A credit risk team builds a logistic regression model and reports Gini = 0.62. How is the Gini coefficient derived from the AUC?
Select an answer to reveal the explanation.
Short Explanation
Here's the deal — you get Gini by doubling AUC and subtracting 1. With AUC = 0.81, that gives 2(0.81) - 1 = 0.62. It just rescales AUC so 0 is random, 1 is perfect discrimination, and -1 is perfectly reversed.
Full Explanation
The correct derivation is Gini = 2 AUC - 1, where AUC is the area under the ROC curve. With AUC = 0.81, Gini = 2(0.81) - 1 = 0.62. Gini normalizes AUC to a -1 to +1 scale where 0 = random, 1 = perfect discrimination, and -1 = perfectly reversed. The AUC - 0.5 formula is wrong because the formula is 2AUC-1, not AUC-0.5. The 1 - AUC formula is wrong; it would give a negative Gini for good models. The AUC^2 formula is wrong; squaring AUC has no standard interpretation.