1. Copyright © 2012 Pearson Education, Inc. All rights reserved Chapter 12 Multiple Regression and Model Building

2. 12 - 2 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure SIA12.1 Layout of condominium complex

3. 12 - 3 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Table SIA12.1

4. Copyright © 2012 Pearson Education, Inc. All rights reserved 12.1 Multiple-Regression Models

5. 12 - 5 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Procedure

6. 12 - 6 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Procedure

7. 12 - 7 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Procedure

8. Copyright © 2012 Pearson Education, Inc. All rights reserved Part l First-Order Models with Quantitative Independent Variables

9. Copyright © 2012 Pearson Education, Inc. All rights reserved 12.2 Estimating and Making Inferences about the  Parameters

10. 12 - 10 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Procedure

11. 12 - 11 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Table 12.1

12. 12 - 12 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 12.1 MINITAB side-by-side scatterplots for the data of Table 12.1

13. 12 - 13 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 12.2 MINITAB analysis of the auction price model

14. 12 - 14 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Procedure

15. 12 - 15 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 12.3 MINITAB graph of for

16. 12 - 16 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 12.4 MINITAB 3-dimensional graph of

17. 12 - 17 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Procedure

18. 12 - 18 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Procedure

19. 12 - 19 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Procedure

20. 12 - 20 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 12.5 Rejection Region for

21. Copyright © 2012 Pearson Education, Inc. All rights reserved 12.3 Evaluating Overall Model Utility

22. 12 - 22 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Procedure

23. 12 - 23 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Procedure

24. 12 - 24 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 12.6 SAS analysis of the auction price model

25. 12 - 25 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Procedure

26. 12 - 26 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Procedure

27. 12 - 27 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Procedure

28. 12 - 28 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Procedure

29. Copyright © 2012 Pearson Education, Inc. All rights reserved 12.4 Using the Model for Estimation and Prediction

30. 12 - 30 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 12.7 MINITAB printout with 95% confidence intervals for grandfather clock model

31. 12 - 31 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure SIA12.2 MINITAB scatterplots for CONDO data

32. 12 - 32 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure SIA12.3 MINITAB regression output for first-order model of condominium unit sale price

33. 12 - 33 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure SIA12.4 MINITAB printout with 95% confidence and prediction intervals

34. Copyright © 2012 Pearson Education, Inc. All rights reserved Part ll Model Building in Multiple Regression

35. Copyright © 2012 Pearson Education, Inc. All rights reserved 12.5 Interaction Models

36. 12 - 36 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 12.8 MINITAB graphs of for

37. 12 - 37 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Procedure

38. 12 - 38 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 12.9 MINITAB 3-dimensional graphs of

39. 12 - 39 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 12.10 Examples of no-interaction and interaction models

40. 12 - 40 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 12.11 MINITAB printout of interaction model of auction price

41. Copyright © 2012 Pearson Education, Inc. All rights reserved Quadratic and Other Higher Order Models 12.6

42. 12 - 42 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 12.12 Graphs of two quadratic models

43. 12 - 43 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Procedure

44. 12 - 44 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Table 12.2

45. 12 - 45 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 12.13 MINITAB scatterplot for electrical usage data

46. 12 - 46 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 12.14 SAS regression output for electrical usage model

47. 12 - 47 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 12.15 MINITAB plot of least squares model for electrical usage

48. 12 - 48 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 12.16 Potential misuse of quadratic model

49. 12 - 49 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Procedure

50. 12 - 50 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 12.17 Graphs for three second-order surfaces

51. Copyright © 2012 Pearson Education, Inc. All rights reserved Qualitative (Dummy) Variable Models 12.7

52. 12 - 52 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 12.18 Bar chart comparing E(y) for males and females

53. 12 - 53 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Procedure

54. 12 - 54 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Procedure

55. 12 - 55 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Table 12.3

56. 12 - 56 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 12.19 MINITAB output for model with dummy variables

57. Copyright © 2012 Pearson Education, Inc. All rights reserved Models with Both Quantitative and Qualitative Variables (Optional) 12.8

58. 12 - 58 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 12.20 Graphs of the relationship between mean sales E(y) and advertising expenditure x

59. 12 - 59 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 12.21 T he relationship between E(y) and x 1 is the same for all media

60. 12 - 60 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 12.22 Parallel response lines for the three media

61. 12 - 61 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 12.23 Different response lines for the three media

62. 12 - 62 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Table 12.4

63. 12 - 63 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 12.24 MINITAB printout of the complete model for the casting media

64. 12 - 64 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 12.25 MINITAB plot of prediction equations for two plants

65. 12 - 65 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 12.26 The relationship between E(y) and x 1 is the same for all media

66. 12 - 66 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 12.27 The response curves have the same shapes, but different y-intercepts

67. 12 - 67 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 12.28 The response curves for the three media differ

68. Copyright © 2012 Pearson Education, Inc. All rights reserved Comparing Nested Models (Optional) 12.9

69. 12 - 69 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Definition

70. 12 - 70 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Procedure

71. 12 - 71 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Table 12.5

72. 12 - 72 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 12.29 SAS printout of complete second-order model for height

73. 12 - 73 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 12.30 Plot of second-order least squares model for Example 12.12

74. 12 - 74 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 12.31 SAS printout of first-order model for height

75. 12 - 75 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Definition

76. 12 - 76 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Procedure

77. 12 - 77 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure SIA12.5 SAS printout of second-order model for condo sale price-quantitative variables only

78. 12 - 78 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure SIA12.6 SAS regression printout for the complete second-order model of condo sale price- qualitative variables added

79. Copyright © 2012 Pearson Education, Inc. All rights reserved Stepwise Regression (Optional) 12.10

80. 12 - 80 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Table 12.6

81. 12 - 81 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 12.32 MINITAB stepwise regression printout for executive salary data

82. Copyright © 2012 Pearson Education, Inc. All rights reserved Multiple Regression Diagnostics Part lll

83. Copyright © 2012 Pearson Education, Inc. All rights reserved Residual Analysis: Checking the Regression Assumptions 12.11

84. 12 - 84 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 12.33 Actual random error  and regression residual

85. 12 - 85 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Definition

86. 12 - 86 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Procedure

87. 12 - 87 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Table 12.7

88. 12 - 88 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 12.34a MINTAB printout for straight- line model of electrical usage

89. 12 - 89 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 12.34b MINITAB printout for quadratic model of electrical usage

90. 12 - 90 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 12.35a MINITAB residual plot for straight-line model of electrical usage

91. 12 - 91 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 12.35b MINITAB residual plot for quadratic model of electrical usage

92. 12 - 92 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 12.36 Residual plots showing changes in the variance of 

93. 12 - 93 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Table 12.8

94. 12 - 94 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Table 12.8 (cont’d)

95. 12 - 95 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 12.37 SPSS regression printout for first-order model of salary

96. 12 - 96 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 12.38 SPSS residual plots for first- order model of salary

97. 12 - 97 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 12.39 SPSS regression printout for model of log salary

98. 12 - 98 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 12.40 SPSS residual plots for model of ln(salary)

99. 12 - 99 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Definition

100. 12 - 100 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Table 12.9

101. 12 - 101 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 12.41 MINITAB regression printout for altered grandfather clock data

102. 12 - 102 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 12.41 MINITAB regression printout for altered grandfather clock data (cont’d)

103. 12 - 103 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 12.42 MINITAB residual plot of altered grandfather clock data

104. 12 - 104 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 12.43 MINITAB regression printout when outlier is deleted

105. 12 - 105 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 12.44 MINITAB residual plot when outlier is deleted

106. 12 - 106 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 12.45a MINITAB graphs of regression residuals for grandfather clock model (outlier included)

107. 12 - 107 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 12.45b MINITAB graphs of regression residuals for grandfather clock model (outlier included) (cont’d)

108. 12 - 108 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 12.46a MINITAB graphs of regression residuals for grandfather clock model (outlier deleted)

109. 12 - 109 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 12.46b MINITAB graphs of regression residuals for grandfather clock model (outlier deleted) (cont’d)

110. 12 - 110 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 12.47 Hypothetical residual plot for time-series data

111. 12 - 111 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Procedure

112. 12 - 112 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure SIA12.7 MINITAB histogram of residuals from second-order model of condo sale price

113. 12 - 113 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure SIA12.8 MINITAB plot of residuals versus predicted values from second-order model of condo sale price

114. 12 - 114 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure SIA12.9 MINITAB list of outliers for the second-order model of condo sale price

115. 12 - 115 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure SIA12.10 MINITAB printout of second- order model of condo sale price with outliers deleted

116. Copyright © 2012 Pearson Education, Inc. All rights reserved Some Pitfalls: Estimability, Multicollinearity, and Extrapolation 12.12

117. 12 - 117 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 12.48 Yield and fertilizer expenditure data three years

118. 12 - 118 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 12.49 Only two x values observed: quadratic model is not estimable

119. 12 - 119 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Definition

120. 12 - 120 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Procedure

121. 12 - 121 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Procedure

122. 12 - 122 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Table 12.10

123. 12 - 123 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 12.50 SAS printout for model of CO content, Example 12.18

124. 12 - 124 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Procedure

125. 12 - 125 Copyright © 2013 Pearson Education, Inc.. All rights reserved. Figure 12.51 Using a regression model outside the experimental region