$(6$ points$)$ Decision Tree with C$4\mathrm{.}5$ Algorithm

In the following questions, you will use the dataset below to train a decision tree which

predicts if students enrolled in a machine learning class would pass $($Yes or No$),$ based on

their previous GPA, number of lectures attended $($out of $10$ lectures the whole semester$),$

and whether or not they studied after class. You will apply C$4\mathrm{.}5$ algorithm to build a

Table $1$: Student dataset

decision tree, namely, the splitting criterion is to maximize the information gain of a

split. As the preparation step, you need to transform the two numeric variables into

categorical variables with the following criteria:

GPA: categorized as 'Low' when GPA ; categorized as 'Medium' when $2\mathrm{.}5$

GPA ; categorized as 'High' when GPA $>3\mathrm{.}5.$

Attendance: categorized as 'Good' when number of lectures attended $>=7$; catego$-$

rized as 'Bad' when number of lectures attended

$(6$ points$)$ Decision Tree with C$4\mathrm{.}5$ AlgorithmIn your calculation, you may need the following logarithm terms. To simplify calculation,

you can use the rounded values below instead of calculating the exact logarithm values.

log$\_(2)((1)/(2))=-1,$log$\_(2)((1)/(3))=-1\mathrm{.}58,$log$\_(2)((2)/(3))=-0\mathrm{.}58,$log$\_(2)((1)/(4))=-2,$log$\_(2)((3)/(4))=-0\mathrm{.}41$

log$\_(2)((1)/(5))=-2\mathrm{.}32,$log$\_(2)((4)/(5))=-0\mathrm{.}32,$log$\_(2)((3)/(7))=-1\mathrm{.}22,$log$\_(2)((4)/(7))=-0\mathrm{.}81$

$(1)$ In iteration $1,$ what is the information gain of splitting on the GPA levels? The

split will produce three children nodes: GPA $=$ 'Low', GPA $=$ 'Medium', GPA $=$

'High'. Pick the closest rounded value below.

A$.0\mathrm{.}26$

B$.0\mathrm{.}40$

C$.0\mathrm{.}60$

D$.0\mathrm{.}74(2)$ In iteration $1,$ what is the best split $($i$.$e$.$ the split with the highest information

gain$)$ among all candidate splits? Namely, this is the split at the root level of the

obtained decision tree.

A$.$ Split on 'GPA' and produce children nodes: GPA $=$ Low, GPA $=$ Medium,

GPA $=$ High.

B$.$ Split on 'Attendance' and produce children nodes: Attendance $=$ Good, At$-$

tendance $=$ Bad.

C$.$ Split on 'Studied' and produce children nodes: Studied $=$ No$,$ Studied $=$ Yes.

D$.$ Split on 'Passed' and produce children nodes: Passed $=$ No$,$ Passed $=$ Yes.