Figures 3.16 and 3.17 show the second and third splitting of the data into regions when applying the classification tree algorithm to the case study. 

a. Calculate the values of the Gini Index for each of the two new regions created by the second split, as well as the Overall Gini Index and the improvement in the overall homogeneity. 

b. Repeat part a for the two new regions created by the third split.

Data from FIGURE 3.16 

The second split of the data, splitting the right region (household income > $89 thousand) into two new regions—those with peak sun hours ≤ 4.25 and those with peak sun hours > 4.25—for the case study.  

Transcribed Image Text:

7 6 5 Peak Sun Hours (PSH) + 2 1 20 XII X9 X14 40 60 80 89 0₂ X5 016 X3 013 100 120 140 160 Household Income ($000s) 06 X10 X4 015 012 O# Yes X# No 08 #=Household number 1 180 200 220 240 4.25