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Question: You have hired a data analyst to help your bank build a classification model for detecting which of your customers are likely to apply for a personal loan. Based on a large sample of past customers who applied/did not apply, the analyst plans to build a classification model with the goal of helping you figure out which customers are most likely to apply for a loan. The analyst ends up building a classification model that he feels should be a good job of prediction. He applies the model to a test set of 15 customers and gets predicted probabilities of applying for a loan from his model as follows:
Case Actual Class Predicted Probability
1 Apply 0.63
2 Not apply 0.7
3 Not apply 0.52
4 Not apply 0.12
5 Apply 0.65
6 Apply 0.76
7 Not apply 0.2
8 Not apply 0.06
9 Not apply 0.9
10 Apply 0.51
11 Not apply 0.32
12 Not apply 0.53
13 Not apply 0.49
14 Not apply 0.62
15 Not apply 0.44
Suppose he decides to use a threshold value of 0.55 to classify a person as someone who will apply for the loan. Based on the test data, what would be the values of:
i) The true positive rate
ii) The false positive rate
iii) The positive predictive value
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