Question

What is a Confusion Matrix, and how do you calculate Accuracy, Precision, and Recall from it?

Hint:

From the confusion matrix:
Accuracy = overall correctness,
Precision = correctness of positive predictions,
Recall = ability to detect actual positives.

Answer 1

Concept: A Confusion Matrix is a performance evaluation tool for classification models. It summarizes prediction results by comparing actual labels with predicted labels, helping analyze model strengths and weaknesses. Step 1: {\color{red}Structure of a Confusion Matrix}
A binary classification confusion matrix contains four components:

• True Positive (TP): Correctly predicted positive cases
• True Negative (TN): Correctly predicted negative cases
• False Positive (FP): Incorrectly predicted positive (Type I error)
• False Negative (FN): Incorrectly predicted negative (Type II error)

Step 2: {\color{red}Accuracy}
Accuracy measures overall correctness of the model: \[ \text{Accuracy} = \frac{TP + TN}{TP + TN + FP + FN} \] It shows the proportion of total correct predictions.
Step 3: {\color{red}Precision}
Precision measures prediction reliability for positive class: \[ \text{Precision} = \frac{TP}{TP + FP} \] It answers: \emph{Out of predicted positives, how many were correct?}
Step 4: {\color{red}Recall (Sensitivity)}
Recall measures the model’s ability to detect actual positives: \[ \text{Recall} = \frac{TP}{TP + FN} \] It answers: \emph{Out of actual positives, how many were correctly identified?} Step 5: {\color{red}Why These Metrics Matter}

• Accuracy works well with balanced datasets
• Precision is important when false positives are costly
• Recall is critical when missing positives is dangerous (e.g., medical diagnosis)