Using the tennis data, build a decision tree by hand, using Information Gain as the criterion and splitting on all possible values of each variable.

1) Provide detailed intermediate steps and show the entropy for all nodes considered.

2) Use the tree to predict if the game will be played for {overcast, mild, normal, weak}. What is the probability of this result using Laplace Correction for probability estimation?

TENNIS DATA

day,outlook,tem,hum,wind,play

d1,sunny,hot,high,weak,no

d2,sunny,hot,high,strong,no

d3,overcast,hot,high,weak,yes

d4,rain,mild,high,weak,yes

d5,rain,cool,normal,weak,yes

d6,rain,cool,normal,strong,no

d7,overcast,cool,normal,strong,yes

d8,sunny,mild,high,weak,no

d9,sunny,cool,normal,weak,yes

d10,rain,mild,normal,weak,yes

d11,sunny,mild,normal,strong,yes

d12,overcast,mild,high,strong,yes

d13,overcast,hot,normal,weak,yes

d14,rain,mild,high,strong,no