True or False: The lower threshold probability results in more claims being investigated.

What is the probability that a claim will be investigated, if the threshold probability is set at 0.4? (Report to two decimal places)

If fraud was predicted by the model for a

particular claim, what is the probability that the claim involved actual fraud?

(Report to two decimal places)

We want to see how many cases the model has correctly predicted fraud if there was actual fraud, and correctly predicted no fraud if there was actually no fraud. Write some R code to generate a contingency (pivot) table comparing actual_fraud with predicted_fraud.

Calculate the proportion of claims where

the model made the correct classification of the fraud status of the claim. 

In what proportion of cases was a Type II error

made – i.e. predicting no fraud when in fact fraud did occur. (Report to two

decimal places)

In what proportion of cases was a Type I error made – i.e. predicting a case of fraud when in fact there was no fraud. (Report to two decimal places)

Create a variable called predicted_fraud which equals "No" if the model’s predictions are less than or equal to 0.4, and "Yes" if the model’s predictions are greater than 0.4. How many cases of fraud were predicted?

HINT: First use the predict() function to calculate the predicted probability of fraud using your model in Part B. Then use the rep() function and conditional statement similarly to the previous question.

Create a variable called actual_fraud which equals "No" if the fraud variable equals 0, and "Yes" if the fraud variable equals 1. How many cases of fraud were detected?

HINT: You can use the rep() function to first fill the actual_fraud

variable with one

response, eg

Suppose you are comparing two claims, Claim A

and Claim B.

Claim A: is from a 30 year-old who earns $60,000pa, claiming less than $5000 and 18 months after their last claim. The accident was

reported to police, witness details were provided, and the accident took place

on a weekday, with the car not driveable afterwards.

Claim B: is from a 50 year-old who earns $120,000pa, claiming less than $5000 and 18 months after their last claim. The accident was

not reported to police, witness details were not provided, and the accident

took place on a weekend, with the car driveable afterwards.

What is the predicted probability of fraud for Claim A? (Report to 4 decimal places)

What is the predicted probability of fraud for Claim B? (Report to 4 decimal places)