12.6 Linear Correlation and Regression 833 Many of the exercises in this section are designed so that they can be done by hand or by using an appropriate form of technology (graphing calculator, spreadsheet, or StatCrunch). Practice the Skills In Exercises 11–18, (a) draw a scatter diagram; (b) determine the value of r, rounded to the nearest thousandth; then use Table 12.9 to (c) determine whether a correlation exists at 0.05; α= and (d) determine whether a correlation exists at 0.01. α= x y 4 8 5 10 6 12 7 12 10 16 12. * x y 8 14 10 12 13 10 16 11 19 8 11. * x y 23 30 35 38 31 27 43 21 49 40 14. * x y 90 3 80 4 60 6 60 5 40 5 20 7 13. * x y 5.3 10.3 4.7 9.6 8.4 12.5 12.7 16.2 4.9 9.8 16. * x y 12 15 16 19 13 45 24 30 100 60 50 28 15. * x y 100 2 80 3 60 5 60 6 40 6 20 8 18. * x y 90 90 70 70 65 65 60 60 50 50 40 40 15 15 17. * In Exercises 19–26, assume that a sample of bivariate data yields the correlation coefficient, r, indicated. Use Table 12.9 for the specified sample size and level of significance to determine whether a linear correlation exists. 19. r 0.92 = when n 10 = at 0.01 α= Yes 20. r 0.43 = when n 17 = at 0.01 α= No 21. r 0.59 = − when n 11 = at 0.05 α= No 22. r 0.89 = − when n 6 = at 0.05 α= Yes 23. r 0.32 = − when n 102 = at 0.01 α= Yes 24. r 0.51 = − when n 13 = at 0.05 α= No 25. r 0.75 = when n 6 = at 0.01 α= No 26. r 0.96 = when n 5 = at 0.01 α= Yes In Exercises 27–34, determine the equation of the line of best fit from the data indicated in the exercise. Round both m and b to the nearest hundredth. 27. Exercises 11 y x 1.26 3.51 = + 28. Exercises 12 y x 0.46 17.03 = − + 29. Exercises 13 y x 0.18 24.82 = + 30. Exercises 14 y x 0.05 7.84 = − + 31. Exercises 15 y x 0.81 5.84 = + 32. Exercises 16 y x 0.36 19.99 = + 33. Exercises 17 y x 0.08 9.50 = − + 34. Exercises 18 y x 1.00 = Problem Solving In Exercises 35– 44, round both m and b to the nearest hundredth. 35. Commuting to a Pet Shelter The following data show the commuting distances and commuting times of six volunteers working at a pet shelter. Distance (miles) 2 15 16 9 21 5 Time (minutes) 5 2530203510 a) Determine the correlation coefficient between the commuting distance and the commuting time. 0.987 b) Determine whether a correlation exists at 0.05. α= Yes *See Instructor Answer Appendix
RkJQdWJsaXNoZXIy NjM5ODQ=