Chapter 12 Multiple Linear Regression and Certain Nonlinear

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Chapter 12 Multiple Linear Regression and Certain Nonlinear Regression Models Copyright © 2010 Pearson

Chapter 12 Multiple Linear Regression and Certain Nonlinear Regression Models Copyright © 2010 Pearson Addison-Wesley. All rights reserved.

Section 12. 1 Introduction Copyright © 2010 Pearson Addison-Wesley. All rights reserved.

Section 12. 1 Introduction Copyright © 2010 Pearson Addison-Wesley. All rights reserved.

Section 12. 2 Estimating the Coefficients Copyright © 2010 Pearson Addison-Wesley. All rights reserved.

Section 12. 2 Estimating the Coefficients Copyright © 2010 Pearson Addison-Wesley. All rights reserved.

Table 12. 1 Data for Example 12. 1 Copyright © 2010 Pearson Addison-Wesley. All

Table 12. 1 Data for Example 12. 1 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 4

Table 12. 2 Data for Example 12. 3 Copyright © 2010 Pearson Addison-Wesley. All

Table 12. 2 Data for Example 12. 3 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 5

Section 12. 3 Linear Regression Model Using Matrices Copyright © 2010 Pearson Addison-Wesley. All

Section 12. 3 Linear Regression Model Using Matrices Copyright © 2010 Pearson Addison-Wesley. All rights reserved.

Table 12. 3 Data for Example 12. 4 Copyright © 2010 Pearson Addison-Wesley. All

Table 12. 3 Data for Example 12. 4 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 7

Section 12. 4 Properties of the Least Squares Estimators Copyright © 2010 Pearson Addison-Wesley.

Section 12. 4 Properties of the Least Squares Estimators Copyright © 2010 Pearson Addison-Wesley. All rights reserved.

Theorem 12. 1 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 9

Theorem 12. 1 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 9

Section 12. 5 Inferences in Multiple Linear Regression Copyright © 2010 Pearson Addison-Wesley. All

Section 12. 5 Inferences in Multiple Linear Regression Copyright © 2010 Pearson Addison-Wesley. All rights reserved.

Figure 12. 1 SAS printout for data in Example 12. 4 Copyright © 2010

Figure 12. 1 SAS printout for data in Example 12. 4 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 11

Section 12. 6 Choice of a Fitted Model through Hypothesis Testing Copyright © 2010

Section 12. 6 Choice of a Fitted Model through Hypothesis Testing Copyright © 2010 Pearson Addison-Wesley. All rights reserved.

Section 12. 7 Special Cases of Orthogonality (Optional) Copyright © 2010 Pearson Addison-Wesley. All

Section 12. 7 Special Cases of Orthogonality (Optional) Copyright © 2010 Pearson Addison-Wesley. All rights reserved.

Table 12. 4 Analysis of Variances for Orthogonal Variables Copyright © 2010 Pearson Addison-Wesley.

Table 12. 4 Analysis of Variances for Orthogonal Variables Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 14

Table 12. 5 Data for Example 12. 8 Copyright © 2010 Pearson Addison-Wesley. All

Table 12. 5 Data for Example 12. 8 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 15

Table 12. 6 Analysis of Variance for Grain Radius Data Copyright © 2010 Pearson

Table 12. 6 Analysis of Variance for Grain Radius Data Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 16

Section 12. 8 Categorical or Indicator Variables Copyright © 2010 Pearson Addison-Wesley. All rights

Section 12. 8 Categorical or Indicator Variables Copyright © 2010 Pearson Addison-Wesley. All rights reserved.

Figure 12. 2 Case of three categories Copyright © 2010 Pearson Addison-Wesley. All rights

Figure 12. 2 Case of three categories Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 18

Table 12. 7 Data for Example 12. 9 Copyright © 2010 Pearson Addison-Wesley. All

Table 12. 7 Data for Example 12. 9 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 19

Figure 12. 3 SAS printout for Example 12. 9 Copyright © 2010 Pearson Addison-Wesley.

Figure 12. 3 SAS printout for Example 12. 9 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 20

Figure 12. 4 Nonparallelism on categorical variables Copyright © 2010 Pearson Addison-Wesley. All rights

Figure 12. 4 Nonparallelism on categorical variables Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 21

Section 12. 9 Sequential Methods for Model Selection Copyright © 2010 Pearson Addison-Wesley. All

Section 12. 9 Sequential Methods for Model Selection Copyright © 2010 Pearson Addison-Wesley. All rights reserved.

Table 12. 8 Data Relating to Infant Length Copyright © 2010 Pearson Addison-Wesley. All

Table 12. 8 Data Relating to Infant Length Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 23

Table 12. 9 t-Values for the Regression Data of Table 12. 8 Copyright ©

Table 12. 9 t-Values for the Regression Data of Table 12. 8 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 24

Section 12. 10 Study of Residuals and Violation of Assumptions (Model Checking) Copyright ©

Section 12. 10 Study of Residuals and Violation of Assumptions (Model Checking) Copyright © 2010 Pearson Addison-Wesley. All rights reserved.

Table 12. 10 Data Set for Case Study 12. 1 Copyright © 2010 Pearson

Table 12. 10 Data Set for Case Study 12. 1 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 26

Table 12. 11 Residual Information for the Data Set for Case Study 12. 1

Table 12. 11 Residual Information for the Data Set for Case Study 12. 1 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 27

Figure 12. 5 R-Student values plotted against predicted values for grasshopper data of Case

Figure 12. 5 R-Student values plotted against predicted values for grasshopper data of Case Study 12. 1 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 28

Section 12. 11 Cross Validation, Cp, and Other Criteria for Model Selection Copyright ©

Section 12. 11 Cross Validation, Cp, and Other Criteria for Model Selection Copyright © 2010 Pearson Addison-Wesley. All rights reserved.

Table 12. 12 Data Set Case Study 12. 2 Copyright © 2010 Pearson Addison-Wesley.

Table 12. 12 Data Set Case Study 12. 2 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 30

Table 12. 13 Comparing Different Regression Models Copyright © 2010 Pearson Addison-Wesley. All rights

Table 12. 13 Comparing Different Regression Models Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 31

Table 12. 14 PRESS Residuals Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 32

Table 12. 14 PRESS Residuals Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 32

Table 12. 15 Data for Example 12. 12 Copyright © 2010 Pearson Addison-Wesley. All

Table 12. 15 Data for Example 12. 12 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 33

Figure 12. 6 SAS printout of all possible subsets on sales data for Example

Figure 12. 6 SAS printout of all possible subsets on sales data for Example 12. 12 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 34

Figure 12. 7 Normal probability plot of residuals using the model x 1 x

Figure 12. 7 Normal probability plot of residuals using the model x 1 x 2 x 3 for Example 12. 12 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 35

Section 12. 12 Special Nonlinear Models for Nonideal Conditions Copyright © 2010 Pearson Addison-Wesley.

Section 12. 12 Special Nonlinear Models for Nonideal Conditions Copyright © 2010 Pearson Addison-Wesley. All rights reserved.

Figure 12. 8 The logistic function Copyright © 2010 Pearson Addison-Wesley. All rights reserved.

Figure 12. 8 The logistic function Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 37

Table 12. 16 Data Set for Example 12. 13 Copyright © 2010 Pearson Addison-Wesley.

Table 12. 16 Data Set for Example 12. 13 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 38

Definition 12. 1 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 39

Definition 12. 1 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 39

Figure 12. 9 SAS output for Review Exercise 12. 72; part I Copyright ©

Figure 12. 9 SAS output for Review Exercise 12. 72; part I Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 40

Figure 12. 10 SAS output for Review Exercise 12. 72; part II Copyright ©

Figure 12. 10 SAS output for Review Exercise 12. 72; part II Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 41

Section 12. 13 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters Copyright

Section 12. 13 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters Copyright © 2010 Pearson Addison-Wesley. All rights reserved.

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