1. Chapter 5 Regression with a Single Regressor: Hypothesis Tests and Confidence Intervals

2. 2 Regression with a Single Regressor: Hypothesis Tests and Confidence Intervals (SW Chapter 5)

3. 3 But first… a big picture view (and review)

4. 4 Object of interest:  1 in,

5. 5 Hypothesis Testing and the Standard Error of (Section 5.1)

6. 6

7. 7 Formula for SE( )

8. 8

9. 9 Summary: To test H 0 :  1 =  1,0 v. H 1 :  1   1,0,

10. 10 Example: Test Scores and STR, California data

11. 11

12. 12 Confidence Intervals for  1 (Section 5.2)

13. 13

14. 14 A concise (and conventional) way to report regressions:

15. 15 OLS regression: reading STATA output

16. 16 Summary of Statistical Inference about  0 and  1 :

17. 17 Regression when X is Binary (Section 5.3)

18. 18 Interpreting regressions with a binary regressor

19. 19

20. 20 Summary: regression when X i is binary (0/1)

21. 21 Heteroskedasticity and Homoskedasticity, and Homoskedasticity-Only Standard Errors (Section 5.4)

22. 22

23. 23 Homoskedasticity in a picture:

24. 24 Heteroskedasticity in a picture:

25. 25 A real-data example from labor economics: average hourly earnings vs. years of education (data source: Current Population Survey):

26. 26 The class size data:

27. 27 So far we have (without saying so) assumed that u might be heteroskedastic.

28. 28 What if the errors are in fact homoskedastic?

29. 29

30. 30 We now have two formulas for standard errors for

31. 31 Practical implications…

32. 32 Heteroskedasticity-robust standard errors in STATA

33. 33 The bottom line:

34. 34 Some Additional Theoretical Foundations of OLS (Section 5.5)

35. 35

36. 36 The Extended Least Squares Assumptions

37. 37 Efficiency of OLS, part I: The Gauss-Markov Theorem

38. 38 The Gauss-Markov Theorem, ctd.

39. 39 Efficiency of OLS, part II:

40. 40 Some not-so-good thing about OLS

41. 41 Limitations of OLS, ctd.

42. 42 Inference if u is Homoskedastic and Normal: the Student t Distribution (Section 5.6)

43. 43

44. 44

45. 45 Practical implication:

46. 46 Summary and Assessment (Section 5.7)