What does the diagonal 45-degree line in an ROC curve indicate?

What does the diagonal 45-degree line in an ROC curve indicate?

• A. It indicates perfect discrimination.
• B. It indicates some predictive power, but not complete.
• C. The diagonal line represents no better than chance.
• D. It represents overfitting.

Answer: (C)

The ROC curve shows how well a binary classifier separates the two classes as you vary the decision threshold, by plotting true positive rate (sensitivity) against false positive rate (1 − specificity). The diagonal 45-degree line from (0,0) to (1,1) is the reference line for no discrimination. On this line, the true positive rate equals the false positive rate for every threshold, which is what happens with random guessing. In other words, the classifier has no real ability to distinguish the positive class from the negative class. The area under this line is 0.5, reflecting performance at chance level. So this diagonal line indicates no better than chance.

The ROC curve shows how well a binary classifier separates the two classes as you vary the decision threshold, by plotting true positive rate (sensitivity) against false positive rate (1 − specificity).

The diagonal 45-degree line from (0,0) to (1,1) is the reference line for no discrimination. On this line, the true positive rate equals the false positive rate for every threshold, which is what happens with random guessing. In other words, the classifier has no real ability to distinguish the positive class from the negative class. The area under this line is 0.5, reflecting performance at chance level. So this diagonal line indicates no better than chance.