The Making Numerical Predictions with Regression Trees subsection of Section 3.3 discusses how, when the outcome is measured by a numerical output variable, the regression tree algorithm splits the data into regions to maximize homogeneity of the regions. At one point, it states that the Regression Index for the two new regions shown in Figure 3.17 are 68.5 and 23.5. Show the calculation that gives each of these two values. 

Data from FIGURE 3.17 

The third split of the data, splitting the lower right region in Figure 3.16 (household income > $89 thousand and peak sun hours ≤ 4.25) into two new regions—those with household income ≤ $206.5 thousand and those with household income > $206.5 thousand—for the case study. 

Transcribed Image Text:

6 S Peak Sun Hours (PSH) 4 2 I I 20 XII X9 X14 1 40 60 Ô 0₁ XS 016 X3 013 80 89 100 120 140 160 Household Income ($000s) 06 180 X10 200 015 012 08 206.5 Installed? O# Yes X# No 220 #=Household number 1 240 4.25