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Regression with Single Regressor: Hypothesis Testing & Confidence Intervals

Understand hypothesis testing, standard error, confidence intervals, OLS regression, binary regressors, heteroskedasticity, Gauss-Markov theorem in OLS, Student t distribution, and practical implications.

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Regression with Single Regressor: Hypothesis Testing & Confidence Intervals

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

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

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

  4. Object of interest: 1 in,

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

  6. Formula for SE( )

  7. Summary: To test H0: 1 = 1,0 v. H1: 11,0,

  8. Example: Test Scores and STR, California data

  9. Confidence Intervals for 1(Section 5.2)

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

  11. OLS regression: reading STATA output

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

  13. Regression when X is Binary(Section 5.3)

  14. Interpreting regressions with a binary regressor

  15. Summary: regression when Xi is binary (0/1)

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

  17. Homoskedasticity in a picture:

  18. Heteroskedasticity in a picture:

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

  20. The class size data:

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

  22. What if the errors are in fact homoskedastic?

  23. We now have two formulas for standard errors for

  24. Practical implications…

  25. Heteroskedasticity-robust standard errors in STATA

  26. The bottom line:

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

  28. The Extended Least Squares Assumptions

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

  30. The Gauss-Markov Theorem, ctd.

  31. Efficiency of OLS, part II:

  32. Some not-so-good thing about OLS

  33. Limitations of OLS, ctd.

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

  35. Practical implication:

  36. Summary and Assessment (Section 5.7)

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