{"id":249618,"date":"2025-07-09T18:00:34","date_gmt":"2025-07-09T18:00:34","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=249618"},"modified":"2025-07-09T18:00:36","modified_gmt":"2025-07-09T18:00:36","slug":"compute-the-misclassification-rate-accuracy-rate-sensitivity-precision-and-specificity-for-the-following-confusion-matrix","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/09\/compute-the-misclassification-rate-accuracy-rate-sensitivity-precision-and-specificity-for-the-following-confusion-matrix\/","title":{"rendered":"Compute the misclassification rate accuracy rate, sensitivity, precision, and specificity for the following confusion matrix"},"content":{"rendered":"\n<pre id=\"preorder-ask-header-text\" class=\"wp-block-preformatted\">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<\/pre>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To compute the misclassification rate, accuracy rate, sensitivity, precision, and specificity, let&#8217;s first define the confusion matrix for a binary classification problem:Confusion&nbsp;Matrix:\\text{Confusion Matrix:}Confusion&nbsp;Matrix:Actual&nbsp;\\PredictedClass&nbsp;1Class&nbsp;2Class&nbsp;1142101Class&nbsp;22400\\begin{array}{|c|c|c|} \\hline \\text{Actual \\textbackslash Predicted} &amp; \\text{Class 1} &amp; \\text{Class 2} \\\\ \\hline \\text{Class 1} &amp; 142 &amp; 101 \\\\ \\text{Class 2} &amp; 240 &amp; 0 \\\\ \\hline \\end{array}Actual&nbsp;\\PredictedClass&nbsp;1Class&nbsp;2\u200bClass&nbsp;1142240\u200bClass&nbsp;21010\u200b\u200b<\/p>\n\n\n\n<p>From the matrix, we can extract the following values:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>True Positives (TP): 142 (Class 1 predicted as Class 1)<\/li>\n\n\n\n<li>False Positives (FP): 101 (Class 2 predicted as Class 1)<\/li>\n\n\n\n<li>True Negatives (TN): 0 (Class 2 predicted as Class 2)<\/li>\n\n\n\n<li>False Negatives (FN): 240 (Class 1 predicted as Class 2)<\/li>\n<\/ul>\n\n\n\n<p>Now, we can compute the following metrics:<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">1. Misclassification Rate:<\/h3>\n\n\n\n<p>This is the fraction of incorrectly predicted instances (either FP or FN) to the total number of instances.Misclassification&nbsp;Rate=FP+FNTP+TN+FP+FN\\text{Misclassification Rate} = \\frac{FP + FN}{TP + TN + FP + FN}Misclassification&nbsp;Rate=TP+TN+FP+FNFP+FN\u200b<\/p>\n\n\n\n<p>Substituting the values:Misclassification&nbsp;Rate=101+240142+0+101+240=341483\u22480.71\\text{Misclassification Rate} = \\frac{101 + 240}{142 + 0 + 101 + 240} = \\frac{341}{483} \\approx 0.71Misclassification&nbsp;Rate=142+0+101+240101+240\u200b=483341\u200b\u22480.71<\/p>\n\n\n\n<p>So, the <strong>misclassification rate<\/strong> is <strong>0.71<\/strong> or <strong>71%<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">2. Accuracy Rate:<\/h3>\n\n\n\n<p>Accuracy is the fraction of correctly predicted instances (either TP or TN) to the total number of instances.Accuracy&nbsp;Rate=TP+TNTP+TN+FP+FN\\text{Accuracy Rate} = \\frac{TP + TN}{TP + TN + FP + FN}Accuracy&nbsp;Rate=TP+TN+FP+FNTP+TN\u200b<\/p>\n\n\n\n<p>Substituting the values:Accuracy&nbsp;Rate=142+0142+0+101+240=142483\u22480.29\\text{Accuracy Rate} = \\frac{142 + 0}{142 + 0 + 101 + 240} = \\frac{142}{483} \\approx 0.29Accuracy&nbsp;Rate=142+0+101+240142+0\u200b=483142\u200b\u22480.29<\/p>\n\n\n\n<p>So, the <strong>accuracy rate<\/strong> is <strong>0.29<\/strong> or <strong>29%<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">3. Sensitivity (Recall):<\/h3>\n\n\n\n<p>Sensitivity is the fraction of actual positive cases (Class 1) that are correctly identified by the classifier. This is also called the <strong>True Positive Rate<\/strong>.Sensitivity=TPTP+FN\\text{Sensitivity} = \\frac{TP}{TP + FN}Sensitivity=TP+FNTP\u200b<\/p>\n\n\n\n<p>Substituting the values:Sensitivity=142142+240=142382\u22480.37\\text{Sensitivity} = \\frac{142}{142 + 240} = \\frac{142}{382} \\approx 0.37Sensitivity=142+240142\u200b=382142\u200b\u22480.37<\/p>\n\n\n\n<p>So, the <strong>sensitivity<\/strong> is <strong>0.37<\/strong> or <strong>37%<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">4. Precision:<\/h3>\n\n\n\n<p>Precision is the fraction of predicted positive cases (Class 1) that are actually positive (Class 1). This is also called the <strong>Positive Predictive Value<\/strong>.Precision=TPTP+FP\\text{Precision} = \\frac{TP}{TP + FP}Precision=TP+FPTP\u200b<\/p>\n\n\n\n<p>Substituting the values:Precision=142142+101=142243\u22480.58\\text{Precision} = \\frac{142}{142 + 101} = \\frac{142}{243} \\approx 0.58Precision=142+101142\u200b=243142\u200b\u22480.58<\/p>\n\n\n\n<p>So, the <strong>precision<\/strong> is <strong>0.58<\/strong> or <strong>58%<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">5. Specificity:<\/h3>\n\n\n\n<p>Specificity is the fraction of actual negative cases (Class 2) that are correctly identified by the classifier. This is also called the <strong>True Negative Rate<\/strong>.Specificity=TNTN+FP\\text{Specificity} = \\frac{TN}{TN + FP}Specificity=TN+FPTN\u200b<\/p>\n\n\n\n<p>Substituting the values:Specificity=00+101=0101=0\\text{Specificity} = \\frac{0}{0 + 101} = \\frac{0}{101} = 0Specificity=0+1010\u200b=1010\u200b=0<\/p>\n\n\n\n<p>So, the <strong>specificity<\/strong> is <strong>0<\/strong> or <strong>0%<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Final Results:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Misclassification Rate: <strong>71%<\/strong><\/li>\n\n\n\n<li>Accuracy Rate: <strong>29%<\/strong><\/li>\n\n\n\n<li>Sensitivity: <strong>37%<\/strong><\/li>\n\n\n\n<li>Precision: <strong>58%<\/strong><\/li>\n\n\n\n<li>Specificity: <strong>0%<\/strong><\/li>\n<\/ul>\n\n\n\n<p>These results suggest that the model is not performing well, as it has a high misclassification rate and low accuracy, sensitivity, and specificity.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-14.jpeg\" alt=\"\" class=\"wp-image-249619\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>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: To compute the misclassification rate, accuracy rate, sensitivity, [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center 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