1. Section 10-3 Chapter 10 Correlation and Regression Correlation
Let’s work Exercise #19 from Section 5.1
Correlation

2. Section 10-3 Exercise #13 Chapter 10 Correlation and Regression
Let’s work Exercise #19 from Section 5.1
Exercise #13

3. For the following exercise, complete these steps.
Draw the scatter plot for the variables.
Compute the value of the correlation coefficient.
State the hypotheses.
Test the significance of the correlation coefficient at  = 0.05, using Table I.
Give a brief explanation of the type of relationship.

4. a. Draw the scatter plot for the variables.
A researcher wishes to determine if a person’s age is related to the number of hours he or she exercises per week. The data for the sample are shown below.
a. Draw the scatter plot for the variables.
Age x 18 26 32 38 52 59
Hours y 10 5 2 3
1.5 1 2 4 6 8 10 20 30 40 50 60
Age
Hours 70

5. b. Compute the value of the correlation coefficient.
Age x 18 26 32 38 52 59
Hours y 10 5 2 3
1.5 1

8. c. State the hypotheses. Age x 18 26 32 38 52 59 Hours y 10 5 2 3 1.5

9. d. Test the significance of the correlation coefficient at  = 0
d. Test the significance of the correlation coefficient at  = 0.05, using Table I.
Age x 18 26 32 38 52 59
Hours y 10 5 2 3
1.5 1

10. e. Give a brief explanation of the type of relationship.
Age x 18 26 32 38 52 59
Hours y 10 5 2 3
1.5 1
There is a significant linear relationship between a person’s age and the number of hours he or she exercises per week.

11. Section 10-3 Exercise #15 Chapter 10 Correlation and Regression
Let’s work Exercise #19 from Section 5.1
Exercise #15

12. For the following exercise, complete these steps.
Draw the scatter plot for the variables.
Compute the value of the correlation coefficient.
State the hypotheses.
Test the significance of the correlation coefficient at  = 0.05, using Table I.
Give a brief explanation of the type of relationship.

13. relationship between the amount of an alumnus’s
The director of an alumni association for a small college wants to determine whether there is any type of
relationship between the amount of an alumnus’s
contribution (in dollars) and the years
the alumnus has been out of school.
The data are shown here.
Years x 1 5 3 10 7 6
Contribution y
500
100
300 50 75 80

14. a. Draw the scatter plot for the variables.
Years x 1 5 3 10 7 6
Contribution y
500
100
300 50 75 80
100
200
300
400
500 2 4 8 6 10 20
Years
Contribution 30

15. b. Compute the value of the correlation coefficient.
Years x 1 5 3 10 7 6
Contribution y
500
100
300 50 75 80

16. b. Compute the value of the correlation coefficient.

17. b. Compute the value of the correlation coefficient.

18. c. State the hypotheses. Years x 1 5 3 10 7 6 Contribution y 500 100
300 50 75 80

19. d. Test the significance of the correlation coefficient at  = 0
d. Test the significance of the correlation coefficient at  = 0.05, using Table I.
Years x 1 5 3 10 7 6
Contribution y
500
100
300 50 75 80

20. e. Give a brief explanation of the type of relationship.
Years x 1 5 3 10 7 6
Contribution y
500
100
300 50 75 80
There is a significant linear relationship between a person’s age and his or her contribution.

21. Section 10-3 Exercise #17 Chapter 10 Correlation and Regression
Let’s work Exercise #19 from Section 5.1
Exercise #17

22. For the following exercise, complete these steps.
Draw the scatter plot for the variables.
Compute the value of the correlation coefficient.
State the hypotheses.
Test the significance of the correlation coefficient at  = 0.05, using Table I.
Give a brief explanation of the type of relationship.

23. Number of larceny crimes, x Number of vandalism crimes y
A criminology student wishes to see if there is a relationship between the number of larceny crimes and the number of vandalism crimes on college campuses in Southwestern Pennsylvania. The data are shown. Is there a relationship between the two
types of crimes?
Number of larceny crimes, x 24 6 16 64 10 25 35
Number of vandalism crimes y 21 3 15 61 20

24. Number of larceny crimes, x Number of vandalism crimes y
a. Draw the scatter plot for the variables.
Number of larceny crimes, x 24 6 16 64 10 25 35
Number of vandalism crimes y 21 3 15 61 20 20 40 60 80 10 30 50
larceny crimes
vandalism crimes 70

25. Number of larceny crimes, x Number of vandalism crimes y
b. Compute the value of the correlation coefficient.
Number of larceny crimes, x 24 6 16 64 10 25 35
Number of vandalism crimes y 21 3 15 61 20
Check the Math, specially n values.!

28. Number of larceny crimes, x Number of vandalism crimes y
c. State the hypotheses.
Number of larceny crimes, x 24 6 16 64 10 25 35
Number of vandalism crimes y 21 3 15 61 20

29. Number of larceny crimes, x Number of vandalism crimes y
d. Test the significance of the correlation coefficient at  = 0.05, using Table I.
Number of larceny crimes, x 24 6 16 64 10 25 35
Number of vandalism crimes y 21 3 15 61 20

30. Number of larceny crimes, x Number of vandalism crimes y
e. Give a brief explanation of the type of relationship.
Number of larceny crimes, x 24 6 16 64 10 25 35
Number of vandalism crimes y 21 3 15 61 20
There is not a significant linear relationship between the number of larceny crimes and the number of vandalism crimes.

31. Section 10-3 Exercise #23 Chapter 10 Correlation and Regression
Let’s work Exercise #19 from Section 5.1
Exercise #23

32. For the following exercise, complete these steps.
Draw the scatter plot for the variables.
Compute the value of the correlation coefficient.
State the hypotheses.
Test the significance of the correlation coefficient at  = 0.05, using Table I.
Give a brief explanation of the type of relationship.

33. Average daily temperature, x Average monthly precipitation, y
The average daily temperature (in degrees Fahrenheit) and the corresponding average monthly precipitation (in inches) for the month of June are shown
here for seven randomly selected cities in
the United States. Determine if there is a
relationship between the two variables.
Average daily temperature, x 86 81 83 89 80 74 64
Average monthly precipitation, y
3.4
1.8
3.5
3.6
3.7
1.5
0.2

34. Average daily temperature, x Average monthly precipitation, y
a. Draw the scatter plot for the variables.
Average daily temperature, x 86 81 83 89 80 74 64
Average monthly precipitation, y
3.4
1.8
3.5
3.6
3.7
1.5
0.2 1 2 3 4 60
Temperature
Precipitation 70 80 90
100 5

35. Average daily temperature, x Average monthly precipitation, y
b. Compute the value of the correlation coefficient.
Average daily temperature, x 86 81 83 89 80 74 64
Average monthly precipitation, y
3.4
1.8
3.5
3.6
3.7
1.5
0.2

38. Average daily temperature, x Average monthly precipitation, y
c. State the hypotheses.
Average daily temperature, x 86 81 83 89 80 74 64
Average monthly precipitation, y
3.4
1.8
3.5
3.6
3.7
1.5
0.2

39. Average daily temperature, x Average monthly precipitation, y
d. Test the significance of the correlation coefficient at  = 0.05, using Table I.
Average daily temperature, x 86 81 83 89 80 74 64
Average monthly precipitation, y
3.4
1.8
3.5
3.6
3.7
1.5
0.2

40. Average daily temperature, x Average monthly precipitation, y
e. Give a brief explanation of the type of relationship.
Average daily temperature, x 86 81 83 89 80 74 64
Average monthly precipitation, y
3.4
1.8
3.5
3.6
3.7
1.5
0.2
There is a significant linear relationship between temperature and precipitation.

41. Section 10-4 Chapter 10 Correlation and Regression Regression
Let’s work Exercise #19 from Section 5.1
Regression

42. Section 10-4 Exercise #13 Chapter 10 Correlation and Regression
Let’s work Exercise #19 from Section 5.1
Exercise #13

43. Find the equation of the regression line and find the y value for the specified x value. Remember that no regression should be done when r is not significant.
Ages and Exercise 1
1.5 3 2 5 10
Hours y 59 52 38 32 26 18
Age x

44. Find y  when x = 35 years. Ages and Exercise 1 1.5 3 2 5 10 Hours y59 52 38 32 26 18
Age x

45. Find y  when x = 35 years. Ages and Exercise 1 1.5 3 2 5 10 Hours y59 52 38 32 26 18
Age x

46. Find y  when x = 35 years. Ages and Exercise 1 1.5 3 2 5 10 Hours y59 52 38 32 26 18
Age x

47. Find y  when x = 35 years. Ages and Exercise 1 1.5 3 2 5 10 Hours y59 52 38 32 26 18
Age x

48. Find y  when x = 35 years. Ages and Exercise 1 1.5 3 2 5 10 Hours y59 52 38 32 26 18
Age x

49. Section 10-4 Exercise #15 Chapter 10 Correlation and Regression
Let’s work Exercise #19 from Section 5.1
Exercise #15

50. Years and Contribution
Find the equation of the regression line and find the y value for the specified x value. Remember that no regression should be done when r is not significant.
Years and Contribution 80 75 50
300
100
500
Contribution y, $ 6 7 10 3 5 1
Years x

51. Years and Contribution
Find y when x = 4 years.
Years and Contribution 80 75 50
300
100
500
Contribution y, $ 6 7 10 3 5 1
Years x

53. Years and Contribution
Find y when x = 4 years.
Years and Contribution 80 75 50
300
100
500
Contribution y, $ 6 7 10 3 5 1
Years x

55. Years and Contribution
Find y when x = 4 years.
Years and Contribution 80 75 50
300
100
500
Contribution y, $ 6 7 10 3 5 1
Years x

56. Section 10-4 Exercise #23 Chapter 10 Correlation and Regression
Let’s work Exercise #19 from Section 5.1
Exercise #23

57. Temperatures ( in. F ) and precipitation (in.)
Find the equation of the regression line and find the y value when x = 70 ºF. Remember that no regression should be done when r is not significant.
0.2 64
1.5
3.7
3.6
3.5
1.8
3.4
Avg. mo. Precip. y 74 80 89 83 81 86
Avg. daily temp. x
Temperatures ( in. F ) and precipitation (in.)

61. Section 10-5 Chapter 10 Correlation and Regression
Let’s work Exercise #19 from Section 5.1
Coefficient of Determination and Standard Error of the Estimate

62. Section 10-5 Exercise #9 Chapter 10 Correlation and Regression
Let’s work Exercise #19 from Section 5.1
Exercise #9

63. Find the coefficients of determination and non-determination when and explain the meaning
49% of the variation of y is due to the variation of x.

64. Find the coefficients of determination and non-determination when and explain the meaning
51% of the variation of y is due
to chance.

65. Section 10-5 Exercise #15 Chapter 10 Correlation and Regression
Let’s work Exercise #19 from Section 5.1
Exercise #15

66. Compute the standard error of the estimate.
The regression line equation was found in Exercise 13 in Section 10-4.

68. Section 10-5 Exercise #19 Chapter 10 Correlation and Regression
Let’s work Exercise #19 from Section 5.1
Exercise #19

69. Find the 90% prediction interval when x = 20 years.
Age x 18 26 32 38 52 59
Hours y 10 5 2 3
1.5 1

72. Section 10-5 Exercise #21 Chapter 10 Correlation and Regression
Let’s work Exercise #19 from Section 5.1
Exercise #21

73. Find the 90% prediction interval when x = 4 years.
Years x 1 5 3 10 7 6
Contributions y, $
500
100
300 50 75 80

76. Section 10-6 Chapter 10 Correlation and Regression Multiple Regression
Let’s work Exercise #19 from Section 5.1
Multiple Regression

77. Section 10-6 Exercise #7 Chapter 10 Correlation and Regression
Let’s work Exercise #19 from Section 5.1
Exercise #7

78. A manufacturer found that a significant relationship exists among the number of hours an assembly line employee works per shift x1, the total
number of items produced x2, and the
number of defective items produced y.
The multiple regression equation is Predict the
number of defective items
produced by an employee who has
worked 9 hours and produced
24 items.

80. Section 10-6 Exercise #9 Chapter 10 Correlation and Regression
Let’s work Exercise #19 from Section 5.1
Exercise #9

81. An educator has found a significant relationship among a college graduate’s IQ x1, score on the verbal section of the SAT x2, and income for the first year
following graduation from college y.
Predict the income of a college graduate
whose IQ is 120 and verbal SAT score is
650. The regression equation is