Section 10-3

1. Chapter 10 Correlation and Regression Section 10-3 Correlation

2. Chapter 10 Correlation and Regression Section 10-3 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. 10 8 6 Hours 4 2 Age 70 20 40 0 10 50 30 60 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.

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

8. c. State the hypotheses.

9. d. Test the significance of the correlation coefficient at  = 0.05, using Table I.

10. e. Give a brief explanation of the type of relationship. There is a significant linear relationship between a person’s age and the number of hours he or she exercises per week.

11. Chapter 10 Correlation and Regression Section 10-3 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. 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.

14. 500 400 300 Contribution 200 100 30 4 6 0 2 10 8 20 Years a. Draw the scatter plot for the variables.

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

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

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

18. c. State the hypotheses.

19. d. Test the significance of the correlation coefficient at  = 0.05, using Table I.

20. e. Give a brief explanation of the type of relationship. There is a significant linear relationship between a person’s age and his or her contribution.

21. Chapter 10 Correlation and Regression Section 10-3 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. 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?

24. 80 60 vandalism crimes 40 20 80 70 20 30 0 10 50 40 60 larceny crimes a. Draw the scatter plot for the variables.

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

28. c. State the hypotheses.

29. d. Test the significance of the correlation coefficient at  = 0.05, using Table I.

30. e. Give a brief explanation of the type of relationship. There is not a significant linear relationship between the number of larceny crimes and the number of vandalism crimes.

31. Chapter 10 Correlation and Regression Section 10-3 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. 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.

34. 5 4 3 Precipitation 2 1 70 80 90 100 0 60 Temperature a. Draw the scatter plot for the variables.

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

38. c. State the hypotheses.

39. d. Test the significance of the correlation coefficient at  = 0.05, using Table I.

40. e. Give a brief explanation of the type of relationship. There is a significant linear relationship between temperature and precipitation.

41. Chapter 10 Correlation and Regression Section 10-4 Regression

42. Chapter 10 Correlation and Regression Section 10-4 Exercise #13

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

44. Ages and Exercise Age x 18 26 32 38 52 59 Hours y 10 5 2 3 1.5 1 Find y  when x = 35 years.

45. Ages and Exercise Age x 18 26 32 38 52 59 Hours y 10 5 2 3 1.5 1 Find y  when x = 35 years.

46. Ages and Exercise Age x 18 26 32 38 52 59 Hours y 10 5 2 3 1.5 1 Find y  when x = 35 years.

47. Ages and Exercise Age x 18 26 32 38 52 59 Hours y 10 5 2 3 1.5 1 Find y  when x = 35 years.

48. Ages and Exercise Age x 18 26 32 38 52 59 Hours y 10 5 2 3 1.5 1 Find y  when x = 35 years.

49. Chapter 10 Correlation and Regression Section 10-4 Exercise #15

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