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Understanding Multiple Regression Analysis: Causality, Bias, and Fit Measures

Learn about omitted variable bias, causality in regression analysis, OLS estimator, fit measures, and the sampling distribution of the OLS estimator. Explore topics such as multicollinearity, control experiments, and interpretation of coefficients.

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Understanding Multiple Regression Analysis: Causality, Bias, and Fit Measures

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Presentation Transcript

  1. Chapter 6 Introduction toMultiple Regression

  2. Outline • Omitted variable bias • Causality and regression analysis • Multiple regression and OLS • Measures of fit • Sampling distribution of the OLS estimator

  3. Omitted Variable Bias (SW Section 6.1)

  4. Omitted variable bias, ctd.

  5. Omitted variable bias, ctd.

  6. Omitted variable bias, ctd.

  7. Omitted variable bias, ctd.

  8. The omitted variable bias formula:

  9. Digression on causality and regression analysis

  10. Ideal Randomized Controlled Experiment • Ideal: subjects all follow the treatment protocol – perfect compliance, no errors in reporting, etc.! • Randomized: subjects from the population of interest are randomly assigned to a treatment or control group (so there are no confounding factors) • Controlled: having a control group permits measuring the differential effect of the treatment • Experiment: the treatment is assigned as part of the experiment: the subjects have no choice, so there is no “reverse causality” in which subjects choose the treatment they think will work best.

  11. Back to class size:

  12. Return to omitted variable bias

  13. The Population Multiple Regression Model (SW Section 6.2)

  14. Interpretation of coefficients in multiple regression

  15. The OLS Estimator in Multiple Regression (SW Section 6.3)

  16. Example: the California test score data

  17. Multiple regression in STATA

  18. Measures of Fit for Multiple Regression (SW Section 6.4)

  19. SER and RMSE

  20. R2and

  21. R2and , ctd.

  22. Measures of fit, ctd.

  23. The Least Squares Assumptions for Multiple Regression (SW Section 6.5)

  24. Assumption #1: the conditional mean of u given the included X’s is zero.

  25. The Sampling Distribution of the OLS Estimator (SW Section 6.6)

  26. Multicollinearity, Perfect and Imperfect (SW Section 6.7)

  27. The dummy variable trap

  28. Perfect multicollinearity, ctd.

  29. Imperfect multicollinearity

  30. Imperfect multicollinearity, ctd.

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