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 which follows lists the times that the 2018 winner, Jeff Browning, arrived at various mileage points along the way.

(a) What was Browning’s average speed?
(b) Graph the data, plotting time on the x-axis and distance on the y-axis. 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 Browning’s average speed? Compare this with your answer to part (a). Which answer do you think is better? Explain your reasoning.

Time (hours) 0 2.494 4.067 6.333 8.083 8.550 9.700 12.150 13.640 17.651 21.083 22.400 24.217 26.339 Miles 0 11.5 18.1 27.8 32.7 35.9 43.9 51.9 58.4 71.9 80.8 85.1 91.2 100.5