Instructor’s Solutions Manual for Cost Accounting, Ninth Canadian Edition 12-19 Decision trees. 1. If Credit Score <= 680 & Income <= $68,500 → DEFAULT If 715 < Credit Score <= 743 → DEFAULT If Credit Score <= 680 & Income > $68,500 → REPAY If 680 < Credit Score <= 715 → REPAY If Credit Score > 743 → REPAY 2. i. DEFAULT ii. REPAY iii. REPAY iv. DEFAULT 3. Brown is correct that something appears to be wrong with the model; in cut 4, loans with a higher credit score (greater than 715) are classified as default, and loans with a lower credit score (less than 715) are classified as repay. This may indicate that the model is overfitting the training data. In this example, Brown’s business understanding helps him appreciate the limits of the model. Although cut 4 may reduce the Gini impurity, it contradicts Brown’s business experience and his knowledge of the economics of the company. Brown would alert the data science team to these anomalies and suggest that they consider other more important variables such as debt-to-income ratio. The data science team might also propose that they prune the decision tree to avoid overfitting. The predictions this model will make on real data have high variance, that is, the predictions on different real-world data will yield some good predictions and some bad ones. Consequently, the model will perform poorly when applied to new data, even though it seems to fit the training data more closely. Decision scientists build less-complex models with some bias in them (they do not fit the training data very well) because these models make predictions with less variance (the model does reasonably well across different data sets). Pruning trees to various depths is a technique to balance the bias-variance tradeoff. The greater the depth of a tree, the lower the bias but the higher the variance of the model because of overfitting. Pruning introduces bias but it also reduces variance. The data scientists and management accountants train different models and determine the model that captures most of the signal without overfitting to the noise. The goal is to choose a model that will work very well in predicting loans that default without incorrectly classifying many loans that repay as defaulting loans. 12-20 Decision trees. 1. If Number of Lines <= 1.5 → LEAVE If 1.5 < Number of Lines <= 3.5 & Months <= 21.5 → LEAVE If 1.5 < Number of Lines <= 3.5 & Months > 21.5 → STAY If Number of Lines > 3.5 → STAY Copyright © 2022 Pearson Canada Inc. 12-6