1. Copyright © 2012 Pearson Education, Inc. All rights reserved. Chapter 9 Special Topics in Regression (Optional)

2. Copyright © 2012 Pearson Education, Inc. All rights reserved. Section 9.1 Introduction

3. Copyright © 2012 Pearson Education, Inc. All rights reserved. Section 9.2 Piecewise Linear Regression

4. Copyright © 2012 Pearson Education, Inc. All rights reserved. 9- 4 Figure 9.1 Relationship between compressive strength (y) and water/cement ratio (x)

5. Copyright © 2012 Pearson Education, Inc. All rights reserved. 9- 5 Figure 9.2 Slopes and y-intercepts for piecewise linear regression

6. Copyright © 2012 Pearson Education, Inc. All rights reserved. 9- 6

7. Copyright © 2012 Pearson Education, Inc. All rights reserved. 9- 7 Figure 9.3 SAS piecewise linear regression printout

8. Copyright © 2012 Pearson Education, Inc. All rights reserved. 9- 8 continued on next slide

9. Copyright © 2012 Pearson Education, Inc. All rights reserved. 9- 9 continued on next slide

10. Copyright © 2012 Pearson Education, Inc. All rights reserved. 9- 10

11. Copyright © 2012 Pearson Education, Inc. All rights reserved. 9- 11 Figure 9.4 MINITAB graph of reading scores

12. Copyright © 2012 Pearson Education, Inc. All rights reserved. 9- 12 Figure 9.5 MINITAB analysis of straight-line model for reading score

13. Copyright © 2012 Pearson Education, Inc. All rights reserved. 9- 13 Figure 9.6 MINITAB graph of reading scores, with quadratic model results

14. Copyright © 2012 Pearson Education, Inc. All rights reserved. 9- 14 Figure 9.7 SAS analysis of piecewise linear model for reading score

15. Copyright © 2012 Pearson Education, Inc. All rights reserved. 9- 15 Figure 9.8 MINITAB graph of predicting reading scores using piecewise regression

16. Copyright © 2012 Pearson Education, Inc. All rights reserved. Section 9.3 Inverse Prediction

17. Copyright © 2012 Pearson Education, Inc. All rights reserved. 9- 17

18. Copyright © 2012 Pearson Education, Inc. All rights reserved. 9- 18

19. Copyright © 2012 Pearson Education, Inc. All rights reserved. 9- 19 Figure 9.9 MINITAB analysis of straight-line model, Example 9.3

20. Copyright © 2012 Pearson Education, Inc. All rights reserved. 9- 20 Figure 9.10 MINITAB scatterplot of data and least squares line, Example 9.3

21. Copyright © 2012 Pearson Education, Inc. All rights reserved. Section 9.4 Weighted Least Squares

22. Copyright © 2012 Pearson Education, Inc. All rights reserved. 9- 22

23. Copyright © 2012 Pearson Education, Inc. All rights reserved. 9- 23 Figure 9.11 MINITAB printout of straight-line model, Example 9.4

24. Copyright © 2012 Pearson Education, Inc. All rights reserved. 9- 24 Figure 9.12 MINITAB plot of residuals against road length, x

25. Copyright © 2012 Pearson Education, Inc. All rights reserved. 9- 25

26. Copyright © 2012 Pearson Education, Inc. All rights reserved. 9- 26 Figure 9.13 MINITAB printout of weighted least squares fit, Example 9.4

27. Copyright © 2012 Pearson Education, Inc. All rights reserved. 9- 27 Figure 9.14 MINITAB plot of weight residuals against road length, x

28. Copyright © 2012 Pearson Education, Inc. All rights reserved. Section 9.5 Modeling Qualitative Dependent Variables

29. Copyright © 2012 Pearson Education, Inc. All rights reserved. Section 9.6 Logistic Regression

30. Copyright © 2012 Pearson Education, Inc. All rights reserved. 9- 30 Figure 9.15 Graph of E(y) for the logistic model

31. Copyright © 2012 Pearson Education, Inc. All rights reserved. 9- 31

32. Copyright © 2012 Pearson Education, Inc. All rights reserved. 9- 32 Figure 9.16 Several chi-square probability distributions

33. Copyright © 2012 Pearson Education, Inc. All rights reserved. 9- 33

34. Copyright © 2012 Pearson Education, Inc. All rights reserved. 9- 34 Figure 9.17 SAS printout of logistic regression on bid status continued on next slide

35. Copyright © 2012 Pearson Education, Inc. All rights reserved. 9- 35 Figure 9.17 SAS printout of logistic regression on bid status (cont’d) continued on next slide

36. Copyright © 2012 Pearson Education, Inc. All rights reserved. 9- 36 Figure 9.17 SAS printout of logistic regression on bid status (cont’d)

37. Copyright © 2012 Pearson Education, Inc. All rights reserved. 9- 37

38. Copyright © 2012 Pearson Education, Inc. All rights reserved. 9- 38 Figure 9.18 SAS analysis of complete second-order logistic model, Example 9.6

39. Copyright © 2012 Pearson Education, Inc. All rights reserved. Section 9.7 Ridge Regression

40. Copyright © 2012 Pearson Education, Inc. All rights reserved. 9- 40 Figure 9.19 Sampling distributions of two estimators of a regression coefficient 

41. Copyright © 2012 Pearson Education, Inc. All rights reserved. 9- 41 Figure 9.20 Ridge trace of  coefficients of a model with three independent variables

42. Copyright © 2012 Pearson Education, Inc. All rights reserved. 9- 42 Figure 9.21 SAS regression printout for model of carbon monoxide content, Example 9.7

43. Copyright © 2012 Pearson Education, Inc. All rights reserved. 9- 43 Figure 9.22 SAS ridge trace for model of carbon monoxide content

44. Copyright © 2012 Pearson Education, Inc. All rights reserved. 9- 44 Figure 9.23a SAS listing of VIFs for ridge regression of carbon monoxide content

45. Copyright © 2012 Pearson Education, Inc. All rights reserved. 9- 45 Figure 9.23b SAS listing of ridge beta estimates and root MSE for carbon monoxide content model

46. Copyright © 2012 Pearson Education, Inc. All rights reserved. Section 9.8 Robust Regression

47. Copyright © 2012 Pearson Education, Inc. All rights reserved. 9- 47 Figure 9.24 Probability distribution of  : normal versus heavy-tailed

48. Copyright © 2012 Pearson Education, Inc. All rights reserved. 9- 48 Figure 9.25 SAS least squares regression printout for fast-food sales model

49. Copyright © 2012 Pearson Education, Inc. All rights reserved. Section 9.9 Nonparametric Regression Models

50. Copyright © 2012 Pearson Education, Inc. All rights reserved. 9- 50 Figure 9.26 SAS robust regression printout for fast-food sales model continued on next slide

51. Copyright © 2012 Pearson Education, Inc. All rights reserved. 9- 51 Figure 9.26 SAS robust regression printout for fast-food sales model (cont’d)

52. Copyright © 2012 Pearson Education, Inc. All rights reserved. 9- 52 Figure 9.27 Scatterplot of data for MS patients