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

Copyright © 2012 Pearson Education, Inc. All rights reserved. Section 3.1 Introduction

Copyright © 2012 Pearson Education, Inc. All rights reserved. Section 3.2 The Straight-Line Probabilistic Model

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

Copyright © 2012 Pearson Education, Inc. All rights reserved Figure 3.1 The straight-line model

Copyright © 2012 Pearson Education, Inc. All rights reserved. Section 3.3 Fitting the Model: The Method of Least Squares

Copyright © 2012 Pearson Education, Inc. All rights reserved. 3- 7

Copyright © 2012 Pearson Education, Inc. All rights reserved Figure 3.2 Scatterplot for data in Table 3.1

Copyright © 2012 Pearson Education, Inc. All rights reserved Figure 3.3 Visual straight-line fit to data in Table 3.1

Copyright © 2012 Pearson Education, Inc. All rights reserved

Copyright © 2012 Pearson Education, Inc. All rights reserved

Copyright © 2012 Pearson Education, Inc. All rights reserved

Copyright © 2012 Pearson Education, Inc. All rights reserved Figure 3.4 Plot of the least squares line y = .1 .7x ^

Copyright © 2012 Pearson Education, Inc. All rights reserved

Copyright © 2012 Pearson Education, Inc. All rights reserved Figure 3.5a SAS printout for advertising-sales regression

Copyright © 2012 Pearson Education, Inc. All rights reserved Figure 3.5b SPSS printout for advertising-sales regression

Copyright © 2012 Pearson Education, Inc. All rights reserved Figure 3.5c MINITAB printout for advertising-sales regression

Copyright © 2012 Pearson Education, Inc. All rights reserved. Section 3.4 Model Assumptions

Copyright © 2012 Pearson Education, Inc. All rights reserved Figure 3.6 The probability distribution of 

Copyright © 2012 Pearson Education, Inc. All rights reserved. Section 3.5 An Estimator of  2

Copyright © 2012 Pearson Education, Inc. All rights reserved

Copyright © 2012 Pearson Education, Inc. All rights reserved Figure 3.7 SAS printout for advertising-sales regression

Copyright © 2012 Pearson Education, Inc. All rights reserved. Section 3.6 Assessing the Utility of the Model: Making Inferences About the Slope  1

Copyright © 2012 Pearson Education, Inc. All rights reserved Figure 3.8 Graphing the model with  1 = 0: y =  0 + 

Copyright © 2012 Pearson Education, Inc. All rights reserved

Copyright © 2012 Pearson Education, Inc. All rights reserved Figure 3.9 Sampling distribution of  1 ^

Copyright © 2012 Pearson Education, Inc. All rights reserved

Copyright © 2012 Pearson Education, Inc. All rights reserved Figure 3.10 Rejection region and calculated t-value for testing whether the slope  1 = 0

Copyright © 2012 Pearson Education, Inc. All rights reserved Figure 3.11 SAS printout for advertising-sales regression

Copyright © 2012 Pearson Education, Inc. All rights reserved

Copyright © 2012 Pearson Education, Inc. All rights reserved. Section 3.7 The Coefficient of Correlation

Copyright © 2012 Pearson Education, Inc. All rights reserved Figure 3.12a&b Values of r and their implications

Copyright © 2012 Pearson Education, Inc. All rights reserved Figure 3.12c&d Values of r and their implications

Copyright © 2012 Pearson Education, Inc. All rights reserved Figure 3.12e&f Values of r and their implications

Copyright © 2012 Pearson Education, Inc. All rights reserved

Copyright © 2012 Pearson Education, Inc. All rights reserved Figure 3.13 MINITAB correlation printout for Example 3.1

Copyright © 2012 Pearson Education, Inc. All rights reserved Figure 3.14 MINITAB scatterplot for Example 3.1

Copyright © 2012 Pearson Education, Inc. All rights reserved

Copyright © 2012 Pearson Education, Inc. All rights reserved

Copyright © 2012 Pearson Education, Inc. All rights reserved Figure 3.15 SPSS correlation analysis of tire data

Copyright © 2012 Pearson Education, Inc. All rights reserved Figure 3.16 SPSS scatterplot of tire data

Copyright © 2012 Pearson Education, Inc. All rights reserved. Section 3.8 The Coefficient of Determination

Copyright © 2012 Pearson Education, Inc. All rights reserved Figure 3.17 A comparison of the sum of squares of deviations for two models

Copyright © 2012 Pearson Education, Inc. All rights reserved

Copyright © 2012 Pearson Education, Inc. All rights reserved Figure 3.18 Portion of SPSS printout for advertising-sales regression

Copyright © 2012 Pearson Education, Inc. All rights reserved Figure 3.19 MINITAB graph of simple linear model relating price (y) to floor height (x)

Copyright © 2012 Pearson Education, Inc. All rights reserved. Section 3.9 Using the Model for Estimation and Prediction

Copyright © 2012 Pearson Education, Inc. All rights reserved Figure 3.20 Estimated mean value and predicted individual value of sales revenue y for x = 4

Copyright © 2012 Pearson Education, Inc. All rights reserved

Copyright © 2012 Pearson Education, Inc. All rights reserved

Copyright © 2012 Pearson Education, Inc. All rights reserved

Copyright © 2012 Pearson Education, Inc. All rights reserved Figure 3.21 SAS printout showing 95% confidence intervals for E(y)

Copyright © 2012 Pearson Education, Inc. All rights reserved Figure 3.22 SAS printout showing 95% prediction intervals for y

Copyright © 2012 Pearson Education, Inc. All rights reserved Figure 3.23 Error of estimating the mean value of y for a given value of x

Copyright © 2012 Pearson Education, Inc. All rights reserved Figure 3.24 Error of predicting a future value of y for a given value of x

Copyright © 2012 Pearson Education, Inc. All rights reserved Figure 3.25 Comparison of widths of 95% confidence and prediction intervals

Copyright © 2012 Pearson Education, Inc. All rights reserved. Section 3.10 A Complete Example

Copyright © 2012 Pearson Education, Inc. All rights reserved

Copyright © 2012 Pearson Education, Inc. All rights reserved Figure 3.26 SAS printout for fire damage linear regression

Copyright © 2012 Pearson Education, Inc. All rights reserved Figure 3.27 Least squares model for the fire damage data

Copyright © 2012 Pearson Education, Inc. All rights reserved. Section 3.11 Regression Through the Origin (Optional)

Copyright © 2012 Pearson Education, Inc. All rights reserved

Copyright © 2012 Pearson Education, Inc. All rights reserved

Copyright © 2012 Pearson Education, Inc. All rights reserved

Copyright © 2012 Pearson Education, Inc. All rights reserved

Copyright © 2012 Pearson Education, Inc. All rights reserved Figure 3.28 SPSS regression through origin printout for Example 3.6

Copyright © 2012 Pearson Education, Inc. All rights reserved Figure 3.29 MINITAB scatterplot for data in Example 3.6

Copyright © 2012 Pearson Education, Inc. All rights reserved Figure 3.30 SPSS spreadsheet with 95% prediction intervals

Copyright © 2012 Pearson Education, Inc. All rights reserved Figure 3.31 Using a straight line to approximate a curvilinear relationship when the true relationship passes through the origin