Ans 5611 2 ˆ 05471 1 ˆ y 25611 10547 x 4 the

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[Ans.: 5611 . 2 0 ˆ , 0547 . 1 1 ˆ . y = 2.5611 1.0547 x ] 4. The following data represent the chemistry grades for a random sample of 10 freshman at a certain college along with their scores on an intelligence test administered while they were still seniors in high school: Test Score, x 65 50 55 65 55 70 65 70 55 70 Chemistry grade, y 85 74 76 90 85 87 94 98 81 91 (a) Estimate the linear regression line. [Ans.: 46 . 33 ˆ 0 , 849 . 0 ˆ 1 . y =33.46+0.849 x ] (b) Calculate r to determine the relationship between the test score and the chemistry grade. [Ans: r = 0.84, strong positive] 5. In order to investigate the relationship between the commuting distance and stress, a researcher collected data for twelve workers commuting to a job in a city on a daily basis. The twelve subjects had their daily commuting distance measured in kilometers and were given a stress test after arriving at their job, measured on a continuous scale from 1 to 10. Higher scores indicate more stress. Worker 1 2 3 4 5 6 7 8 9 10 11 12 Distance, x 12.8 17.8 9.8 13.6 16.8 4.5 10.4 14.1 18.4 16.3 14.6 15.5 Stress level, y 7.5 8.1 4.8 6.3 9.5 4.5 6.3 6.7 8.1 6.9 7.2 7.9 (a) Estimate the regression line. [Ans.: 7832 . 2 ˆ 0 , 3062 . 0 ˆ 1 , Y = 2.7832 + 0.3062 X ] (b) Estimate the stress level for the commuting distance of 9.8. [Ans.: y = 5.784] (c) How much variation of stress level can be explained by distance and how strong is the correlation between both distance and stress level? [ Ans: r 2 = 0.7309 About 73.09% of total variation in stress level can be explained by the variation in distance. r = 0.8549 strong postive relationship]
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