What is the purpose of a "Confusion Matrix" in logistic regression analysis?

Question

BlackTom AI · Accepted Answer

A confusion matrix tabulates predicted versus actual class labels, enabling direct comparison of model classifications to true outcomes.

1. Relevant knowledge points and concepts
- A confusion matrix is a 2×2 (for binary classification) table showing True Positives (TP), False Positives (FP), False Negatives (FN), and True Negatives (TN).
- It is used with classification models (including logistic regression) to evaluate predictive performance and to derive metrics such as accuracy, precision, recall (sensitivity), specificity, and F1 score.

2. Step-by-step reasoning process
- Fit a logistic regression model that outputs predicted classes (positive/negative).
- For each observation, record whether the model prediction matches the actual label.
- Aggregate the counts into the confusion matrix cells: TP, FP, FN, TN.
- Use those counts to assess how well predictions align with reality.

3. Example calculations with intermediate steps
Suppose: TP = 50, FP = 20, FN = 10, TN = 120 (total = 200).
- Accuracy = (TP + TN) / Total = (50 + 120) / 200 = 170 / 200 = 0.85 (85%).
- Precision = TP / (TP + FP) = 50 / (50 + 20) = 50 / 70 ≈ 0.714 (71.4%).
- Recall (Sensitivity) = TP / (TP + FN) = 50 / (50 + 10) = 50 / 60 ≈ 0.833 (83.3%).
- F1 score = 2 * (Precision * Recall) / (Precision + Recall) = 2 * (0.714 * 0.833) / (0.714 + 0.833) ≈ 0.769 (76.9%).

4. Why the correct answer is correct
- The confusion matrix directly compares predicted classifications against actual outcomes by construction: each cell counts agreements and disagreements between predicted and actual labels. This allows interpretation of different error types and supports metric computation.

5. Why the other options are incorrect
- "To calculate the average income of buyers." — unrelated to classification outcome counts.
- "To determine the decay rate of advertising." — concerns time-series or decay modeling, not classification evaluation.
- "To find the optimal price point." — pertains to pricing/optimization, not to tabulating predictive classifications.

6. Conclusion
The correct purpose is to compare predicted classifications against actual outcomes, matching the provided answer: "To compare predicted classifications against actual outcomes."

What is the purpose of a "Confusion Matrix" in logistic regression analysis?单项选择题

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