Question

Given the training set below:

Age	Income	Student	Credit_rating	Buys_computer
<=30	high	no	fair	no
<=30	high	no	excellent	no
31…40	high	no	fair	no
>40	medium	no	fair	yes
<=30	low	no	fair	yes
>40	high	no	fair	no
>40	low	yes	fair	yes
>40	low	yes	excellent	no
31…40	low	yes	excellent	yes
<=30	medium	no	fair	no
<=30	low	yes	fair	yes
>40	medium	yes	fair	yes
<=30	medium	yes	excellent	no
31…40	medium	no	excellent	no
31…40	high	yes	fair	yes
>40	medium	no	excellent	yes

The information gain for attribute Credit_rating is:

Group of answer choices

1. 0.049

2. 0.244

3. 0.261

4. 0.488

5. 0.004

Answer 1

In column Credit_rating, we have 6 excellents and 10 fairs. So, Entropy of Credit_rating is
$-\frac{6}{16}log_2(\frac{6}{16})-\frac{10}{16}log_2(\frac{10}{16})$
= 0.954

Now, we split Credit_rating based on Buys_computer. When Buys_computer is yes, we have 6 fairs and 2 excellents. When Buys_computer is no, we have 4 fairs and 4 excellents.
Entropy of Buys_computer=yes is
$-\frac{6}{8}log_2(\frac{6}{8})-\frac{2}{8}log_2(\frac{2}{8})$

= 0.811

Entropy of Buys_computer=no is

4 -log() - logo 8

= 1

Entropy of Credit_rating based on Buys_computer is

= 0.9055

So, Information gain from Credit_rating is 0.954 - 0.9055 = 0.0485 ~ 0.049

So, the answer is 0.049