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

download ECONOMETRICS I CHAPTER 8 MULTIPLE REGRESSION ANALYSIS: THE PROBLEM OF INFERENCE Textbook: Damodar N. Gujarati (2004) Basic Econometrics, 4th edition, The.

of 79

  • date post

    16-Dec-2015
  • Category

    Documents

  • view

    296
  • download

    7

Embed Size (px)

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

  • Slide 1
  • ECONOMETRICS I CHAPTER 8 MULTIPLE REGRESSION ANALYSIS: THE PROBLEM OF INFERENCE Textbook: Damodar N. Gujarati (2004) Basic Econometrics, 4th edition, The McGraw-Hill Companies
  • Slide 2
  • 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).
  • Slide 3
  • 8.1 THE NORMALITY ASSUMPTION ONCE AGAIN
  • Slide 4
  • Slide 5
  • 8.2 EXAMPLE 8.1: CHILD MORTALITY EXAMPLE REVISITED
  • Slide 6
  • Slide 7
  • 8.3 HYPOTHESIS TESTING IN MULTIPLE REGRESSION: GENERAL COMMENTS
  • Slide 8
  • 8.4 HYPOTHESIS TESTING ABOUT INDIVIDUAL REGRESSION COEFFICIENTS
  • Slide 9
  • Slide 10
  • Slide 11
  • Slide 12
  • Slide 13
  • Slide 14
  • 8.5 TESTING THE OVERALL SIGNIFICANCE OF THE SAMPLE REGRESSION
  • Slide 15
  • The Analysis of Variance Approach to Testing the Overall Significance of an Observed Multiple Regression: The F Test
  • Slide 16
  • Slide 17
  • Slide 18
  • Slide 19
  • Testing the Overall Significance of a Multiple Regression: The F Test
  • Slide 20
  • Slide 21
  • An Important Relationship between R 2 and F
  • Slide 22
  • Slide 23
  • 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.
  • Slide 24
  • An Important Relationship between R 2 and F
  • Slide 25
  • Testing the Overall Significance of a Multiple Regression in Terms of R 2
  • Slide 26
  • The Incremental or Marginal Contribution of an Explanatory Variable
  • Slide 27
  • Slide 28
  • Slide 29
  • This F value is highly significant, as the computed p value is 0.0008.
  • Slide 30
  • The Incremental or Marginal Contribution of an Explanatory Variable
  • Slide 31
  • Slide 32
  • Slide 33
  • Slide 34
  • Slide 35
  • 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).
  • Slide 36
  • The Incremental or Marginal Contribution of an Explanatory Variable
  • Slide 37
  • Slide 38
  • Slide 39
  • Slide 40
  • 8.6 TESTING THE EQUALITY OF TWO REGRESSION COEFFICIENTS
  • Slide 41
  • Slide 42
  • Slide 43
  • Slide 44
  • Slide 45
  • 8.7 RESTRICTED LEAST SQUARES: TESTING LINEAR EQUALITY RESTRICTIONS
  • Slide 46
  • Slide 47
  • Slide 48
  • Slide 49
  • Slide 50
  • Slide 51
  • Slide 52
  • Slide 53
  • Slide 54
  • Slide 55
  • General F Testing
  • Slide 56
  • Slide 57
  • Slide 58
  • Slide 59
  • Slide 60
  • Slide 61
  • Slide 62
  • Slide 63
  • Slide 64
  • 8.8 TESTING FOR STRUCTURAL OR PARAMETER STABILITY OF REGRESSION MODELS: THE CHOW TEST
  • Slide 65
  • Slide 66
  • Slide 67
  • Slide 68
  • Slide 69
  • Slide 70
  • Slide 71
  • Slide 72
  • Slide 73
  • Slide 74
  • Slide 75
  • Slide 76
  • Slide 77
  • Slide 78
  • Slide 79