Copyright © 2012 Pearson Education, Inc. All rights reserved. Chapter 3 Simple Linear Regression.

Chapter 3

Simple Linear Regression

Section 3.1

Introduction

Section 3.2

Straight-Line Probabilistic Model

Figure 3.1 The straight-line model

Section 3.3

Fitting the Model: The Method of Least Squares

Figure 3.2 Scatterplot for data in Table 3.1

Figure 3.3 Visual straight-line fit to data in Table 3.1

Figure 3.4 Plot of the least squares line y = .1 .7x^

Figure 3.5a SAS printout for advertising-sales regression

Figure 3.5b SPSS printout for advertising-sales regression

Figure 3.5c MINITAB printout for advertising-sales regression

Section 3.4

Model Assumptions

Figure 3.6 The probability distribution of

Section 3.5

An Estimator of 2

Figure 3.7 SAS printout for advertising-sales regression

Section 3.6

Assessing the Utility of the Model: Making Inferences About the Slope 1

Figure 3.8 Graphing the model with 1 = 0: y = 0 +

Figure 3.9 Sampling distribution of 1^

Figure 3.10 Rejection region and calculated t-value for testing whether the slope 1 = 0

Figure 3.11 SAS printout for advertising-sales regression

Section 3.7

The Coefficient of Correlation

Figure 3.12a&b Values of r and their implications

Figure 3.12c&d Values of r and their implications

Figure 3.12e&f Values of r and their implications

Figure 3.13 MINITAB correlation printout for Example 3.1

Figure 3.14 MINITAB scatterplot for Example 3.1

Figure 3.15 SPSS correlation analysis of tire data

Figure 3.16 SPSS scatterplot of tire data

Section 3.8

The Coefficient of Determination

Figure 3.17 A comparison of the sum of squares of deviations for two models

Figure 3.18 Portion of SPSS printout for advertising-sales regression

Figure 3.19 MINITAB graph of simple linear model relating price (y) to floor height (x)

Section 3.9

Using the Model for Estimation and Prediction

Figure 3.20 Estimated mean value and predicted individual value of sales revenue y for x = 4

Figure 3.21 SAS printout showing 95% confidence intervals for E(y)

Figure 3.22 SAS printout showing 95% prediction intervals for y

Figure 3.23 Error of estimating the mean value of y for a given value of x

Figure 3.24 Error of predicting a future value of y for a given value of x

Figure 3.25 Comparison of widths of 95% confidence and prediction intervals

Section 3.10

A Complete Example

Figure 3.26 SAS printout for fire damage linear regression

Figure 3.27 Least squares model for the fire damage data

Section 3.11

Regression Through the Origin (Optional)

Figure 3.28 SPSS regression through origin printout for Example 3.6

Figure 3.29 MINITAB scatterplot for data in Example 3.6

Figure 3.30 SPSS spreadsheet with 95% prediction intervals

Figure 3.31 Using a straight line to approximate a curvilinear relationship when the true relationship passes through the origin

Copyright © 2012 Pearson Education, Inc. All rights reserved. Chapter 3 Simple Linear Regression.

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