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

Copyright © 2012 Pearson Education, Inc. All rights reserved.

Chapter 3

Simple Linear Regression


Section 3.1

Introduction


Section 3.2

The

Straight-Line Probabilistic Model

Copyright © 2012 Pearson Education, Inc. All rights reserved.3- 4


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

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