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Analyzing Interactions Between Independent Variables in Regression Models

This analysis explores interactions between independent variables, focusing on binary and continuous variables. It examines coefficients in interactions of two binary variables and binary-continuous pairings, illustrating their regression lines. The example highlights the relationship between Test Score, STR (Student-Teacher Ratio), and HiEL (High EL). Additionally, we test hypotheses about interaction effects, assessing non-linear influences on test scores with respect to different STR levels and interactions between PctEL (Percentage of English Learners) and STR. Regression function interpretations are supported by visual plots.

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Analyzing Interactions Between Independent Variables in Regression Models

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  1. Interactions Between Independent Variables (SW Section 8.3)

  2. (a) Interactions of two binary vars

  3. Interpreting the coefficients

  4. Example

  5. (b) Interactions of continuous and binary variables

  6. Binary-continuous interactions: the two regression lines

  7. Example: TestScore, STR, and HiEL (=1 if PctEL >10)

  8. Testing Hypotheses about Interaction Effects

  9. (c) Interactions of continuous vars

  10. Example: TestScore, STR, PctEL

  11. Testing Hypotheses about Interaction Effects

  12. Application: Nonlinear Effects on Test Scores of the Student-Teacher Ratio (SW Section 8.4)

  13. 1. Are there different effects for different STR levels?

  14. 2. Are there interactions between PctEL and STR?

  15. What is a good “base” specification?

  16. Tests of joint hypotheses:

  17. Interpreting the regression functions via plots:

  18. Comparing the regressions with interactions:

  19. Application: Berg Dale & Krueger (QJE, 2002)

  20. Application: Berg Dale & Krueger (QJE, 2002)

  21. Application: Berg Dale & Krueger (QJE, 2002)

  22. Application: Berg Dale & Krueger (QJE, 2002)

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