1. CHAPTER 8 MULTIPLE REGRESSION ANALYSIS: THE PROBLEM OF INFERENCE
ECONOMETRICS I
CHAPTER 8 MULTIPLE REGRESSION ANALYSIS: THE PROBLEM OF 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 the normal distribution with zero mean and constant variance σ2.
With normality assumption we find that the OLS estimators of the partial regression coefficients are best linear unbiased estimators (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 ABOUT INDIVIDUAL REGRESSION COEFFICIENTS

9. 8.4 HYPOTHESIS TESTING ABOUT INDIVIDUAL REGRESSION COEFFICIENTS

10. 8.4 HYPOTHESIS TESTING ABOUT INDIVIDUAL REGRESSION COEFFICIENTS

11. 8.4 HYPOTHESIS TESTING ABOUT INDIVIDUAL REGRESSION COEFFICIENTS

12. 8.4 HYPOTHESIS TESTING ABOUT INDIVIDUAL REGRESSION COEFFICIENTS

13. 8.4 HYPOTHESIS TESTING ABOUT INDIVIDUAL REGRESSION COEFFICIENTS

14. 8.5 TESTING THE OVERALL SIGNIFICANCE OF 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 Multiple Regression in 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

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 ESS and hence the R2 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 (− )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

51. 8.7 RESTRICTED LEAST SQUARES: TESTING LINEAR EQUALITY RESTRICTIONS

52. 8.7 RESTRICTED LEAST SQUARES: TESTING LINEAR EQUALITY RESTRICTIONS

53. 8.7 RESTRICTED LEAST SQUARES: TESTING LINEAR EQUALITY RESTRICTIONS

54. 8.7 RESTRICTED LEAST SQUARES: TESTING LINEAR EQUALITY RESTRICTIONS

55. General F Testing

56. General F Testing

57. General F Testing

58. General F Testing

59. General F Testing

60. General F Testing

61. General F Testing

62. General F Testing

63. General F Testing

64. 8.8 TESTING FOR STRUCTURAL OR PARAMETER STABILITY OF REGRESSION MODELS: THE CHOW TEST

65. 8.8 TESTING FOR STRUCTURAL OR PARAMETER STABILITY OF REGRESSION MODELS: THE CHOW TEST

66. 8.8 TESTING FOR STRUCTURAL OR PARAMETER STABILITY OF REGRESSION MODELS: THE CHOW TEST

67. 8.8 TESTING FOR STRUCTURAL OR PARAMETER STABILITY OF REGRESSION MODELS: THE CHOW TEST

68. 8.8 TESTING FOR STRUCTURAL OR PARAMETER STABILITY OF REGRESSION MODELS: THE CHOW TEST

69. 8.8 TESTING FOR STRUCTURAL OR PARAMETER STABILITY OF REGRESSION MODELS: THE CHOW TEST

70. 8.8 TESTING FOR STRUCTURAL OR PARAMETER STABILITY OF REGRESSION MODELS: THE CHOW TEST

71. 8.8 TESTING FOR STRUCTURAL OR PARAMETER STABILITY OF REGRESSION MODELS: THE CHOW TEST

72. 8.8 TESTING FOR STRUCTURAL OR PARAMETER STABILITY OF REGRESSION MODELS: THE CHOW TEST

73. 8.8 TESTING FOR STRUCTURAL OR PARAMETER STABILITY OF REGRESSION MODELS: THE CHOW TEST

74. 8.8 TESTING FOR STRUCTURAL OR PARAMETER STABILITY OF REGRESSION MODELS: THE CHOW TEST

75. 8.8 TESTING FOR STRUCTURAL OR PARAMETER STABILITY OF REGRESSION MODELS: THE CHOW TEST

76. 8.8 TESTING FOR STRUCTURAL OR PARAMETER STABILITY OF REGRESSION MODELS: THE CHOW TEST

77. 8.8 TESTING FOR STRUCTURAL OR PARAMETER STABILITY OF REGRESSION MODELS: THE CHOW TEST

78. 8.8 TESTING FOR STRUCTURAL OR PARAMETER STABILITY OF REGRESSION MODELS: THE CHOW TEST

79. 8.8 TESTING FOR STRUCTURAL OR PARAMETER STABILITY OF REGRESSION MODELS: THE CHOW TEST