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Understanding Dummy Variables and Regression Analysis in Economics

This presentation covers critical concepts in economics, specifically focusing on dummy variables, hypothesis testing, and multiple regression analysis. Participants will explore examples showcasing the impact of different categories, class years on GPA, and the interaction effects of study hours across majors. The analysis will include evaluations using the F-statistic and discussion on the significance of race as a group, along with the implications of multiple regression results. Essential for students preparing for individual oral presentations.

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Understanding Dummy Variables and Regression Analysis in Economics

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  1. Economics 105: Statistics Go over GH 22 & 23 GH 24 due Monday Individual Oral Presentations … see RAP handout. Dates are Tue April 24th and Thur April 26th in lab. But we can’t fit them all into 75 minutes … so extra sessions to be announced.

  2. Dummy Variable Example (with 2 categories) • E[ GPA | EconMajor = 1] = ? • E[ GPA | EconMajor = 0] = ? • Take the difference to interpret EconMajor

  3. Dummy Variable Example (More than 2 categories) • Model the effect of class year on GPA, controlling for study hours

  4. Interaction Effect Example • Does the effect of study hours on GPA differ by major?

  5. Hypothesis Tests on Several Regression Coefficients • Consider the model (expanding on GH 22) • Is “race” as a group significant?

  6. Hypothesis Tests on Several Regression Coefficients

  7. Hypothesis Tests on Several Regression Coefficients • To test • Use F statistic • Impose the restrictions to get “restricted” terms • m is the number of restrictions • Reject H0 if Intuition?

  8. Hypothesis Tests on Several Regression Coefficients

  9. Hypothesis Tests on Several Regression Coefficients

  10. Hypothesis Tests on Several Regression Coefficients

  11. Multiple Regression: Example where Sign Switches Correlations Rating Age Income Rating 1.000 0.587 0.885 Age 0.587 1.000 0.829 Income 0.885 0.829 1.000 Survey of 75 consumers Rating = rating of likelihood of purchase of a PDA (e.g., palm pilot) on a scale of 1-10, 10 indicating highest likelihood. Age = age in years Income = income in thousands of dollars

  12. Multiple Regression: Example where Sign Switches Regression of Rating on Age Estimate Std Error t Ratio Prob>|t| Intercept 2.067 0.487 4.24 <.0001 Age 0.059 0.009 6.19 <.0001 Regression of Rating on Income Term Estimate Std Error t Ratio Prob>|t| Intercept -0.596 0.352 -1.69 0.0951 Income 0.070 0.004 16.20 <.0001

  13. Multiple Regression: Example where Sign Switches Multiple Regression Estimates Term Estimate Std Err t Ratio Prob>|t| Intercept -0.736 0.295 -2.50 0.0149 Age -0.047 0.008 -5.74 <.0001 Income 0.101 0.006 15.63 <.0001 Conclusions?

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