Probability statistics for engineers and scientists 9th by walpole myers chapter 11

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Chapter 11

Simple Linear

Regression

and Correlation

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Section 11.1

Introduction to

Linear

Regression

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Figure 11.1 A linear relationship;

 0 : intercept;  1 : slope

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Section 11.2

The Simple

Linear

Regression (SLR) Model

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Figure 11.2 Hypothetical (x,y) data

scattered around the true regression

line for n = 5

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Table 11.1 Measures of Reduction in

Solids and Oxygen Demand

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Figure 11.3 Scatter diagram with

regression lines

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Figure 11.4 Individual observations

around true regression line

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Section 11.3

Least Squares

and the Fitted

Model

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Figure 11.5 Comparing  i with the

residual, e i

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Figure 11.6 Residuals as vertical

deviations

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Section 11.4

Properties of the Least Squares

Estimators

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Theorem 11.1

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Section 11.5

Inferences

Concerning the Regression

Coefficients

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Figure 11.7 MINITAB printout for

t-test for data of Example 11.1

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Figure 11.8 The hypothesis

H 0 :  1 = 0 is not rejected

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Figure 11.9 The hypothesis

H 0 :  1 = 0 is rejected

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Figure 11.10 Plots depicting a

very good fit and a poor fit

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Section 11.6

Prediction

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Figure 11.11 Confidence limits for the

mean value of Y|x

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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

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Figure 11.13 SAS printout for

Example 11.27

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Section 11.7

Choice of a

Regression

Model

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Section 11.8

Analysis-of-Variance

Approach

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Table 11.2 Analysis of Variances

for Testing  1 = 0

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Figure 11.14 MINITAB printout of simple

linear regression for chemical oxygen

demand reduction data; part I

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Figure 11.15 MINITAB printout of simple

linear regression for chemical oxygen

demand reduction data; part II

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Table 11.3 Analysis of Variance

for Testing Linearity of Regression

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Figure 11.16 Connect linear model

with no lack-of-fit component

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Figure 11.17 Incorrect linear

model with lack-of-fit component

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Table 11.4 Data for Example 11.8

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Table 11.5 Analysis of Variance

on Yield-Temperature Data

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Figure 11.18 SAS printout, showing

analysis of data of Example 11.8

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Section 11.10

Data Plots and

Transformations

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Table 11.6 Some Useful

Transformations to Linearize

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Figure 11.19 Diagrams depicting

functions listed in Table 11.6

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Table 11.7 Data for Example 11.9

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Figure 11.20 Pressure and

volume data and fitted regression

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Figure 11.21 Ideal residual plot

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Figure 11.22 Residual plot depicting

heterogeneous error variance

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Section 11.11

Simple Linear

Regression Case Study

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Table 11.8 Density and Stiffness

for 30 Particleboards

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Figure 11.23 Scatter plot of the

wood density data

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Figure 11.24 Residual plot for the

wood density data

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Figure 11.25 Normal probability plot

of residuals for wood density data

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Section 11.12

Correlation

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Figure 11.26 Residual plot using the

log transformation for the wood density

data

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Figure 11.27 Normal probability plot of

residuals using the log transformation

for the wood density data

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Table 11.9 Data on 29 Loblolly

Pines for Example 11.10

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Figure 11.28 Scatter diagram showing

zero correlation

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partial analysis of data of Review

Exercise 11.54

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Exercise 11.55

continued on next slide

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Exercise 11.55 (cont’d)

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residual plot of Review Exercise 11.55

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Potential

Misconceptions and Hazards;

Relationship to

Material in Other Chapters

Section 11.13

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