Imagine you are building a decision tree to predict whether a personal loan given to a person would result in a payoff (i.e., the person pays off the loan) or default (the person fails to pay back the loan). Your entire data set consists of 30 examples: 16 belong to the "default" class. 14 belong to the "payoff' class. The examples contain two features, "Balance" and "Residence." "Balance" refers to the amount of money the person has in their savings and checking accounts at the time of the loan, which can take on two values: " < $50K" or "a $50K." "Residence" refers to whether or not the person owns their home or rents and can take on two values: "OWN" or "RENT." As stated, the class label for y can be either "default" or "payoff." Before splitting the parent region into child regions, the entropy of y in the parent region is: H(y parent) -loga ()-loga () 0.99 After splitting the parent region into two child regions CL and CR, the weighted average of the entropy of y over the child regions is the sum r(CL)H(yCL)+(CR)H(y|CR) where r(cz) is the ratio of the number of examples in child region cz, divided by the number of total examples in the parent region prior to a split. r(CR) is the ratio of the number of examples in child region CR divided by the number of total examples in the parent region prior to a split. The goal is to find a "good split" that will yield a low weighted average entropy of the partitioned child regions. Calculate the entropy for the parent node and see how much uncertainty exists by splitting on "Balance." The blue circles represent people from the "payoff' class and the red circles are people from the "default" class. Splitting the parent node on the "Balance" attribute gives us two child nodes: " < $50K" or " $50K." Review the graphic below to see how the data is split. Entire population (30 instances) 0:16 0:14 p()=16/30=0.53 P)-14/30-0.47 Balance < 50K Balance > 50K p()=12/13=0.92 p()=1/13=0.08 0:12 :1 :4 :13 p()=4/17=0.24 p()-13/17-0.76 What is the entropy of the root node if we split on "Balance"? 0.37 99