{"id":181437,"date":"2026-02-19T13:25:44","date_gmt":"2026-02-19T12:25:44","guid":{"rendered":"https:\/\/liora.io\/en\/?p=181437"},"modified":"2026-02-19T13:25:45","modified_gmt":"2026-02-19T12:25:45","slug":"what-is-a-root-mean-square-error","status":"publish","type":"post","link":"https:\/\/liora.io\/en\/what-is-a-root-mean-square-error","title":{"rendered":"What is a root mean square error?"},"content":{"rendered":".elementor-heading-title{padding:0;margin:0;line-height:1}.elementor-widget-heading .elementor-heading-title[class*=elementor-size-]&gt;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}<p><strong><\/strong><\/p><p><strong>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.<\/strong><\/p><strong>\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.<\/p><\/strong><p><\/p>\t\t\n\t\t<p>There are many other model validation indicators, such as coefficient of determination, bias and mean absolute error.<\/p>\t\t\n\t\t\t<h2>How is it calculated?<\/h2>\t\t\n\t\t<p>Its formula is as follows:<\/p>\t\t\n\t\t\t\n.elementor-widget-image{text-align:center}.elementor-widget-image a{display:inline-block}.elementor-widget-image a img[src$=&#8221;.svg&#8221;]{width:48px}.elementor-widget-image img{vertical-align:middle;display:inline-block}\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t<p>n: number of measurements<\/p><p>yi: values predicted by the model<\/p><p>yi : observed values<\/p><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\n\t\t\t<h3>Application:<\/h3>\t\t\n\t\t<p>The <strong>blue dots represent observed values<\/strong> and the orange<a href=\"https:\/\/liora.io\/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\n\t\t\t\t\t\t\t\t\t\t\t\t<figure>\n\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" src=\"https:\/\/liora.io\/app\/uploads\/2022\/06\/eqm1.jpg\" title=\"\" alt=\"eqm(1)\" loading=\"lazy\">\t\t\t\t\t\t\t\t\t\t\t<figcaption><\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\n\t\t\t<h2>Where is it used?<\/h2>\t\t\n\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:\/\/liora.io\/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:\/\/liora.io\/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:\/\/liora.io\/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\n\t\t\t<h2>How to control validation indicators?<\/h2>\t\t\n\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:\/\/liora.io\/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 Liora.<\/p><p>Our professional training courses enable you to learn the <a href=\"https:\/\/liora.io\/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:\/\/liora.io\/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 Liora&#8217;s training courses!<\/p>\t\t\n\t\t\t\n<div class=\"wp-block-buttons is-layout-flex wp-block-buttons-is-layout-flex is-content-justification-center\"><div class=\"wp-block-button \"><a class=\"wp-block-button__link wp-element-button \" href=\"\/en\/courses\/data-ai\/\">Discover Liora&#8217;s training courses<\/a><\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>.elementor-heading-title{padding:0;margin:0;line-height:1}.elementor-widget-heading .elementor-heading-title[class*=elementor-size-]&gt;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} 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 [&hellip;]<\/p>\n","protected":false},"author":76,"featured_media":207476,"comment_status":"open","ping_status":"open","sticky":false,"template":"elementor_theme","format":"standard","meta":{"_acf_changed":false,"editor_notices":[],"footnotes":""},"categories":[2433],"class_list":["post-181437","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-data-ai"],"acf":[],"_links":{"self":[{"href":"https:\/\/liora.io\/en\/wp-json\/wp\/v2\/posts\/181437","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/liora.io\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/liora.io\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/liora.io\/en\/wp-json\/wp\/v2\/users\/76"}],"replies":[{"embeddable":true,"href":"https:\/\/liora.io\/en\/wp-json\/wp\/v2\/comments?post=181437"}],"version-history":[{"count":2,"href":"https:\/\/liora.io\/en\/wp-json\/wp\/v2\/posts\/181437\/revisions"}],"predecessor-version":[{"id":207477,"href":"https:\/\/liora.io\/en\/wp-json\/wp\/v2\/posts\/181437\/revisions\/207477"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/liora.io\/en\/wp-json\/wp\/v2\/media\/207476"}],"wp:attachment":[{"href":"https:\/\/liora.io\/en\/wp-json\/wp\/v2\/media?parent=181437"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/liora.io\/en\/wp-json\/wp\/v2\/categories?post=181437"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}