$11-22$ Gini impurity. Laurie Rech is a management accountant at Donnelly Bank, which has recently

suffered significant loan losses. Rech and her team are worried that they do not fully understand the risk

profile of their loans, so they would like some way of identifying loans that are likely to default. One team

member suggests developing a decision tree so that loans can be quickly and easily classified as "likely to

default" or "likely to repay."

After plotting and inspecting a sample of seven loans $($three loans that defaulted and four loans that

repaid$),$ Rech and her team notice there are two different cuts that result in only one misplaced observation:

Credit Score $=650$ and Income $=$$$70,000.$ Based on this, they conclude that either would be fine to use as

the first node for their decision tree.

Are Rech and her team correct that the two cuts are equivalent? Which one would you choose to be

the first node of the decision tree?

Why might Rech care about Gini impurities when making decisions?