Consider the below confusion matrix generated by a classification model. The…

1. The confusion matrix shows the classification results of a model that predicts whether a tumor is Benign or Malignant. Total observations N = 170.

Actual Benign predicted as Benign = 50
Actual Benign predicted as Malignant = 15
Actual Malignant predicted as Benign = 5
Actual Malignant predicted as Malignant = 100

1. Case 1: When Benign is considered as the positive class

True Positive (TP) = 50
False Negative (FN) = 15
False Positive (FP) = 5
True Negative (TN) = 100

Accuracy = (TP + TN) / Total
Accuracy = (50 + 100) / 170 = 150 / 170 = 0.882

Precision = TP / (TP + FP)
Precision = 50 / (50 + 5) = 50 / 55 = 0.909

Recall = TP / (TP + FN)
Recall = 50 / (50 + 15) = 50 / 65 = 0.769

F1 Score = 2 × (Precision × Recall) / (Precision + Recall)
F1 = 2 × (0.909 × 0.769) / (0.909 + 0.769) = 0.833

1. Case 2: When Malignant is considered as the positive class

True Positive (TP) = 100
False Negative (FN) = 5
False Positive (FP) = 15
True Negative (TN) = 50

Accuracy = (TP + TN) / Total
Accuracy = (100 + 50) / 170 = 150 / 170 = 0.882

Precision = TP / (TP + FP)
Precision = 100 / (100 + 15) = 100 / 115 = 0.870

Recall = TP / (TP + FN)
Recall = 100 / (100 + 5) = 100 / 105 = 0.952

F1 Score = 2 × (Precision × Recall) / (Precision + Recall)
F1 = 2 × (0.870 × 0.952) / (0.870 + 0.952) = 0.909

1. Final result

When Benign is positive
Accuracy = 0.882
Precision = 0.909
Recall = 0.769
F1 Score = 0.833

When Malignant is positive
Accuracy = 0.882
Precision = 0.870
Recall = 0.952
F1 Score = 0.909

This shows that the model detects Malignant cases with higher recall compared to Benign cases.