Chapter 11 Simple Linear Regression and Correlation.

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

Table 11.1 Measures of Reduction in Solids and Oxygen Demand

Figure 11.3 Scatter diagram with regression lines

Figure 11.4 Individual observations around true regression line

Section 11.3 Least Squares and the Fitted Model

Figure 11.5 Comparing ei with the residual, ei

Figure 11.6 Residuals as vertical deviations

Section 11.4 Properties of the Least Squares Estimators

Section 11.5 Inferences Concerning the Regression Coefficients

Figure 11.7 MINITAB printout for t-test for data of Example 11.1

Figure 11.8 The hypothesis H0: b1 = 0 is not rejected

Figure 11.9 The hypothesis H0: b1 = 0 is rejected

Figure 11.10 Plots depicting a very good fit and a poor fit

Section 11.6 Prediction

Figure 11.11 Confidence limits for the mean value of Y|x

Figure 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

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

Section 11.9 Test for Linearity of Regression: Data with Repeated Observations

Table 11.3 Analysis of Variance for Testing Linearity of Regression

Figure 11.16 Connect linear model with no lack-of-fit component

Figure 11.17 Incorrect linear model with lack-of-fit component

Table 11.5 Analysis of Variance on Yield-Temperature Data

Figure 11.18 SAS printout, showing analysis of data of Example 11.8

Section 11.10 Data Plots and Transformations

Table 11.6 Some Useful Transformations to Linearize

Figure 11.19 Diagrams depicting functions listed in Table 11.6

Figure 11.20 Pressure and volume data and fitted regression

Figure 11.21 Ideal residual plot

Figure 11.22 Residual plot depicting heterogeneous error variance

Section 11.11 Simple Linear Regression Case Study

Table 11.8 Density and Stiffness for 30 Particleboards

Figure 11.23 Scatter plot of the wood density data

Figure 11.24 Residual plot for the wood density data

Figure 11.25 Normal probability plot of residuals for wood density data

Section 11.12 Correlation

Figure 11.26 Residual plot using the log transformation for the wood density data

Table 11.9 Data on 29 Loblolly Pines for Example 11.10

Figure 11.28 Scatter diagram showing zero correlation

Figure 11.29 SAS printout, showing partial analysis of data of Review Exercise 11.54

Figure 11.30 SAS printout, showing partial analysis of data of Review Exercise 11.55 (cont’d)

Figure 11.31 SAS printout, showing residual plot of Review Exercise 11.55

Section 11.13 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters

Chapter 11 Simple Linear Regression and Correlation.

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Chapter 11 Simple Linear Regression and Correlation.

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