Chapter 11 Simple Linear Regression and Correlation
Section 11.1 Introduction to Linear Regression
Figure 11.1 A linear relationship; b0: intercept; b1: slope Copyright © 2010 Pearson Addison-Wesley. All rights reserved.
Section 11.2 The Simple Linear Regression (SLR) Model
Figure 11.2 Hypothetical (x,y) data scattered around the true regression line for n = 5 Copyright © 2010 Pearson Addison-Wesley. All rights reserved.
Table 11.1 Measures of Reduction in Solids and Oxygen Demand Copyright © 2010 Pearson Addison-Wesley. All rights reserved.
Figure 11.3 Scatter diagram with regression lines Copyright © 2010 Pearson Addison-Wesley. All rights reserved.
Figure 11.4 Individual observations around true regression line Copyright © 2010 Pearson Addison-Wesley. All rights reserved.
Section 11.3 Least Squares and the Fitted Model
Figure 11.5 Comparing ei with the residual, ei Copyright © 2010 Pearson Addison-Wesley. All rights reserved.
Figure 11.6 Residuals as vertical deviations Copyright © 2010 Pearson Addison-Wesley. All rights reserved.
Section 11.4 Properties of the Least Squares Estimators
Theorem 11.1 Copyright © 2010 Pearson Addison-Wesley. All rights reserved.
Section 11.5 Inferences Concerning the Regression Coefficients
Figure 11.7 MINITAB printout for t-test for data of Example 11.1 Copyright © 2010 Pearson Addison-Wesley. All rights reserved.
Figure 11.8 The hypothesis H0: b1 = 0 is not rejected Copyright © 2010 Pearson Addison-Wesley. All rights reserved.
Figure 11.9 The hypothesis H0: b1 = 0 is rejected Copyright © 2010 Pearson Addison-Wesley. All rights reserved.
Figure 11.10 Plots depicting a very good fit and a poor fit Copyright © 2010 Pearson Addison-Wesley. All rights reserved.
Section 11.6 Prediction
Figure 11.11 Confidence limits for the mean value of Y|x Copyright © 2010 Pearson Addison-Wesley. All rights reserved.
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 limits for the future responses Copyright © 2010 Pearson Addison-Wesley. All rights reserved.
Figure 11.13 SAS printout for Example 11.27 Copyright © 2010 Pearson Addison-Wesley. All rights reserved.
Section 11.7 Choice of a Regression Model
Section 11.8 Analysis-of-Variance Approach
Table 11.2 Analysis of Variances for Testing b1 = 0 Copyright © 2010 Pearson Addison-Wesley. All rights reserved.
Section 11.9 Test for Linearity of Regression: Data with Repeated Observations
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.
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.
Table 11.3 Analysis of Variance for Testing Linearity of Regression Copyright © 2010 Pearson Addison-Wesley. All rights reserved.
Figure 11.16 Connect linear model with no lack-of-fit component Copyright © 2010 Pearson Addison-Wesley. All rights reserved.
Figure 11.17 Incorrect linear model with lack-of-fit component Copyright © 2010 Pearson Addison-Wesley. All rights reserved.
Table 11.4 Data for Example 11.8 Copyright © 2010 Pearson Addison-Wesley. All rights reserved.
Table 11.5 Analysis of Variance on Yield-Temperature Data Copyright © 2010 Pearson Addison-Wesley. All rights reserved.
Figure 11.18 SAS printout, showing analysis of data of Example 11.8 Copyright © 2010 Pearson Addison-Wesley. All rights reserved.
Section 11.10 Data Plots and Transformations
Table 11.6 Some Useful Transformations to Linearize Copyright © 2010 Pearson Addison-Wesley. All rights reserved.
Figure 11.19 Diagrams depicting functions listed in Table 11.6 Copyright © 2010 Pearson Addison-Wesley. All rights reserved.
Table 11.7 Data for Example 11.9 Copyright © 2010 Pearson Addison-Wesley. All rights reserved.
Figure 11.20 Pressure and volume data and fitted regression Copyright © 2010 Pearson Addison-Wesley. All rights reserved.
Figure 11.21 Ideal residual plot Copyright © 2010 Pearson Addison-Wesley. All rights reserved.
Figure 11.22 Residual plot depicting heterogeneous error variance Copyright © 2010 Pearson Addison-Wesley. All rights reserved.
Section 11.11 Simple Linear Regression Case Study
Table 11.8 Density and Stiffness for 30 Particleboards Copyright © 2010 Pearson Addison-Wesley. All rights reserved.
Figure 11.23 Scatter plot of the wood density data Copyright © 2010 Pearson Addison-Wesley. All rights reserved.
Figure 11.24 Residual plot for the wood density data Copyright © 2010 Pearson Addison-Wesley. All rights reserved.
Figure 11.25 Normal probability plot of residuals for wood density data Copyright © 2010 Pearson Addison-Wesley. All rights reserved.
Section 11.12 Correlation
Figure 11.26 Residual plot using the log transformation for the wood density data Copyright © 2010 Pearson Addison-Wesley. All rights reserved.
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.
Table 11.9 Data on 29 Loblolly Pines for Example 11.10 Copyright © 2010 Pearson Addison-Wesley. All rights reserved.
Figure 11.28 Scatter diagram showing zero correlation Copyright © 2010 Pearson Addison-Wesley. All rights reserved.
Figure 11.29 SAS printout, showing partial analysis of data of Review Exercise 11.54 Copyright © 2010 Pearson Addison-Wesley. All rights reserved.
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
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.
Figure 11.31 SAS printout, showing residual plot of Review Exercise 11.55 Copyright © 2010 Pearson Addison-Wesley. All rights reserved.
Section 11.13 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters