Imagine you are working on a machine learning model to predict whether or not a loan should

be approved based on certain customer attributes. You decide to use a decision tree classifier

for this task. The dataset you have includes the following features: Credit Score $($numeric$),$

Annual Income $($numeric$),$ and Marital Status $($categorical $-$ Single, Married, Divorced$).$

Question: Splitting a Node in a Decision Tree Given a subset of the dataset:

Table $4$: Data Samples

If you were to split this dataset at the root node of a decision tree, which feature would

you choose and why?

Describe the criterion $($e$.$g$.,$ Gini impurity, entropy$)$ you would use to decide on the

best split.

Calculate the chosen criterion for each feature to determine the first split. Show your

calculations.

Discuss how the tree would further split after the first decision. What would be the

next steps?

Explain how a decision tree makes predictions once it is fully grown.

Discuss one advantage and one limitation of using decision trees for this kind of clas$-$

sification problem.

Instructions: Use a simple criterion like Gini impurity or entropy for your calculations.

Explain your rationale for choosing the split feature based on the calculation results. Con$-$

sider how binary splits are made for categorical variables. Provide a general explanation

of growing the tree further after the initial split. Discuss the decision$-$making process of a

decision tree and how it applies to new data.