Chapter 7 Hypothesis Tests and Confidence Intervals in Multiple Regression.

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Presentation transcript:

Chapter 7 Hypothesis Tests and Confidence Intervals in Multiple Regression

2 Outline

3 Hypothesis Tests and Confidence Intervals for a Single Coefficient in Multiple Regression (SW Section 7.1)

4 Example: The California class size data

5 Standard errors in multiple regression in STATA

6 Tests of Joint Hypotheses (SW Section 7.2)

7 Tests of joint hypotheses, ctd.

8 Why can’t we just test the coefficients one at a time?

9 Suppose t 1 and t 2 are independent (for this calculation).

10

11 The F-statistic

12 The F-statistic testing  1 and  2 :

13 Large-sample distribution of the F-statistic

14

15 Computing the p-value using the F-statistic:

16 F-test example, California class size data:

17

18 The “restricted” and “unrestricted” regressions

19 Simple formula for the homoskedasticity-only F-statistic:

20 Example:

21 The homoskedasticity-only F-statistic – summary

22 Digression: The F distribution

23 The F q,n–k–1 distribution:

24 Another digression: A little history of statistics…

25 A little history of statistics, ctd…

26 Summary: the homoskedasticity-only F- statistic and the F distribution

27 Summary: testing joint hypotheses

28 Testing Single Restrictions on Multiple Coefficients (SW Section 7.3)

29 Testing single restrictions on multiple coefficients, ctd.

30 Method 1: Rearrange (“transform”) the regression

31 Rearrange the regression, ctd.

32 Method 2: Perform the test directly

33 Confidence Sets for Multiple Coefficients (SW Section 7.4)

34 Joint confidence sets ctd.

35

36 Confidence set based on inverting the F-statistic

37 An example of a multiple regression analysis – and how to decide which variables to include in a regression…

38 A general approach to variable selection and “model specification”

39 Digression about measures of fit…

40 Back to the test score application:

41 More California data…

42 Digression on presentation of regression results

43

44 Summary: Multiple Regression

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