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 NFL athletes who have recently signed new contracts. Each observation (NFL athlete) includes values for percentage of the 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 pruned tree. The pruned tree (as applied to the data on 506 NFL athletes) follows.

a. Titus Johnston’s variable values are: SnapPercent = 96, Awards = 6, and GamesMissed = 3.

How much guaranteed money does the regression tree predict that a player with Titus Johnson’s profile should earn in their 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)?

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83.86 17.3 23.8 294 instances SnapPercent > 83.86 20.3 10.8 150 instances SnapPercent 14.3 18.7 144 instances SnapPercent 80.08 > 80.08 85.85 90.26 22.5 84.4 506 instances SnapPercent > 90.26 > 85.85 24.9 32.8 123 instances Games Missed 6.5 29.7 79.3 212 instances Awards 4 18.6 13.6 12.3 16.2 75 instances 16.4 13.0 69 instances 40 instances 20.9 8.4 110 instances SnapPercent 88.31 > 88.31 27.1 64.0 47 instances 20.4 7.3 61 instances 21.6 9.0 49 instances > 6.5 >4 36.5 65.3 89 instances SnapPercent 95.27 23.5 8.5 76 instances 32.5 42.5 48 instances > 95.27 41.1 51.4 41 instances