Question $1$

Using average homogeneity as the splitting criterion, what is the best splitting variable for the root node of the decision tree for superheroes?

A$.$

Cape

B$.$

Mask

C$.$

Tie

D$.$

Ears

E$.$

Smokes

$5$ points $$

Question $2$

After you identify which variable gives the best split at the root node for the superheros, you have two sets of data for the next step. $$In one set are the superheroes who have value Y for the splitting variable at the root node. $$In the other set are the superheros who have value N for the splitting variable at the root node.

When you try to identify at the next step the best splitting variable for the set that has value N at the root node, you should find that more than one variable gives highest average homogeneity for splitting. $$Which variables give equal highest average homogeneity when used to split this set?

A$.$

Cape, Ears, Smokes

B$.$

Mask, Ears, Smokes

C$.$

Tie, Ears, Smokes

D$.$

Cape, Tie, Ears

E$.$

Mask, Cape, Tie

$1$ points $$

Question $3$

Which of the following is the correct way that the decision trees created from the data on superheros identify Batgirl as Good? Note that all options below give information that is correct for Batgirl, but only one of the options reflects a path in the decision trees that can be derived from the data.

A$.$

Cape Y

B$.$

Mask Y$,$ Cape Y

C$.$

Ears Y$,$ Tie N$,$ Mask Y

D$.$

Mask Y

E$.$

Tie N$,$ Ears Y$,$ Smokes N

$1$ points $$

Question $4$

Which of the following is NOT a way that the decision trees created from the data on superheros identify the Riddler as bad? $$Note that all options below give information that is correct for the Riddler, but only one of the options does not fit with a sequence of steps through any of the decision trees that can be derived from the data.

A$.$

Cape N$,$ Ears N$,$ Smokes N$,$ Tie N$.$

B$.$

Cape N$,$ Smokes N$,$ Tie N$.$

C$.$

Cape N$,$ Mask Y$.$

D$.$

Cape N$,$ Ears N$,$ Tie N$.$

E$.$

Cape N$,$ Ears N$,$ Mask Y$.$