTRICTED LEAST SQUARES: TESTING LINEAR EQUALITY RESTRICTIONS

  46. 8.7 RESTRICTED LEAST SQUARES: TESTING LINEAR EQUALITY RESTRICTIONS

  47. 8.7 RESTRICTED LEAST SQUARES: TESTING LINEAR EQUALITY RESTRICTIONS

  48. 8.7 RESTRICTED LEAST SQUARES: TESTING LINEAR EQUALITY RESTRICTIONS

  49. 8.7 RESTRICTED LEAST SQUARES: TESTING LINEAR EQUALITY RESTRICTIONS

  50. 8.7 RESTRICTED LEAST SQUARES: TESTING LINEAR EQUALITY RESTRICTIONS

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