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

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

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

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

5. Copyright © 2012 Pearson Education, Inc. All rights reserved. 3- 5 Figure 3.1 The straight-line model

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

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

8. Copyright © 2012 Pearson Education, Inc. All rights reserved. 3- 8 Figure 3.2 Scatterplot for data in Table 3.1

9. Copyright © 2012 Pearson Education, Inc. All rights reserved. 3- 9 Figure 3.3 Visual straight-line fit to data in Table 3.1

10. Copyright © 2012 Pearson Education, Inc. All rights reserved. 3- 10

11. Copyright © 2012 Pearson Education, Inc. All rights reserved. 3- 11

12. Copyright © 2012 Pearson Education, Inc. All rights reserved. 3- 12

13. Copyright © 2012 Pearson Education, Inc. All rights reserved. 3- 13 Figure 3.4 Plot of the least squares line y = .1 .7x ^

14. Copyright © 2012 Pearson Education, Inc. All rights reserved. 3- 14

15. Copyright © 2012 Pearson Education, Inc. All rights reserved. 3- 15 Figure 3.5a SAS printout for advertising-sales regression

16. Copyright © 2012 Pearson Education, Inc. All rights reserved. 3- 16 Figure 3.5b SPSS printout for advertising-sales regression

17. Copyright © 2012 Pearson Education, Inc. All rights reserved. 3- 17 Figure 3.5c MINITAB printout for advertising-sales regression

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

19. Copyright © 2012 Pearson Education, Inc. All rights reserved. 3- 19 Figure 3.6 The probability distribution of 

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

21. Copyright © 2012 Pearson Education, Inc. All rights reserved. 3- 21

22. Copyright © 2012 Pearson Education, Inc. All rights reserved. 3- 22 Figure 3.7 SAS printout for advertising-sales regression

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

24. Copyright © 2012 Pearson Education, Inc. All rights reserved. 3- 24 Figure 3.8 Graphing the model with  1 = 0: y =  0 + 

25. Copyright © 2012 Pearson Education, Inc. All rights reserved. 3- 25

26. Copyright © 2012 Pearson Education, Inc. All rights reserved. 3- 26 Figure 3.9 Sampling distribution of  1 ^

27. Copyright © 2012 Pearson Education, Inc. All rights reserved. 3- 27

28. Copyright © 2012 Pearson Education, Inc. All rights reserved. 3- 28 Figure 3.10 Rejection region and calculated t-value for testing whether the slope  1 = 0

29. Copyright © 2012 Pearson Education, Inc. All rights reserved. 3- 29 Figure 3.11 SAS printout for advertising-sales regression

30. Copyright © 2012 Pearson Education, Inc. All rights reserved. 3- 30

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

32. Copyright © 2012 Pearson Education, Inc. All rights reserved. 3- 32 Figure 3.12a&b Values of r and their implications

33. Copyright © 2012 Pearson Education, Inc. All rights reserved. 3- 33 Figure 3.12c&d Values of r and their implications

34. Copyright © 2012 Pearson Education, Inc. All rights reserved. 3- 34 Figure 3.12e&f Values of r and their implications

35. Copyright © 2012 Pearson Education, Inc. All rights reserved. 3- 35

36. Copyright © 2012 Pearson Education, Inc. All rights reserved. 3- 36 Figure 3.13 MINITAB correlation printout for Example 3.1

37. Copyright © 2012 Pearson Education, Inc. All rights reserved. 3- 37 Figure 3.14 MINITAB scatterplot for Example 3.1

38. Copyright © 2012 Pearson Education, Inc. All rights reserved. 3- 38

39. Copyright © 2012 Pearson Education, Inc. All rights reserved. 3- 39

40. Copyright © 2012 Pearson Education, Inc. All rights reserved. 3- 40 Figure 3.15 SPSS correlation analysis of tire data

41. Copyright © 2012 Pearson Education, Inc. All rights reserved. 3- 41 Figure 3.16 SPSS scatterplot of tire data

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

43. Copyright © 2012 Pearson Education, Inc. All rights reserved. 3- 43 Figure 3.17 A comparison of the sum of squares of deviations for two models

44. Copyright © 2012 Pearson Education, Inc. All rights reserved. 3- 44

45. Copyright © 2012 Pearson Education, Inc. All rights reserved. 3- 45 Figure 3.18 Portion of SPSS printout for advertising-sales regression

46. Copyright © 2012 Pearson Education, Inc. All rights reserved. 3- 46 Figure 3.19 MINITAB graph of simple linear model relating price (y) to floor height (x)

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

48. Copyright © 2012 Pearson Education, Inc. All rights reserved. 3- 48 Figure 3.20 Estimated mean value and predicted individual value of sales revenue y for x = 4

49. Copyright © 2012 Pearson Education, Inc. All rights reserved. 3- 49

50. Copyright © 2012 Pearson Education, Inc. All rights reserved. 3- 50

51. Copyright © 2012 Pearson Education, Inc. All rights reserved. 3- 51

52. Copyright © 2012 Pearson Education, Inc. All rights reserved. 3- 52 Figure 3.21 SAS printout showing 95% confidence intervals for E(y)

53. Copyright © 2012 Pearson Education, Inc. All rights reserved. 3- 53 Figure 3.22 SAS printout showing 95% prediction intervals for y

54. Copyright © 2012 Pearson Education, Inc. All rights reserved. 3- 54 Figure 3.23 Error of estimating the mean value of y for a given value of x

55. Copyright © 2012 Pearson Education, Inc. All rights reserved. 3- 55 Figure 3.24 Error of predicting a future value of y for a given value of x

56. Copyright © 2012 Pearson Education, Inc. All rights reserved. 3- 56 Figure 3.25 Comparison of widths of 95% confidence and prediction intervals

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

58. Copyright © 2012 Pearson Education, Inc. All rights reserved. 3- 58

59. Copyright © 2012 Pearson Education, Inc. All rights reserved. 3- 59 Figure 3.26 SAS printout for fire damage linear regression

60. Copyright © 2012 Pearson Education, Inc. All rights reserved. 3- 60 Figure 3.27 Least squares model for the fire damage data

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

62. Copyright © 2012 Pearson Education, Inc. All rights reserved. 3- 62

63. Copyright © 2012 Pearson Education, Inc. All rights reserved. 3- 63

64. Copyright © 2012 Pearson Education, Inc. All rights reserved. 3- 64

65. Copyright © 2012 Pearson Education, Inc. All rights reserved. 3- 65

66. Copyright © 2012 Pearson Education, Inc. All rights reserved. 3- 66 Figure 3.28 SPSS regression through origin printout for Example 3.6

67. Copyright © 2012 Pearson Education, Inc. All rights reserved. 3- 67 Figure 3.29 MINITAB scatterplot for data in Example 3.6

68. Copyright © 2012 Pearson Education, Inc. All rights reserved. 3- 68 Figure 3.30 SPSS spreadsheet with 95% prediction intervals

69. Copyright © 2012 Pearson Education, Inc. All rights reserved. 3- 69 Figure 3.31 Using a straight line to approximate a curvilinear relationship when the true relationship passes through the origin