7. The following table lists a dataset collected in an electronics shop showing details of customers and whether they responded to a special offer to buy a new laptop.

This dataset has been used to build a decision tree to predict which customers will respond to future special offers. The decision tree, created using the ID3 algorithm, is shown below.

a. The information gain (calculated using entropy) of the feature AGE at the root node of the tree is 0.247. A colleague has suggested that the STUDENT feature would be better at the root node of the tree. Show that this is not the case.

b. Yet another colleague has suggested that the ID feature would be a very effective at the root node of the tree. Would you agree with this suggestion?

ID AGE INCOME STUDENT CREDIT BUYS 1 40 low yes bad yes 619 > 40 low yes good no 7 31-40 low yes good yes 8