Refer to the exhibit: [ROC Curve graph and table] An analyst examined logistic regression models for predicting whether a customer would make a purchase. The ROC curve displayed summarizes the models.

Question

Options

• AAbout 25% of the customers who did make a purchase are correctly classified as making a purchase.
• BAbout 50% of the customers who did make a purchase are correctly classified as making a purchase.
• CAbout 85% of the customers who did make a purchase are correctly classified as making a purchase.
• DAbout 95% of the customers who did make a purchase are correctly classified as making a purchase.

• A
  9% (4)
• B
  15% (7)
• C
  72% (34)
• D
  4% (2)

Explanation

On an ROC curve, the X-axis represents the False Positive Rate (proportion of non-purchasers incorrectly classified as purchasers) and the Y-axis represents the True Positive Rate (proportion of actual purchasers correctly classified). Since the decision rule produces a 25% FPR, you locate x = 0.25 on the curve and read up to the Y-axis - for the selected model this yields approximately 85% TPR, making C correct.

Why the distractors are wrong:

• A (25%) would mean TPR = FPR = 0.25, which describes the diagonal "random guess" line, not a useful model.
• B (50%) is below the curve at FPR = 0.25; the selected model clearly outperforms that level.
• D (95%) is too optimistic - achieving a 95% TPR at only 25% FPR would require a near-perfect model, which is not what the curve shows.

Memory tip: Think of ROC as "X marks the cost, Y marks the reward." The FPR given in the problem is always your X-coordinate - just drop a vertical line at that value, find where it hits the selected model's curve, and read the Y-coordinate for your answer.

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