ROC curves
Below is the graph we covered in class when we discussed ROC curves. You will need this graph for some parts of this complex question.

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QUESTION:
Name the x-axis and the y-axis on the above graph.

The x-axis is [Fill in the blank]
.
The y-axis is [Fill in the blank]
.

Question

ROC curves
Below is the graph we covered in class when we discussed ROC curves. You will need this graph for some parts of this complex question.

=======================================================================================================
QUESTION:
Name the x-axis and the y-axis on the above graph.

The x-axis is [Fill in the blank]
.
The y-axis is [Fill in the blank]
.

BlackTom AI · Accepted Answer

ROC curves plot classifier trade-offs using false positive rate on the horizontal axis and true positive rate on the vertical axis.

1) Relevant concepts:
- True Positive Rate (TPR, also called sensitivity or recall) = TP / (TP + FN). It measures the proportion of actual positives correctly identified.
- False Positive Rate (FPR) = FP / (FP + TN). It measures the proportion of actual negatives incorrectly labeled positive (equivalently 1 − specificity).
- An ROC point is (FPR, TPR) for a given decision threshold; the diagonal 45° line represents a random classifier (TPR = FPR).

2) Step-by-step reasoning:
- By definition an ROC curve plots TPR versus FPR as the decision threshold varies. That means the horizontal coordinate is FPR and the vertical coordinate is TPR.
- Example: suppose TP = 80, FN = 20, FP = 30, TN = 70. Then compute:
   - TPR = 80 / (80 + 20) = 80 / 100 = 0.80
   - FPR = 30 / (30 + 70) = 30 / 100 = 0.30
  The ROC point for that threshold is at (0.30, 0.80) — x = FPR, y = TPR.

3) Intermediate steps / calculations are shown above for the example to illustrate how coordinates are computed from confusion-matrix counts.

4) Why this is correct:
- Standard ROC definitions in statistics and machine learning specify the x-axis as false positive rate (or 1 − specificity) and the y-axis as true positive rate (sensitivity/recall). The plotted curves in the provided figure and the 45-degree reference line align with that convention.

5) Why other possible labels are incorrect:
- Precision (positive predictive value) is not on ROC plots; precision–recall curves plot precision vs. recall.
- Specificity would be 1 − FPR; if specificity were on the x-axis the curve orientation would be reversed from the standard ROC convention.
- Accuracy is a single scalar at a threshold, not the standard ROC axis.

Conclusion: The x-axis is false positive rate and the y-axis is true positive rate, matching the provided correct answers.

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