Question

A decision tree is built to determine individuals likely to default on an unsecured loan. the null hypothesis states that an individual will not default on the loan. the decision tree correctly classifies 80% of the instances in a test dataset. fifteen percent of the mistakes made by the model are type 1 errors. what can be said about the performance of the model?

a) the accuracy of the model for correctly determining those individuals who did not default on their loan was at least 75%.
b) the accuracy of the model for correctly determining those individuals who defaulted on their loan was at least 75%.
c) the majority of errors made by the model accepted individuals who defaulted.
d) the majority of errors made by the model rejected individuals who did not default.

Answer 1

The decision tree has a majority of Type II errors, hence it's more likely to incorrectly accept individuals who default. Answer options (c) and (d) are correct: the model's accuracy for predicting non-defaults is at least 75% and most errors are due to falsely accepting defaulters.

Step-by-step explanation:

The decision tree's overall accuracy is 80%, but we want to consider errors related to individuals defaulting on their loans. A Type I error is when we incorrectly predict a default (the null hypothesis is rejected falsely), and a Type II error is when we fail to predict a default (the null hypothesis is falsely not rejected). The question states that 15% of the mistakes are Type I errors.

Since the model correctly classifies 80% of instances, this means 20% are incorrect. Out of these, Type I errors constitute 15% of 20% (which is 3%). Thus, the major errors are actually Type II, implying the model is more prone to predicting non-default when the individual does default. This suggests that:

• The model's accuracy for correctly predicting non-defaults (the null hypothesis, where a default is not expected) is at least 75% (80% - 5% Type II errors).
• The accuracy is less reliable for predicting defaults, as Type II errors dominate.
• Therefore, answer options (c) and (d) can be concluded. Most errors made are Type II, meaning the model accepts individuals who default more than it incorrectly rejects individuals who do not default.