If you think a marathon is a long race, consider the Hardrock 100, a 100.5 mile running race held in southwestern Colorado. The chart at right lists the times that the 2008 winner, Kyle Skaggs, arrived at various mileage points along the way.

a. What was Skagg's average speed?

b. Graph the data, plotting time on the -axis and distance on the -axis. You will need to convert the time from hours and minutes into hours. Do the data appear to lie approximately on a straight line?

c. Find the equation for the least squares line, fitting distance as a linear function of time.

d. Calculate the correlation coefficient. Does it indicate a good fit of the least squares line to the data?

e. Based on your answer to part d, what is a good value for Skagg’s average speed? Compare this with your answer to part a. Which answer do you think is better? Explain your reasoning.

Transcribed Image Text:

Time (hr:min) Miles 0 0 2:19 3:43 5:36 7:05 7:30 8:30 10:36 11:56 15:14 17:49 18:58 20:50 23:23 11.5 18.9 27.8 32.8 36.0 43.9 51.5 58.4 71.8 80.9 85.2 91.3 100.5