{"id":181437,"date":"2024-04-09T18:55:12","date_gmt":"2024-04-09T17:55:12","guid":{"rendered":"https:\/\/datascientest.com\/en\/?p=181437"},"modified":"2024-03-03T19:09:31","modified_gmt":"2024-03-03T18:09:31","slug":"what-is-a-root-mean-square-error","status":"publish","type":"post","link":"https:\/\/datascientest.com\/en\/what-is-a-root-mean-square-error","title":{"rendered":"What is a root mean square error?"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"181437\" class=\"elementor elementor-181437\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-3561f7d e-flex e-con-boxed e-con\" data-id=\"3561f7d\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-d3252ed elementor-widget elementor-widget-heading\" data-id=\"d3252ed\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-heading-title{padding:0;margin:0;line-height:1}.elementor-widget-heading .elementor-heading-title[class*=elementor-size-]>a{color:inherit;font-size:inherit;line-height:inherit}.elementor-widget-heading .elementor-heading-title.elementor-size-small{font-size:15px}.elementor-widget-heading .elementor-heading-title.elementor-size-medium{font-size:19px}.elementor-widget-heading .elementor-heading-title.elementor-size-large{font-size:29px}.elementor-widget-heading .elementor-heading-title.elementor-size-xl{font-size:39px}.elementor-widget-heading .elementor-heading-title.elementor-size-xxl{font-size:59px}<\/style><h2 class=\"elementor-heading-title elementor-size-default\"><p>The root mean square error (RMSE) is an indicator for verifying the reliability of a model. This tool studies the discrepancies between the values actually observed and the values predicted by the model.<\/p>\n<p>The squared error is a value that is always positive. The closer the values obtained with the model are to the observed values, the smaller the deviations and the closer to zero the squared error.<\/p> <p>Square error is a positive value.<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-08146d7 elementor-widget elementor-widget-text-editor\" data-id=\"08146d7\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-widget-text-editor.elementor-drop-cap-view-stacked .elementor-drop-cap{background-color:#69727d;color:#fff}.elementor-widget-text-editor.elementor-drop-cap-view-framed .elementor-drop-cap{color:#69727d;border:3px solid;background-color:transparent}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap{margin-top:8px}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap-letter{width:1em;height:1em}.elementor-widget-text-editor .elementor-drop-cap{float:left;text-align:center;line-height:1;font-size:50px}.elementor-widget-text-editor .elementor-drop-cap-letter{display:inline-block}<\/style>\t\t\t\t<p>There are many other model validation indicators, such as coefficient of determination, bias and mean absolute error.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-0dc5193 e-flex e-con-boxed e-con\" data-id=\"0dc5193\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-aafba0b elementor-widget elementor-widget-heading\" data-id=\"aafba0b\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">How is it calculated?<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-75eec65 elementor-widget elementor-widget-text-editor\" data-id=\"75eec65\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>Its formula is as follows:<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-d2c0061 elementor-widget elementor-widget-image\" data-id=\"d2c0061\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-widget-image{text-align:center}.elementor-widget-image a{display:inline-block}.elementor-widget-image a img[src$=\".svg\"]{width:48px}.elementor-widget-image img{vertical-align:middle;display:inline-block}<\/style>\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2022\/06\/equation-eqm.jpg\" title=\"\" alt=\"equation-eqm\" loading=\"lazy\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-452e31c elementor-widget elementor-widget-text-editor\" data-id=\"452e31c\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>n: number of measurements<\/p><p>yi: values predicted by the model<\/p><p>yi : observed values<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-4d42fcb e-flex e-con-boxed e-con\" data-id=\"4d42fcb\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-f2be6e2 elementor-widget elementor-widget-text-editor\" data-id=\"f2be6e2\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><strong>The root-mean-square error has several characteristics:<\/strong><\/p><ul><li>It differs from other indicators in that it is easy to calculate.<\/li><li>It is an indicator that is sensitive to outliers. In fact, by squaring the value of the deviations, each anomaly has a significant weighting in the calculation of the RMS error. To reduce the impact of anomalies, some use the root mean square as a model estimator.<\/li><li>This can be difficult to interpret. Indeed, a root mean square error of 15 can be a guarantee of reliability if the mean of the observed values is greater than 1000.<\/li><li>However, a root mean square error of 15 means that a model is highly unreliable if the mean of observed values is less than 100.<\/li><li>So it&#8217;s always important to relate the root mean square error to the mean of observed values when judging a model&#8217;s reliability.<\/li><\/ul>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-dac8fdf e-flex e-con-boxed e-con\" data-id=\"dac8fdf\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-a34babf elementor-widget elementor-widget-heading\" data-id=\"a34babf\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Application:<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-82d7297 elementor-widget elementor-widget-text-editor\" data-id=\"82d7297\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>The <strong>blue dots represent observed values<\/strong> and the orange<a href=\"https:\/\/datascientest.com\/en\/calculate-correlation-between-two-variables-how-do-you-measure-dependence\"> regression<\/a> is the behavioral model established by the Data Scientist. Let&#8217;s calculate the mean square error of the model:<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7861879 elementor-widget elementor-widget-image\" data-id=\"7861879\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2022\/06\/eqm1.jpg\" title=\"\" alt=\"eqm(1)\" loading=\"lazy\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\"><\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-b9ff0e8 elementor-widget elementor-widget-image\" data-id=\"b9ff0e8\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2022\/06\/eqm2.jpg\" title=\"\" alt=\"eqm(2)\" loading=\"lazy\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\"><\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-9c6b0ab elementor-widget elementor-widget-image\" data-id=\"9c6b0ab\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2022\/06\/eqm3.jpg\" title=\"\" alt=\"eqm(3)\" loading=\"lazy\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-aa490de e-flex e-con-boxed e-con\" data-id=\"aa490de\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-f2c899a elementor-widget elementor-widget-heading\" data-id=\"f2c899a\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Where is it used?<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-aa8ac11 elementor-widget elementor-widget-text-editor\" data-id=\"aa8ac11\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>The<strong> root mean square error<\/strong>, like other validation indicators, is being used more and more with the explosion in <a href=\"https:\/\/datascientest.com\/en\/artificial-intelligence-definition\">artificial intelligence<\/a> and the growing development of predictive behavior models. Indeed, they are indispensable for verifying the relevance of a model.<\/p><p>It is therefore a tool used by <a href=\"https:\/\/datascientest.com\/en\/vpn-what-is-it-what-does-it-have-to-do-with-data-science\">data scientists<\/a>, who are responsible not only for data analysis but also for implementing predictive algorithms within companies.<\/p><p>The root mean square error is already being applied in a wide range of fields, where the establishment of predictive models is essential. These include economics, with its<a href=\"https:\/\/datascientest.com\/en\/quantitative-analysis-what-is-it-and-how-do-i-become-a-quant\"> stock market<\/a> forecasting models, meteorology, with its atmospheric behavior models, and materials science, with its mechanical strength models.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-67f8814 e-flex e-con-boxed e-con\" data-id=\"67f8814\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-ae3d537 elementor-widget elementor-widget-heading\" data-id=\"ae3d537\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">How to control validation indicators?<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-d17b3e5 elementor-widget elementor-widget-text-editor\" data-id=\"d17b3e5\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>As you can see, mastery of the various validation indicators is essential in the fields of Data Science and <a href=\"https:\/\/datascientest.com\/en\/machine-learning-engineer-bootcamp-why-is-it-interesting\">Machine Learning.<\/a> To acquire these notions, and all the skills required for data science, you can opt for DataScientest.<\/p><p>Our professional training courses enable you to learn the <a href=\"https:\/\/datascientest.com\/en\/data-manager-vs-data-product-manager\">Data Science professions<\/a> such as Data Scientist, Data Analyst or Machine Learning Engineer. By the end of the course, you&#8217;ll have mastered programming, databases, <a href=\"https:\/\/datascientest.com\/en\/distributed-architecture-definition-and-relationship-to-big-data\">Big Data frameworks<\/a>, Machine Learning and DataViz.<\/p><p>Learners receive a diploma certified by the Universit\u00e9 des Mines de Paris or the Universit\u00e9 Paris Sorbonne, and are ready to enter the Data Science profession.<\/p><p>All our courses can be taken as Bootcamp or Continuing Education in a 100% distance learning format.<\/p><p>Don&#8217;t waste another moment and discover DataScientest&#8217;s training courses!<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-13a476d elementor-align-center button-principale elementor-widget elementor-widget-button\" data-id=\"13a476d\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm elementor-animation-grow\" href=\"https:\/\/datascientest.com\/en\/data-courses\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Discover DataScientest's training courses<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>The root mean square error (RMSE) is an indicator for verifying the reliability of a model. This tool studies the discrepancies between the values actually observed and the values predicted by the model. The squared error is a value that is always positive. The closer the values obtained with the model are to the observed [&hellip;]<\/p>\n","protected":false},"author":67,"featured_media":181438,"comment_status":"open","ping_status":"open","sticky":false,"template":"elementor_theme","format":"standard","meta":{"content-type":"","inline_featured_image":false},"categories":[2425],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v21.7 (Yoast SEO v21.7) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>What is a root mean square error?<\/title>\n<meta name=\"description\" content=\"Root Mean Square Error (RMSE) is a widely used metric for evaluating the accuracy of a predictive model. It measures the average magnitude of the errors between predicted values and actual values in a dataset.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/datascientest.com\/en\/what-is-a-root-mean-square-error\" \/>\n<meta property=\"og:locale\" content=\"en_GB\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"What is a root mean square error?\" \/>\n<meta property=\"og:description\" content=\"The root mean square error (RMSE) is an indicator for verifying the reliability of a model. 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