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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. = X (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. O A contestant who has not trained at all in the last month can expect to complete the 5K in -16.5 minutes. Each additional mile of training reduces the time needed to complete the 5K by -16.5 minutes. (d) Use your answer from part (b) to predict the time needed to complete the 5K if a runner trained 91 miles last month. Round to one decimal place. minutes

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. = X (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. O A contestant who has not trained at all in the last month can expect to complete the 5K in -16.5 minutes. Each additional mile of training reduces the time needed to complete the 5K by -16.5 minutes. (d) Use your answer from part (b) to predict the time needed to complete the 5K if a runner trained 91 miles last month. Round to one decimal place. minutes

MATLAB: An Introduction with Applications
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 on Training and 5K Race Completion Time** 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 displayed in the table below. | **Miles Trained** | 65 | 78 | 90 | 91 | 104 | 112 | |-------------------|----|----|----|----|-----|-----| | **Time (Minutes)** | 23 | 26 | 34 | 39 | 42 | 50 | **Tasks:** (a) **Determine the Correlation Coefficient** Calculate and provide the correlation coefficient for the data. *Round to one decimal place.* (b) **Regression Equation** Use statistical software or tools to write the regression equation that predicts the time it takes a contestant to complete the race using miles trained as the explanatory variable. Provide the missing parts of the equation below, rounding values to one decimal place. \[ \hat{y} = \_\_ + \_\_ x \] (c) **Interpret y-intercept** Interpret the \( y \)-intercept in the context of this scenario. Choose the correct interpretation from the options provided: - 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. - A contestant who has not trained at all in the last month can expect to complete the 5K in -16.5 minutes. - Each additional mile of training reduces the time needed to complete the 5K by -16.5 minutes. (d) **Prediction Using Regression** Utilize your answer from part (b) to predict the time needed to complete the 5K if a runner trained 91 miles last month. *Round to one decimal place.* \[ \text{prediction: }\_\_ \text{ minutes} \]
Transcribed Image Text:**Research on Training and 5K Race Completion Time** 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 displayed in the table below. | **Miles Trained** | 65 | 78 | 90 | 91 | 104 | 112 | |-------------------|----|----|----|----|-----|-----| | **Time (Minutes)** | 23 | 26 | 34 | 39 | 42 | 50 | **Tasks:** (a) **Determine the Correlation Coefficient** Calculate and provide the correlation coefficient for the data. *Round to one decimal place.* (b) **Regression Equation** Use statistical software or tools to write the regression equation that predicts the time it takes a contestant to complete the race using miles trained as the explanatory variable. Provide the missing parts of the equation below, rounding values to one decimal place. \[ \hat{y} = \_\_ + \_\_ x \] (c) **Interpret y-intercept** Interpret the \( y \)-intercept in the context of this scenario. Choose the correct interpretation from the options provided: - 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. - A contestant who has not trained at all in the last month can expect to complete the 5K in -16.5 minutes. - Each additional mile of training reduces the time needed to complete the 5K by -16.5 minutes. (d) **Prediction Using Regression** Utilize your answer from part (b) to predict the time needed to complete the 5K if a runner trained 91 miles last month. *Round to one decimal place.* \[ \text{prediction: }\_\_ \text{ minutes} \]
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