Question

A binary logistic regression classification model was fit on a sample size of 1000 players to predict whether a player will pass (Success) or fail (Fail) a level. The model correctly predicted 309 players to pass and correctly predicted 107 players to fail. It incorrectly predicted 270 players to pass and incorrectly predicted 314 players to fail. What is the Sensitivity, Specificity and Accuracy of this model?

(A) Sensitivity = 0.496, Specificity = 0.416, Accuracy = 0.284
(B) Sensitivity = 0.416, Specificity = 0.284, Accuracy = 0.496
(C) Sensitivity = 0.496, Specificity = 0.284, Accuracy = 0.416
(D) Sensitivity = 0.284, Specificity = 0.496, Accuracy = 0.416

Answer 1

Answer: C

Step-by-step explanation: The sensitivity of a classification model is the proportion of true positives (TP) out of all actual positives (TP + false negatives (FN)). The specificity is the proportion of true negatives (TN) out of all actual negatives (TN + false positives (FP)). The accuracy is the proportion of correct predictions (TP + TN) out of the total number of predictions.

In this case, the model correctly predicted 309 players to pass, but there were actually 309 + 314 = 623 players who failed, so the number of false negatives (FN) is 314. The model correctly predicted 107 players to fail, but there were actually 107 + 270 = 377 players who passed, so the number of false positives (FP) is 270.

Therefore, the sensitivity is TP / (TP + FN) = 309 / (309 + 314) = 0.496, and the specificity is TN / (TN + FP) = 107 / (107 + 270) = 0.284. The accuracy is (TP + TN) / (TP + TN + FP + FN) = (309 + 107) / 1000 = 0.416.

Therefore, the correct answer is (C) Sensitivity = 0.496, Specificity = 0.284, Accuracy = 0.416.