Question: 1. In the tab labeled Decision Tree Rules, write out the rules for the full decision tree given in Exhibit 1. 2. Using the decision
1. In the tab labeled "Decision Tree Rules", write out the rules for the full decision tree given in Exhibit 1.
2. Using the decision tree in Exhibit 1, classify each loan in the validation sample (See Exhibit 2), as repay or default. Calculate the proportion of loans correctly classified (Part 1, Column 5)
3. Calculate the overall likelihood value for the full decision tree (Part 1, Columns 6 & 7)
4. Prune the tree at depth 3. In the tab labeled "Decision Tree Rules", write out the rules for the
pruned decision tree.
5. Using the pruned tree, classify each loan in the validation sample as repay or default (if the
probably of default is greater than 0.5 classify the loan as default). Calculate the proportions of
loans correctly classified. (Part 1, Column 8)
6. Calculate the overall likelihood value for the pruned decision tree (Part 1, Columns 9 and 10)
7. As the management accounting team, which model would you use for decision making? Explain.
| Exhibit 2: Validation Data Set: | ||||||||||||||
| GIVEN INFORMATION | FULL DECISION TREE | PRUNED DECISION TREE | ||||||||||||
| Observation | Income | Credit Score | Actual Outcome (y) | Predicted Outcome based on Full Decision Tree | ? | Probability of Default (p) (for Repay enter 0.01, for Default enter 0.99) | Likelihood Value (py x (1-p)1-y) | Predicted Outcome based on Pruned Decision Tree | ? | Probability of Default (p) (for Repay enter 0.01, for Default enter 0.99) | Likelihood Value (py x (1-p)1-y) | |||
| (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | |||||
| 1 | $85,000 | 710 | (0) Repay | 0 | 0 | ? | 0.01 | 0.99 | ? | ? | ? | ? | 1 | |
| 2 | $62,000 | 650 | (1) Default | 1 | 1 | ? | 0.99 | 0.99 | ? | ? | ? | ? | 1 | |
| 3 | $72,000 | 660 | (0) Repay | 0 | 0 | ? | 0.01 | 0.99 | ? | ? | ? | ? | 1 | |
| 4 | $75,000 | 640 | (0) Repay | 0 | 0 | ? | 0.01 | 0.99 | ? | ? | ? | ? | 1 | |
| 5 | $71,000 | 680 | (0) Repay | 0 | 0 | ? | 0.01 | 0.99 | ? | ? | ? | ? | 1 | |
| 6 | $59,000 | 705 | (0) Repay | 0 | 1 | ? | 0.99 | 0.01 | ? | ? | ? | ? | 0 | |
| 7 | $48,000 | 690 | (1) Default | 1 | 0 | ? | 0.01 | 0.01 | ? | ? | ? | ? | 0 | |
| 8 | $57,000 | 685 | (0) Repay | 0 | 1 | ? | 0.99 | 0.01 | ? | ? | ? | ? | 0 | |
| Correct Classification Rate: | Overall Likelihood | Correct Classification Rate: | Overall Likelihood | |||||||||||
| Correct Classification Rate: | 1 | ? | ? | ? | ? |
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