Question $4$: Decision trees

The data in Table $1$ shows attributes that might influence a family's decision on

where to go for their vacation. The target variable is whether the family chose the

destination $($Yes or No$).$

Table $1$: Vacation destination attributes and family's choices.

$($a$)$ Explain what Entropy and Information Gain represent in the context of the

ID$3$ algorithm to construct decision trees. Explain what these values mean in

practice.

$($b$)$ Calculate the base Entropy of this data set. Show every step of your calcula$-$

tion, including how you determine the ratios.

$($c$)$ Calculate the Information Gain for each of the attributes. Show all the ratios,

steps and calculations.

$($d$)$ Based on your calculations, which attribute$($s$)$ will be used as the root node

of the decision tree? Explain why.

$($e$)$ Discuss how ID$3$ proceeds once it has determined the root node. Use your

root node as an example to start your discussion. Indicate how the dataset

gets modified in the next steps of the algorithm.