A84 ODD ANSWERS 35. (a) x y 10 20 30 40 50 5 10 15 20 25 30 35 (b) The point (44, 8) may be an outlier. (c) The point (44, 8) is not an influential point because the slopes and y-intercepts of the regression lines with the point included and without the point included are not significantly different. 37. ny = 654.536x - 1214.857 39. y = 93.028(1.712)x Number of bacteria Number of hours x y 1 2 3 4 5 6 7 1000 2000 3000 4000 5000 0 0 8 5000 41. ny = -78.929x + 576.179 43. y = 782.300x-1.251 x y 1 2 3 4 5 6 7 8 100 200 300 400 500 600 700 50 0 9 750 45. y = 25.035 + 19.599 ln x 64 8 13 76 47. The logarithmic equation is a better model for the data. The graph of the logarithmic equation fits the data better than the regression line. Section 9.2 Activity (page 496) 1 – 4. Answers will vary. Section 9.3 (page 504) 1. The total variation is the sum of the squares of the differences between the y-values of each ordered pair and the mean of the y-values of the ordered pairs, or g(yi - y) 2. 3. The unexplained variation is the sum of the squares of the differences between the observed y-values and the predicted y-values, or g(yi - nyi) 2. 5. Two variables that have perfect positive or perfect negative linear correlation have a correlation coefficient of 1 or -1, respectively. In either case, the coefficient of determination is 1, which means that 100% of the variation in the response variable is explained by the variation in the explanatory variable. 7. 0.216. About 21.6% of the variation is explained. About 78.4% of the variation is unexplained. 9. 0.916. About 91.6% of the variation is explained. About 8.4% of the variation is unexplained. 11. (a) 0.592. About 59.2% of the variation is explained by the relationship between the number of offerings and proceeds and about 40.8% of the variation is unexplained. (b) 9270.785. The standard error of estimate of the proceeds for a specific number of offerings is about 9,270,785,000. 13. (a) 0.764. About 76.4% of the variation is explained by the relationship between the goals allowed and points and about 23.6% of the variation is unexplained. (b) 6.593. The standard error of estimate of the points for a specific number of goals allowed is about 6.593. 15. (a) 0.845. About 84.5% of the variation is explained by the relationship between the percentage of employment in STEM occupations and mean annual wage and about 15.5% of the variation is unexplained. (b) 4.427. The standard error of estimate of the mean annual wage for a specific percentage of employment in STEM occupations is about $4427. 17. (a) 0.902. About 90.2% of the variation is explained by the relationship between the marketed productions of natural gas in the U.S. and the exports of natural gas from the U.S. and about 9.8% of the variation is unexplained. (b) 488.612. The standard error of estimate of the exports of natural gas for a specific marketed production of natural gas is about 488,612,000,000 cubic feet. 19. (a) 0.700. About 70% of the variation is explained by the relationship between the new vehicle sales of Ford and General Motors and about 30% of the variation is unexplained. (b) 199.143. The standard error of estimate of the new vehicle sales of General Motors for a specific amount of new vehicle sales of Ford is about 199,143 new vehicles. 21. 25,681.536 6 y 6 73,259.544 You can be 95% confident that the proceeds will be between $25,681,536,000 and $73,259,544,000 when the number of initial offerings is 200 issues. 23. 62.72 6 y 6 87.99 You can be 90% confident that the total points earned will be between 63 and 88 when the number of goals allowed is 140.
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