A82 ODD ANSWERS 16. d. You would not expect age and height to be correlated. 17. b. You would expect a negative linear correlation between age and balance on student loans. 18. a. You would expect the relationship between age and body temperature to be fairly constant. 19. Sample answer: People who can afford more valuable homes will live longer because they have more money to take care of themselves. 21. Sample answer: Ice cream sales are higher when the weather is warm and people are outside more often. This is when homicide rates go up as well. 23. (a) x y Age (in years) Vocabulary size 1 2 3 4 5 6 500 1000 1500 2000 2500 3000 (b) 0.979 (c) Strong positive correlation. As age increases, the number of words in children’s vocabulary tends to increase. (d) There is enough evidence at the 1% level of significance to conclude that there is a significant linear correlation between children’s ages and number of words in their vocabulary. 25. (a) 140 160 180 48 50 52 54 56 x Maximum weight (in kilograms) Jump height (in centimeters) 58 60 62 64 66 200 220 y (b) 0.756 (c) Strong positive linear correlation. As the maximum weight for one repetition of a half squat increases, the jump height tends to increase. (d) There is enough evidence at the 1% level of significance to conclude that there is a significant linear correlation between maximum weight for one repetition of a half squat and jump height. 27. (a) x Earnings per share (in dollars) Dividends per share (in dollars) y 12345678910 1 2 3 4 (b) 0.7257 (c) Strong positive linear correlation. As the earnings per share increase, the dividends per share tend to increase. (d) There is not enough evidence at the 1% level of significance to conclude that there is a significant linear correlation between earnings per share for the companies and their dividends per share. 29. The correlation coefficient gets weaker, going from r ≈ 0.979 to r ≈ 0.863. 31. The correlation coefficient gets stronger, going from r ≈ 0.756 to r ≈ 0.908. 33. There is not enough evidence at the 1% level of significance to conclude that there is a significant linear correlation between vehicle weight and the variability in braking distance on a dry surface. 35. There is enough evidence at the 5% level of significance to conclude that there is a significant linear correlation between the maximum weight for one repetition of a half squat and the jump height. 37. r ≈ -0.975. The correlation coefficient remains unchanged when the x-values and y-values are switched. Section 9.1 Activity (page 485) 1 – 4. Answers will vary. Section 9.2 (page 490) 1. A residual is the difference between the observed y-value of a data point and the predicted y-value on the regression line for the x-coordinate of the data point. A residual is positive when the data point is above the line, negative when the point is below the line, and zero when the observed y-value equals the predicted y-value. 3. Substitute a value of x into the equation of a regression line and solve for ny. 5. The correlation between variables must be significant. 7. b 8. a 9. e 10. c 11. f 12. d 13. b 14. c 15. d 16. a 17. ny = 0.092x - 18.834 x Height (in feet) Number of stories y 700 900 1100 40 50 60 70 80 (a) 69 stories (b) 59 stories (c) 55 stories (d) It is not meaningful to predict the value of y for x = 650 feet because x = 650 feet is outside the range of the original data.
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