Chapter 11 Simple Linear Regression and Correlation Copyright

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Chapter 11 Simple Linear Regression and Correlation Copyright © 2010 Pearson Addison-Wesley. All rights

Chapter 11 Simple Linear Regression and Correlation Copyright © 2010 Pearson Addison-Wesley. All rights reserved.

Section 11. 1 Introduction to Linear Regression Copyright © 2010 Pearson Addison-Wesley. All rights

Section 11. 1 Introduction to Linear Regression Copyright © 2010 Pearson Addison-Wesley. All rights reserved.

Figure 11. 1 A linear relationship; b 0: intercept; b 1: slope Copyright ©

Figure 11. 1 A linear relationship; b 0: intercept; b 1: slope Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 3

Section 11. 2 The Simple Linear Regression (SLR) Model Copyright © 2010 Pearson Addison-Wesley.

Section 11. 2 The Simple Linear Regression (SLR) Model Copyright © 2010 Pearson Addison-Wesley. All rights reserved.

Figure 11. 2 Hypothetical (x, y) data scattered around the true regression line for

Figure 11. 2 Hypothetical (x, y) data scattered around the true regression line for n = 5 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 5

Table 11. 1 Measures of Reduction in Solids and Oxygen Demand Copyright © 2010

Table 11. 1 Measures of Reduction in Solids and Oxygen Demand Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 6

Figure 11. 3 Scatter diagram with regression lines Copyright © 2010 Pearson Addison-Wesley. All

Figure 11. 3 Scatter diagram with regression lines Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 7

Figure 11. 4 Individual observations around true regression line Copyright © 2010 Pearson Addison-Wesley.

Figure 11. 4 Individual observations around true regression line Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 8

Section 11. 3 Least Squares and the Fitted Model Copyright © 2010 Pearson Addison-Wesley.

Section 11. 3 Least Squares and the Fitted Model Copyright © 2010 Pearson Addison-Wesley. All rights reserved.

Figure 11. 5 Comparing ei with the residual, ei Copyright © 2010 Pearson Addison-Wesley.

Figure 11. 5 Comparing ei with the residual, ei Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 10

Figure 11. 6 Residuals as vertical deviations Copyright © 2010 Pearson Addison-Wesley. All rights

Figure 11. 6 Residuals as vertical deviations Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 11

Section 11. 4 Properties of the Least Squares Estimators Copyright © 2010 Pearson Addison-Wesley.

Section 11. 4 Properties of the Least Squares Estimators Copyright © 2010 Pearson Addison-Wesley. All rights reserved.

Theorem 11. 1 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 13

Theorem 11. 1 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 13

Section 11. 5 Inferences Concerning the Regression Coefficients Copyright © 2010 Pearson Addison-Wesley. All

Section 11. 5 Inferences Concerning the Regression Coefficients Copyright © 2010 Pearson Addison-Wesley. All rights reserved.

Figure 11. 7 MINITAB printout for -test for data of Example 11. 1 Copyright

Figure 11. 7 MINITAB printout for -test for data of Example 11. 1 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. t 15

Figure 11. 8 The hypothesis H 0: b 1 = 0 is not rejected

Figure 11. 8 The hypothesis H 0: b 1 = 0 is not rejected Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 16

Figure 11. 9 The hypothesis H 0: b 1 = 0 is rejected Copyright

Figure 11. 9 The hypothesis H 0: b 1 = 0 is rejected Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 17

Figure 11. 10 Plots depicting a very good fit and a poor fit Copyright

Figure 11. 10 Plots depicting a very good fit and a poor fit Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 18

Section 11. 6 Prediction Copyright © 2010 Pearson Addison-Wesley. All rights reserved.

Section 11. 6 Prediction Copyright © 2010 Pearson Addison-Wesley. All rights reserved.

Figure 11. 11 Confidence limits for the mean value of Y|x Copyright © 2010

Figure 11. 11 Confidence limits for the mean value of Y|x Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 20

Figure 11. 12 Confidence and prediction intervals for the chemical oxygen demand reduction data;

Figure 11. 12 Confidence and prediction intervals for the chemical oxygen demand reduction data; inside bands indicate the confidence limits for the mean responses and outside bands indicate the prediction for the future responses Copyright © 2010 Pearson Addison-Wesley. All rights reserved. limits 21

Figure 11. 13 SAS printout for Example 11. 27 Copyright © 2010 Pearson Addison-Wesley.

Figure 11. 13 SAS printout for Example 11. 27 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 22

Section 11. 7 Choice of a Regression Model Copyright © 2010 Pearson Addison-Wesley. All

Section 11. 7 Choice of a Regression Model Copyright © 2010 Pearson Addison-Wesley. All rights reserved.

Section 11. 8 Analysis-of-Variance Approach Copyright © 2010 Pearson Addison-Wesley. All rights reserved.

Section 11. 8 Analysis-of-Variance Approach Copyright © 2010 Pearson Addison-Wesley. All rights reserved.

Table 11. 2 Analysis of Variances for Testing b 1 = 0 Copyright ©

Table 11. 2 Analysis of Variances for Testing b 1 = 0 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 25

Section 11. 9 Test for Linearity of Regression: Data with Repeated Observations Copyright ©

Section 11. 9 Test for Linearity of Regression: Data with Repeated Observations Copyright © 2010 Pearson Addison-Wesley. All rights reserved.

Figure 11. 14 MINITAB printout of simple linear regression for chemical oxygen demand reduction

Figure 11. 14 MINITAB printout of simple linear regression for chemical oxygen demand reduction data; part I Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 27

Figure 11. 15 MINITAB printout of simple linear regression for chemical oxygen demand reduction

Figure 11. 15 MINITAB printout of simple linear regression for chemical oxygen demand reduction data; part II Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 28

Table 11. 3 Analysis of Variance for Testing Linearity of Regression Copyright © 2010

Table 11. 3 Analysis of Variance for Testing Linearity of Regression Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 29

Figure 11. 16 Connect linear model with no lack-of-fit component Copyright © 2010 Pearson

Figure 11. 16 Connect linear model with no lack-of-fit component Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 30

Figure 11. 17 Incorrect linear model with lack-of-fit component Copyright © 2010 Pearson Addison-Wesley.

Figure 11. 17 Incorrect linear model with lack-of-fit component Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 31

Table 11. 4 Data for Example 11. 8 Copyright © 2010 Pearson Addison-Wesley. All

Table 11. 4 Data for Example 11. 8 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 32

Table 11. 5 Analysis of Variance on Yield-Temperature Data Copyright © 2010 Pearson Addison-Wesley.

Table 11. 5 Analysis of Variance on Yield-Temperature Data Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 33

Figure 11. 18 SAS printout, showing analysis of data of Example 11. 8 Copyright

Figure 11. 18 SAS printout, showing analysis of data of Example 11. 8 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 34

Section 11. 10 Data Plots and Transformations Copyright © 2010 Pearson Addison-Wesley. All rights

Section 11. 10 Data Plots and Transformations Copyright © 2010 Pearson Addison-Wesley. All rights reserved.

Table 11. 6 Some Useful Transformations to Linearize Copyright © 2010 Pearson Addison-Wesley. All

Table 11. 6 Some Useful Transformations to Linearize Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 36

Figure 11. 19 Diagrams depicting functions listed in Table 11. 6 Copyright © 2010

Figure 11. 19 Diagrams depicting functions listed in Table 11. 6 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 37

Table 11. 7 Data for Example 11. 9 Copyright © 2010 Pearson Addison-Wesley. All

Table 11. 7 Data for Example 11. 9 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 38

Figure 11. 20 Pressure and volume data and fitted regression Copyright © 2010 Pearson

Figure 11. 20 Pressure and volume data and fitted regression Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 39

Figure 11. 21 Ideal residual plot Copyright © 2010 Pearson Addison-Wesley. All rights reserved.

Figure 11. 21 Ideal residual plot Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 40

Figure 11. 22 Residual plot depicting heterogeneous error variance Copyright © 2010 Pearson Addison-Wesley.

Figure 11. 22 Residual plot depicting heterogeneous error variance Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 41

Section 11. 11 Simple Linear Regression Case Study Copyright © 2010 Pearson Addison-Wesley. All

Section 11. 11 Simple Linear Regression Case Study Copyright © 2010 Pearson Addison-Wesley. All rights reserved.

Table 11. 8 Density and Stiffness for 30 Particleboards Copyright © 2010 Pearson Addison-Wesley.

Table 11. 8 Density and Stiffness for 30 Particleboards Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 43

Figure 11. 23 Scatter plot of the wood density data Copyright © 2010 Pearson

Figure 11. 23 Scatter plot of the wood density data Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 44

Figure 11. 24 Residual plot for the wood density data Copyright © 2010 Pearson

Figure 11. 24 Residual plot for the wood density data Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 45

Figure 11. 25 Normal probability plot of residuals for wood density data Copyright ©

Figure 11. 25 Normal probability plot of residuals for wood density data Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 46

Section 11. 12 Correlation Copyright © 2010 Pearson Addison-Wesley. All rights reserved.

Section 11. 12 Correlation Copyright © 2010 Pearson Addison-Wesley. All rights reserved.

Figure 11. 26 Residual plot using the log transformation for the wood density data

Figure 11. 26 Residual plot using the log transformation for the wood density data Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 48

Figure 11. 27 Normal probability plot of residuals using the log transformation for the

Figure 11. 27 Normal probability plot of residuals using the log transformation for the wood density data Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 49

Table 11. 9 Data on 29 Loblolly Pines for Example 11. 10 Copyright ©

Table 11. 9 Data on 29 Loblolly Pines for Example 11. 10 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 50

Figure 11. 28 Scatter diagram showing zero correlation Copyright © 2010 Pearson Addison-Wesley. All

Figure 11. 28 Scatter diagram showing zero correlation Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 51

Figure 11. 29 SAS printout, showing partial analysis of data of Review Exercise 11.

Figure 11. 29 SAS printout, showing partial analysis of data of Review Exercise 11. 54 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 52

Figure 11. 30 SAS printout, showing partial analysis of data of Review Exercise 11.

Figure 11. 30 SAS printout, showing partial analysis of data of Review Exercise 11. 55 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. continued on next slide 53

Figure 11. 30 SAS printout, showing partial analysis of data of Review Exercise 11.

Figure 11. 30 SAS printout, showing partial analysis of data of Review Exercise 11. 55 (cont’d) Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 54

Figure 11. 31 SAS printout, showing residual plot of Review Exercise 11. 55 Copyright

Figure 11. 31 SAS printout, showing residual plot of Review Exercise 11. 55 Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 55

Section 11. 13 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters Copyright

Section 11. 13 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters Copyright © 2010 Pearson Addison-Wesley. All rights reserved.

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