**Research on Training for a 5K Race**Research was conducted on the amount of training for a 5K race and the time a contestant took to run the race. The researcher recorded the number of miles a contestant ran during the last month of training and the time it took the contestant to complete the 5K. The results are below:| Miles Trained | 66 | 71 | 83 | 100 | 110 | 110 | 110 ||---------------|----|----|----|-----|-----|-----|-----|| Time (Minutes)| 23 | 27 | 35 | 35 | 45 | 47 | 47 |**(a)** Give the correlation coefficient. *Round to one decimal place.* ⎕**(b)** Use technology to write the regression equation that predicts the time it takes a contestant to complete the race by using the miles trained as the explanatory variable. *Complete the missing parts of the equation below, rounding values to one decimal place.*\( \hat{y} = \) ⎕ + ⎕\(x\)**(c)** Interpret the \( y \)-intercept in the context of this scenario.- ( ) Each additional mile of training reduces the time needed to complete the 5K by 0.5 minutes.- ( ) A contestant who has not trained at all in the last month can expect to complete the 5K in -6.7 minutes.- ( ) Each additional mile of training reduces the time needed to complete the 5K by -6.7 minutes.- ( ) A contestant who has not trained at all in the last month can expect to complete the 5K in 0.5 minutes.**(d)** Use your answer from part (b) to predict the time needed to complete the 5K if a runner trained 100 miles last month. *Round to one decimal place.*⎕ minutes

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Research was conducted on the amount of training for 5K race and the time a contestant took to run the race. The researcher recorded the number of miles a contestant ran during the last month of training and the time it took the contestant to complete the 5K. The results are below. Miles Trained 65 78 90 91 104 112 Time (Minutes) 23 26 34 39 42 50 (a) Give the correlation coefficient. Round to one decimal place. (b) Use technology to write the regression equation that predicts the time it takes a contestant to complete the race by using the miles trained as the explanatory variable. Complete the missing parts of the equation below, rounding values to one decimal place. ý (c) Interpret the y-intercept in the context of this scenario. O Each additional mile of training reduces the time needed to complete the 5K by 0.6 minutes. A contestant who has not trained at all in the last month can expect to complete the 5K in 0.6 minutes. X O A contestant who has not trained at all in the last…
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