1. Copyright © 2012 Pearson Education, Inc. All rights reserved. Chapter 4 Multiple Regression Models

2. Copyright © 2012 Pearson Education, Inc. All rights reserved. Section 4.1 General Form of a Multiple Regression Model

3. Copyright © 2012 Pearson Education, Inc. All rights reserved. 4- 3

4. Copyright © 2012 Pearson Education, Inc. All rights reserved. Section 4.2 Model Assumptions

5. Copyright © 2012 Pearson Education, Inc. All rights reserved. Section 4.3 A First-Order Model with Quantitative Predictors

6. Copyright © 2012 Pearson Education, Inc. All rights reserved. 4- 6

7. Copyright © 2012 Pearson Education, Inc. All rights reserved. 4- 7

8. Copyright © 2012 Pearson Education, Inc. All rights reserved. 4- 8 Figure 4.1 Graphs of E(y) = 1+ 2x 1 = x 2 for x 2 = 0,1,2

9. Copyright © 2012 Pearson Education, Inc. All rights reserved. Section 4.4 Fitting the Model: The Method of Least Squares

10. Copyright © 2012 Pearson Education, Inc. All rights reserved. 4- 10

11. Copyright © 2012 Pearson Education, Inc. All rights reserved. 4- 11 Figure 4.2 MINITAB side-by-side scatterplots for the data of Table 4.1

12. Copyright © 2012 Pearson Education, Inc. All rights reserved. 4- 12 Figure 4.3 SAS regression output for the auction price model, Example 4.1

13. Copyright © 2012 Pearson Education, Inc. All rights reserved. Section 4.5 Estimation of  2, the Variance of 

14. Copyright © 2012 Pearson Education, Inc. All rights reserved. 4- 14

15. Copyright © 2012 Pearson Education, Inc. All rights reserved. Section 4.6 Testing the Utility of a Model: The Analysis of Variance F-Test

16. Copyright © 2012 Pearson Education, Inc. All rights reserved. 4- 16

17. Copyright © 2012 Pearson Education, Inc. All rights reserved. 4- 17 Figure 4.4 Rejection region for the global F-test

18. Copyright © 2012 Pearson Education, Inc. All rights reserved. 4- 18 Figure 4.5 MINITAB regression printout for grandfather clock model

19. Copyright © 2012 Pearson Education, Inc. All rights reserved. Section 4.7 Inferences About the Individual  Parameters

20. Copyright © 2012 Pearson Education, Inc. All rights reserved. 4- 20

21. Copyright © 2012 Pearson Education, Inc. All rights reserved. 4- 21

22. Copyright © 2012 Pearson Education, Inc. All rights reserved. 4- 22 Figure 4.6 SAS regression output for the auction price model, Example 4.4

23. Copyright © 2012 Pearson Education, Inc. All rights reserved. Multiple Coefficients of Determination: R 2 and R 2 Section 4.8 a

24. Copyright © 2012 Pearson Education, Inc. All rights reserved. 4- 24 Figure 4.7 A portion of the SPSS regression output for the auction price model

25. Copyright © 2012 Pearson Education, Inc. All rights reserved. Section 4.9 Using the Model for Estimation and Prediction

26. Copyright © 2012 Pearson Education, Inc. All rights reserved. 4- 26 Figure 4.8 MINITAB printout with 95% confidence intervals for grandfather clock model

27. Copyright © 2012 Pearson Education, Inc. All rights reserved. Section 4.10 An Interaction Model with Quantitative Predictors

28. Copyright © 2012 Pearson Education, Inc. All rights reserved. 4- 28 Figure 4.9 Graphs of 1 + 2x 1 – x 2 + x 1 x 2 for x 2 = 0,1,2

29. Copyright © 2012 Pearson Education, Inc. All rights reserved. 4- 29

30. Copyright © 2012 Pearson Education, Inc. All rights reserved. 4- 30 Figure 4.10 Examples of no- interaction and interaction models

31. Copyright © 2012 Pearson Education, Inc. All rights reserved. 4- 31 Figure 4.11 MINITAB regression printout for grandfather clock model with interaction

32. Copyright © 2012 Pearson Education, Inc. All rights reserved. Section 4.11 A Quadratic (Second-Order) Model with a Quantitative Predictor

33. Copyright © 2012 Pearson Education, Inc. All rights reserved. 4- 33 Figure 4.12 Graphs for two quadratic models

34. Copyright © 2012 Pearson Education, Inc. All rights reserved. 4- 34

35. Copyright © 2012 Pearson Education, Inc. All rights reserved. 4- 35

36. Copyright © 2012 Pearson Education, Inc. All rights reserved. 4- 36 Figure 4.13 SPSS scatterplot for data of Example 4.7

37. Copyright © 2012 Pearson Education, Inc. All rights reserved. 4- 37 Figure 4.14 SPSS output for quadratic model of Example 4.7

38. Copyright © 2012 Pearson Education, Inc. All rights reserved. 4- 38 Figure 4.15 MINITAB graph of least squares fit for the quadratic model

39. Copyright © 2012 Pearson Education, Inc. All rights reserved. 4- 39 Figure 4.16 Potential misuse of quadratic model

40. Copyright © 2012 Pearson Education, Inc. All rights reserved. Section 4.12 More Complex Multiple Regression Models (Optional)

41. Copyright © 2012 Pearson Education, Inc. All rights reserved. 4- 41

42. Copyright © 2012 Pearson Education, Inc. All rights reserved. 4- 42

43. Copyright © 2012 Pearson Education, Inc. All rights reserved. 4- 43

44. Copyright © 2012 Pearson Education, Inc. All rights reserved. 4- 44 Figure 4.17 Graph of E(y) = 1 + 7x 1 - 10x 2 + 5x 1 x 2 – + 3

45. Copyright © 2012 Pearson Education, Inc. All rights reserved. 4- 45

46. Copyright © 2012 Pearson Education, Inc. All rights reserved. 4- 46

47. Copyright © 2012 Pearson Education, Inc. All rights reserved. 4- 47 Figure 4.18 SAS multiple regression output for Example 4.8

48. Copyright © 2012 Pearson Education, Inc. All rights reserved. 4- 48

49. Copyright © 2012 Pearson Education, Inc. All rights reserved. 4- 49

50. Copyright © 2012 Pearson Education, Inc. All rights reserved. 4- 50

51. Copyright © 2012 Pearson Education, Inc. All rights reserved. 4- 51 Figure 4.19 MINITAB multiple regression output for Example 4.9

52. Copyright © 2012 Pearson Education, Inc. All rights reserved. 4- 52

53. Copyright © 2012 Pearson Education, Inc. All rights reserved. 4- 53 Figure 4.20 MINITAB multiple regression output for Example 4.10

54. Copyright © 2012 Pearson Education, Inc. All rights reserved. 4- 54

55. Copyright © 2012 Pearson Education, Inc. All rights reserved. 4- 55

56. Copyright © 2012 Pearson Education, Inc. All rights reserved. Section 4.13 A Test for Comparing Nested Models

57. Copyright © 2012 Pearson Education, Inc. All rights reserved. 4- 57

58. Copyright © 2012 Pearson Education, Inc. All rights reserved. 4- 58 Figure 4.21 Rejection region for the F-test Ho:  4 =  5 = 0

59. Copyright © 2012 Pearson Education, Inc. All rights reserved. 4- 59 Figure 4.22 SAS output for complete model, Example 4.11

60. Copyright © 2012 Pearson Education, Inc. All rights reserved. 4- 60 Figure 4.23 SAS output for reduced model, Example 4.11

61. Copyright © 2012 Pearson Education, Inc. All rights reserved. Section 4.14 A Complete Example

62. Copyright © 2012 Pearson Education, Inc. All rights reserved. 4- 62 Figure 4.24 SAS output for complete second-order model for road cost

63. Copyright © 2012 Pearson Education, Inc. All rights reserved. 4- 63 Figure 4.25 SAS output for reduced model for road cost

64. Copyright © 2012 Pearson Education, Inc. All rights reserved. 4- 64 Figure 4.26 Plot of the least squares lines for the reduced model

65. Copyright © 2012 Pearson Education, Inc. All rights reserved. 4- 65 Figure 4.27 SAS output showing prediction intervals for reduced model