Compute the misclassification rate accuracy rate, sensitivity, precision, and specificity for the following confusion matrix (Round your final answers to 2 decimal places:) Actual Class Class Class Predicted Class 142 Predicted Class 101 240 Misclassification rate Accuracy rate Sensitivity Precision Specificity
The Correct Answer and Explanation is:
Let’s break down the confusion matrix and compute the necessary metrics. We need to calculate the following:
- Misclassification rate: This is the proportion of all predictions that were incorrect.
- Accuracy rate: This is the proportion of correct predictions out of all predictions.
- Sensitivity (also called recall or true positive rate): This measures the proportion of actual positives that were correctly identified.
- Precision: This measures the proportion of predicted positives that were actually positive.
- Specificity: This measures the proportion of actual negatives that were correctly identified.
From your confusion matrix:
- True Positives (TP) = 142
- False Positives (FP) = 101
- False Negatives (FN) = 240
- True Negatives (TN) = 0 (since it’s not mentioned, we assume no true negatives)
Formulas:
- Misclassification Rate: Misclassification Rate=FP+FNTotal Samples=101+240142+101+240+0=341483=0.71\text{Misclassification Rate} = \frac{FP + FN}{\text{Total Samples}} = \frac{101 + 240}{142 + 101 + 240 + 0} = \frac{341}{483} = 0.71Misclassification Rate=Total SamplesFP+FN=142+101+240+0101+240=483341=0.71
- Accuracy Rate: Accuracy Rate=TP+TNTotal Samples=142+0142+101+240+0=142483=0.29\text{Accuracy Rate} = \frac{TP + TN}{\text{Total Samples}} = \frac{142 + 0}{142 + 101 + 240 + 0} = \frac{142}{483} = 0.29Accuracy Rate=Total SamplesTP+TN=142+101+240+0142+0=483142=0.29
- Sensitivity (True Positive Rate): Sensitivity=TPTP+FN=142142+240=142382=0.37\text{Sensitivity} = \frac{TP}{TP + FN} = \frac{142}{142 + 240} = \frac{142}{382} = 0.37Sensitivity=TP+FNTP=142+240142=382142=0.37
- Precision: Precision=TPTP+FP=142142+101=142243=0.58\text{Precision} = \frac{TP}{TP + FP} = \frac{142}{142 + 101} = \frac{142}{243} = 0.58Precision=TP+FPTP=142+101142=243142=0.58
- Specificity (True Negative Rate): Specificity=TNTN+FP=00+101=0\text{Specificity} = \frac{TN}{TN + FP} = \frac{0}{0 + 101} = 0Specificity=TN+FPTN=0+1010=0
Summary of Results:
- Misclassification Rate: 0.71
- Accuracy Rate: 0.29
- Sensitivity: 0.37
- Precision: 0.58
- Specificity: 0.00
These calculations show that the model has a high misclassification rate, meaning most of the predictions are incorrect, and the accuracy rate is quite low as well. The sensitivity indicates the model is not good at identifying the positive class, while the precision suggests that when it does predict positive, it’s correct about half the time. The specificity is zero, which means it fails to correctly identify any negatives (assuming the lack of true negatives).
