Disney World Marathon 2020. The runDisney events began in 1994 and have become massively popular since. Although 2020 presented some struggles and led to some changes, a brand-new marathon course was introduced in the same year. The following table shows the record of 30 randomly selected runners. Speed (mph) Time (minutes) Speed (mph) Time (minutes) 8.55 142.317 3.68 174.167 9.48 147.033 3.75 174.317 9.34 147.467 3.80 174.600 9.17 159.350 3.91 206.317 8.34 164.167 4.78 176.183 8.35 169.767 4.73 176.317 3.86 165.867 4.76 177.217 3.72 168.400 4.69 177.817 4.52 171.483 3.69 177.650 4.38 172.050 3.71 178.050 4.40 173.367 3.73 178.450 4.40 173.517 3.68 194.533 5.30 173.667 3.63 179.117 5.42 173.800 3.63 179.483 3.63 173.983 3.88 179.600

a. Write a first-order model for completion time (y) as a function of speed (x).

b. Write a second-order model for complete times y as a function of speed x.

c. Construct a scatterplot for these data. Which of the models from parts a and b appears to be the better choice for explaining the variation in completion time?

d. Fit the model of part b to the data and investigate its usefulness. Is there evidence of a curvilinear relationship between completion time and age? Try using a = .05.

e. Based on your analysis in part

d, which of the models from parts a and b better explains the variation in completion time? Compare your answer with your preliminary conclusion from part c.