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You collect data on nine customers of an e-commerce website and wish to predict whether each makes a purchase. The features are whether free shipping was offered, the time spent on the site (minutes), and whether the customer subscribes to the newsletter.
| Customer | Free Shipping | Time Spent (min) | Newsletter Subscriber | Purchase |
|---|---|---|---|---|
| 1 | No | 12 | Yes | Yes |
| 2 | Yes | 20 | Yes | Yes |
| 3 | Yes | 12 | Yes | No |
| 4 | No | 20 | No | No |
| 5 | No | 5 | Yes | Yes |
| 6 | No | 20 | Yes | Yes |
| 7 | Yes | 12 | No | No |
| 8 | Yes | 5 | No | No |
| 9 | No | 12 | No | No |
Build the decision tree that maximizes information gain at each split. Then limit the tree to depth two (the root counts as depth zero).
What is the training error rate (misclassified points divided by all points) of this depth-limited tree?