1. Copyright © 2012 Pearson Education, Inc. All rights reserved. Chapter 5 Principles of Model Building

2. Copyright © 2012 Pearson Education, Inc. All rights reserved. Section 5.1 Introduction: Why Model Building Is Important

3. Copyright © 2012 Pearson Education, Inc. All rights reserved. Section 5.2 The Two Types of Independent Variables: Quantitative and Qualitative

4. Copyright © 2012 Pearson Education, Inc. All rights reserved. Section 5.3 Models with a Single Quantitative Independent Variable

5. Copyright © 2012 Pearson Education, Inc. All rights reserved. 5- 5 Figure 5.1 Modeling exam score, y, as a function of study time, x

6. Copyright © 2012 Pearson Education, Inc. All rights reserved. 5- 6

7. Copyright © 2012 Pearson Education, Inc. All rights reserved. 5- 7

8. Copyright © 2012 Pearson Education, Inc. All rights reserved. 5- 8

9. Copyright © 2012 Pearson Education, Inc. All rights reserved. 5- 9 Figure 5.2 Graphs for two second-order polynomial models

10. Copyright © 2012 Pearson Education, Inc. All rights reserved. 5- 10 Figure 5.3 Example of the use of a quadratic model

11. Copyright © 2012 Pearson Education, Inc. All rights reserved. 5- 11 Figure 5.4 Graphs of two third-order polynomial models

12. Copyright © 2012 Pearson Education, Inc. All rights reserved. 5- 12

13. Copyright © 2012 Pearson Education, Inc. All rights reserved. 5- 13

14. Copyright © 2012 Pearson Education, Inc. All rights reserved. 5- 14 Figure 5.5 MINITAB scatterplot for power load data

15. Copyright © 2012 Pearson Education, Inc. All rights reserved. 5- 15 Figure 5.6 MINITAB output for third-order model of power load

16. Copyright © 2012 Pearson Education, Inc. All rights reserved. 5- 16 Figure 5.7 MINITAB output for second-order model of power load

17. Copyright © 2012 Pearson Education, Inc. All rights reserved. Section 5.4 First-Order Models with Two or More Quantitative Independent Variables

18. Copyright © 2012 Pearson Education, Inc. All rights reserved. 5- 18 Figure 5.8 Response surface for first-order model with two quantitative independent variables

19. Copyright © 2012 Pearson Education, Inc. All rights reserved. 5- 19

20. Copyright © 2012 Pearson Education, Inc. All rights reserved. 5- 20 Figure 5.9 Contour lines of E(y) for x 2 = 1,2,3 (first-order model)

21. Copyright © 2012 Pearson Education, Inc. All rights reserved. Section 5.5 Second-Order Models with Two or More Quantitative Independent Variables

22. Copyright © 2012 Pearson Education, Inc. All rights reserved. 5- 22 Figure 5.10 Response surface for an interaction model (second-order)

23. Copyright © 2012 Pearson Education, Inc. All rights reserved. 5- 23 Figure 5.11 Contour lines of E(y) for x 2 = 1,2,3 (first-order model plus interaction)

24. Copyright © 2012 Pearson Education, Inc. All rights reserved. 5- 24

25. Copyright © 2012 Pearson Education, Inc. All rights reserved. 5- 25

26. Copyright © 2012 Pearson Education, Inc. All rights reserved. 5- 26 Figure 5.12 Graphs of three second-order surfaces

27. Copyright © 2012 Pearson Education, Inc. All rights reserved. 5- 27 Figure 5.13 Contours of E(y) for x 2 = -1,0,1 (complete second-order model)

28. Copyright © 2012 Pearson Education, Inc. All rights reserved. 5- 28

29. Copyright © 2012 Pearson Education, Inc. All rights reserved. 5- 29

30. Copyright © 2012 Pearson Education, Inc. All rights reserved. 5- 30 Figure 5.14 SAS output for complete second-order model of quality

31. Copyright © 2012 Pearson Education, Inc. All rights reserved. 5- 31 Figure 5.15 Graph of second-order least squares model for Example 5.3

32. Copyright © 2012 Pearson Education, Inc. All rights reserved. Section 5.6 Coding Quantitative Independent Variables (Optional)

33. Copyright © 2012 Pearson Education, Inc. All rights reserved. 5- 33

34. Copyright © 2012 Pearson Education, Inc. All rights reserved. 5- 34

35. Copyright © 2012 Pearson Education, Inc. All rights reserved. 5- 35 Figure 5.16 MINITAB printout for the quadratic model, Example 5.4

36. Copyright © 2012 Pearson Education, Inc. All rights reserved. 5- 36 Figure 5.17 MINITAB descriptive statistics for temperature, x

37. Copyright © 2012 Pearson Education, Inc. All rights reserved. 5- 37

38. Copyright © 2012 Pearson Education, Inc. All rights reserved. 5- 38 Figure 5.18 MINITAB printout for the quadratic model with coded temperature

39. Copyright © 2012 Pearson Education, Inc. All rights reserved. Section 5.7 Models with One Qualitative Independent Variable

40. Copyright © 2012 Pearson Education, Inc. All rights reserved. 5- 40

41. Copyright © 2012 Pearson Education, Inc. All rights reserved. 5- 41

42. Copyright © 2012 Pearson Education, Inc. All rights reserved. 5- 42

43. Copyright © 2012 Pearson Education, Inc. All rights reserved. 5- 43 Figure 5.19 SPSS printout for dummy variable model, Example 5.5

44. Copyright © 2012 Pearson Education, Inc. All rights reserved. Section 5.8 Models with Two Qualitative Independent Variables

45. Copyright © 2012 Pearson Education, Inc. All rights reserved. 5- 45

46. Copyright © 2012 Pearson Education, Inc. All rights reserved. 5- 46 Figure 5.20 Main effects model: Mean response as a function of F and B when F and B affect E(y) independently

47. Copyright © 2012 Pearson Education, Inc. All rights reserved. 5- 47

48. Copyright © 2012 Pearson Education, Inc. All rights reserved. 5- 48 Figure 5.21 Interaction model: Mean response as a function of F and B when F and B interact to affect E(y)

49. Copyright © 2012 Pearson Education, Inc. All rights reserved. 5- 49

50. Copyright © 2012 Pearson Education, Inc. All rights reserved. 5- 50

51. Copyright © 2012 Pearson Education, Inc. All rights reserved. 5- 51 Figure 5.22 SAS printout for main effects model, Example 5.10

52. Copyright © 2012 Pearson Education, Inc. All rights reserved. 5- 52 Figure 5.23 SAS printout for interaction model, Example 5.10

53. Copyright © 2012 Pearson Education, Inc. All rights reserved. 5- 53 Figure 5.24 MINITAB graph of sample means for engine performance

54. Copyright © 2012 Pearson Education, Inc. All rights reserved. 5- 54 Figure 5.25 SAS printout for nested model F-test of interaction

55. Copyright © 2012 Pearson Education, Inc. All rights reserved. Section 5.9 Models with Three or More Qualitative Independent Variables

56. Copyright © 2012 Pearson Education, Inc. All rights reserved. 5- 56

57. Copyright © 2012 Pearson Education, Inc. All rights reserved. Section 5.10 Models with Both Quantitative and Qualitative Independent Variables

58. Copyright © 2012 Pearson Education, Inc. All rights reserved. 5- 58 Figure 5.26 Model for E(y) as a function of engine speed

59. Copyright © 2012 Pearson Education, Inc. All rights reserved. 5- 59 Figure 5.27 Model for E(y) as a function of fuel type and engine speed (no interaction)

60. Copyright © 2012 Pearson Education, Inc. All rights reserved. 5- 60 Figure 5.28 Graph of E(y) as a function of fuel type and engine speed (interaction)

61. Copyright © 2012 Pearson Education, Inc. All rights reserved. 5- 61 Figure 5.29 A graphical portrayal of three factors - two qualitative and one quantitative - on DDT level

62. Copyright © 2012 Pearson Education, Inc. All rights reserved. 5- 62 Figure 5.30 DDT curves for stages 1 and 2

63. Copyright © 2012 Pearson Education, Inc. All rights reserved. Section 5.11 External Model Validation (Optional)

64. Copyright © 2012 Pearson Education, Inc. All rights reserved. 5- 64 Figure 5.31 MINITAB printout for the multiplicative model of executive salary