Society of Actuaries (SOA) PA Practice Exam

What does an AUC value of 0.5 indicate about a predictive model?

1. The model perfectly predicts the outcome

2. The model is worse than random guessing

3. The model performs no better than random selection

4. The model provides highly accurate predictions

The correct answer is: The model performs no better than random selection

An AUC (Area Under the Curve) value of 0.5 suggests that the predictive model's performance is equivalent to that of random guessing. The AUC is a measure used to evaluate the performance of a binary classification model; it represents the probability that a randomly chosen positive instance is ranked higher than a randomly chosen negative instance. When the AUC is 0.5, it indicates that the model does not have any discriminative power to differentiate between the positive and negative classes. In other words, the model has a 50% chance of correctly identifying a positive case versus a negative case, which is no better than what would be achieved by making random guesses. This level of performance implies that the model lacks predictive capability and is essentially not useful for making informed decisions.