3. Athlete Contract Negotiations (regression tree). Casey Deesel is a sports agent negotiating a contract for Titus Johnston, an athlete in the National Football League

(NFL). An important aspect of any NFL contract is the amount of guaranteed money over the life of the contract. Casey has gathered data on 506 NFL athletes who have recently signed new contracts. Each observation (NFL athlete) includes values for percentage of his team’s plays that the athlete is on the field (SnapPercent), the number of awards an athlete has received recognizing on-field performance

(Awards), the number of games the athlete has missed due to injury (GamesMissed), and millions of dollars of guaranteed money in the athlete’s most recent contract (Money, dependent variable).

Casey has trained a full regression tree on 304 observations and then used the validation set to prune the tree to obtain a best-pruned tree. The best-pruned tree (as applied to the 202 observations in the validation set) is:

a. Titus Johnston’s variable values are: SnapPercent 5 96, Awards 5 7, and GamesMissed 5 3. How much guaranteed money does the regression tree predict that a player with Titus Johnson’s profile should earn in his contract?

b. Casey feels that Titus was denied an additional award in the past season due to some questionable voting by some sports media. If Titus had won this additional award, how much additional guaranteed money would the regression tree predict for Titus versus the prediction in part (a)?

c. As Casey reviews the best-pruned tree, he is confused by the leaf node corresponding to the sequence of decision rules of “SnapPercent > 90.28, SnapPercent Explain this part of the regression tree to Casey by referring to how the best-pruned tree is obtained.

SnapPercent 85.09 SnapPercent 90.28 106 96 SnapPercent 95.37 53 53 71 25 Awards Awards 14.73 20.71 6.75 7.25 48 23 11 14 Games Missed GamesMissed 1.5 32.52 2.5 46.73 0 48 0 11 50 23.61 47.83 32.74