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Chapter 8

Chapter 8. Nonlinear Regression Functions. Nonlinear Regression Functions (SW Chapter 8). The TestScore – STR relation looks linear (maybe)…. But the TestScore – Income relation looks nonlinear. Nonlinear Regression Population Regression Functions – General Ideas (SW Section 8.1).

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Chapter 8

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  1. Chapter 8 Nonlinear Regression Functions

  2. Nonlinear Regression Functions(SW Chapter 8)

  3. The TestScore – STR relation looks linear (maybe)…

  4. But the TestScore – Income relation looks nonlinear...

  5. Nonlinear Regression Population Regression Functions – General Ideas (SW Section 8.1)

  6. The general nonlinear population regression function

  7. Nonlinear Functions of a Single Independent Variable (SW Section 8.2)

  8. 1. Polynomials in X

  9. Example: the TestScore – Income relation

  10. Estimation of the quadratic specification in STATA

  11. Interpreting the estimated regression function:

  12. Interpreting the estimated regression function, ctd:

  13. Estimation of a cubic specification in STATA

  14. Summary: polynomial regression functions

  15. 2. Logarithmic functions of Y and/or X

  16. The three log regression specifications:

  17. I. Linear-log population regression function

  18. Linear-log case, continued

  19. Example: TestScore vs. ln(Income)

  20. The linear-log and cubic regression functions

  21. II. Log-linear population regression function

  22. Log-linear case, continued

  23. III. Log-log population regression function

  24. Log-log case, continued

  25. Example: ln( TestScore) vs. ln( Income)

  26. Example: ln( TestScore) vs. ln( Income), ctd.

  27. The log-linear and log-log specifications:

  28. Summary: Logarithmic transformations

  29. Other nonlinear functions (and nonlinear least squares) (SW App. 8.1)

  30. Negative exponential growth

  31. Nonlinear Least Squares

  32. Interactions Between Independent Variables (SW Section 8.3)

  33. (a) Interactions between two binary variables

  34. Interpreting the coefficients

  35. Example: TestScore, STR, English learners

  36. (b) Interactions between continuous and binary variables

  37. Binary-continuous interactions: the two regression lines

  38. Binary-continuous interactions, ctd.

  39. Interpreting the coefficients

  40. Example: TestScore, STR, HiEL(=1 if PctEL 10)

  41. Example, ctd: Testing hypotheses

  42. (c) Interactions between two continuous variables

  43. Interpreting the coefficients:

  44. Example: TestScore, STR, PctEL

  45. Example, ctd: hypothesis tests

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