{"id":179855,"date":"2024-05-21T17:46:07","date_gmt":"2024-05-21T16:46:07","guid":{"rendered":"https:\/\/datascientest.com\/en\/?p=179855"},"modified":"2024-02-25T18:37:45","modified_gmt":"2024-02-25T17:37:45","slug":"understanding-correlation-coefficient-definition-and-applications","status":"publish","type":"post","link":"https:\/\/datascientest.com\/en\/understanding-correlation-coefficient-definition-and-applications","title":{"rendered":"Understanding Correlation Coefficient: Definition and Applications"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"179855\" class=\"elementor elementor-179855\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-84882fc e-flex e-con-boxed e-con\" data-id=\"84882fc\" 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-f757f77 elementor-widget elementor-widget-heading\" data-id=\"f757f77\" 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\">To better understand data, it's essential to analyze its relationships. And to facilitate this analysis when faced with tens of thousands of lines of data, there are mathematical formulas. In particular, the correlation coefficient. <\/h2>\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-84a56a9 e-flex e-con-boxed e-con\" data-id=\"84a56a9\" 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-e41190b elementor-widget elementor-widget-heading\" data-id=\"e41190b\" 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\">What is the correlation coefficient?<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6cde6fa elementor-widget elementor-widget-heading\" data-id=\"6cde6fa\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">Relationship and dependence between two variables<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-528c5fb elementor-widget elementor-widget-text-editor\" data-id=\"528c5fb\" 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>Before we can understand the <strong>correlation coefficient,<\/strong> we need to <a href=\"https:\/\/datascientest.com\/en\/sequences-and-series-understanding-these-two-mathematical-concepts\">understand the relationships between the different variables in a dataset.<\/a> Thus, if the values of a variable Y depend on the value x (or vice versa), there is a relationship between these two variables. Knowledge of X (or Y) should then make it possible to predict the other variable Y (or X).<\/p><p>For example, a company&#8217;s profit margin depends (in part) on the price of its products or services. There is therefore a correlation between these two values.<\/p><p><a href=\"https:\/\/datascientest.com\/en\/expected-goals-understand-the-math-behind-it\">In mathematics<\/a>, this <strong>relationship is expressed as follows:<\/strong> Y=f(X). Here, Y is considered the dependent variable, and X is the independent variable.<\/p><p>However, just because X allows us to deduce Y does not mean that the converse is true.<\/p><p>And to find out whether there is a <a href=\"https:\/\/datascientest.com\/en\/classification-algorithms-definition-and-main-models\">correlation between two variables<\/a>, you can use the correlation coefficient formula. But first, we need to define the form of a relationship.<\/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-87c5b77 elementor-widget elementor-widget-heading\" data-id=\"87c5b77\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">The form of the relationship between two variables<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-94a7188 elementor-widget elementor-widget-text-editor\" data-id=\"94a7188\" 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 simplest tool for establishing the form of the relationship between two variables is a graphical representation. <a href=\"https:\/\/datascientest.com\/en\/creating-stunning-excel-charts-a-step-by-step-guide\">Using a diagram,<\/a> we can cross-reference the modalities of X and Y, with X on the x-axis and Y on the y-axis. This diagram can then be used to characterize the relationship between the variables according to 3 parameters:<\/p><ul><li><strong>Intensity:<\/strong> the relationship between variables can be strong, weak or null. It is strong if the units have similar values for X and Y. Visually, this translates into a cloud of points with values close together.<\/li><li>Conversely, if the values close to X are far from Y, the relationship is weak. And if they are very far apart (without any guideline), the relationship is zero. In other words, it&#8217;s not possible to predict Y from X.<\/li><li><strong>Shape:<\/strong> the relationship can be linear and monotonic (a straight line on the graph), non-linear and monotonic (a strictly increasing or decreasing curve) or non-linear and non-monotonic (the curve will be both increasing and decreasing, like a parabola or hyperbola).<\/li><li><strong>Meaning:<\/strong> this applies to monotonic relationships. The correlation is said to be positive when the two variables move in the same direction, or negative when they move in opposite directions.<\/li><\/ul>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-74249ec elementor-widget elementor-widget-text-editor\" data-id=\"74249ec\" 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>Depending on the<strong> shape of the relationship<\/strong>, you&#8217;ll need to select the right tools. In particular, the correlation coefficient formula.<\/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-057743c elementor-widget elementor-widget-heading\" data-id=\"057743c\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">The correlation coefficient formula<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-9a6cabd elementor-widget elementor-widget-text-editor\" data-id=\"9a6cabd\" 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>correlation coefficient<\/strong> is used to study monotonic relationships (whether linear or not). But depending on their linearity, two types of <strong>correlation coefficient<\/strong> are used (<a href=\"https:\/\/datascientest.com\/en\/pearson-and-spearman-correlations-a-guide-to-understanding-and-applying-correlation-methods\">Pearson or Spearman<\/a>), which we&#8217;ll look at in the next paragraph.<\/p><p>The formula used then differs according to the type of relationship. But it is always written in this form &#8220;r&#8221;.<\/p><p>The<strong> correlation coefficient<\/strong> can be used to link a multitude of variables. For example, the relationship between height and intelligence, price and margins, population size and pollution, caloric intake and disease, etc.<\/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-f20c64d elementor-widget elementor-widget-image\" data-id=\"f20c64d\" 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<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\/2023\/07\/coefficient-de-correlation.png\" title=\"\" alt=\"\" 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-3bc7baa elementor-align-center button-principale elementor-widget elementor-widget-button\" data-id=\"3bc7baa\" 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-scientist-course\">\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\">Learn all about the correlation coefficient<\/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<div class=\"elementor-element elementor-element-01ffd45 e-flex e-con-boxed e-con\" data-id=\"01ffd45\" 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-fbb8a31 elementor-widget elementor-widget-heading\" data-id=\"fbb8a31\" 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\">What are the different correlation coefficients?<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-0c228b1 elementor-widget elementor-widget-heading\" data-id=\"0c228b1\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">Pearson correlation coefficient<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-092617f elementor-widget elementor-widget-text-editor\" data-id=\"092617f\" 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 aim is to<a href=\"https:\/\/datascientest.com\/en\/quantitative-analysis-what-is-it-and-how-do-i-become-a-quant\"> study linear and monotonic relationships.<\/a><\/p><p>The formula for Pearson&#8217;s correlation coefficient 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-2525144 elementor-widget elementor-widget-shortcode\" data-id=\"2525144\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\"><math xmlns='http:\/\/www.w3.org\/1998\/Math\/MathML'>\n  <mi> r <\/mi>\n  <mrow>\n    <mo> ( <\/mo>\n      <mi> X <\/mi>\n      <mo> , <\/mo>\n      <mi> Y <\/mi>\n    <mo> ) <\/mo>\n  <\/mrow>\n  <mo> = <\/mo>\n  <mfrac>\n    <mrow>\n      <mi> C <\/mi>\n      <mi> o <\/mi>\n      <mi> v <\/mi>\n      <mrow>\n        <mo> ( <\/mo>\n          <mi> X <\/mi>\n          <mo> , <\/mo>\n          <mi> Y <\/mi>\n        <mo> ) <\/mo>\n      <\/mrow>\n    <\/mrow>\n    <mrow>\n      <msub>\n        <mrow>\n          <mi> &#x03C3; <!-- greek small letter sigma --> <\/mi>\n        <\/mrow>\n        <mrow>\n          <mi> x <\/mi>\n        <\/mrow>\n      <\/msub>\n      <mo> . <\/mo>\n      <msub>\n        <mrow>\n          <mi> &#x03C3; <!-- greek small letter sigma --> <\/mi>\n        <\/mrow>\n        <mrow>\n          <mi> y <\/mi>\n        <\/mrow>\n      <\/msub>\n    <\/mrow>\n  <\/mfrac>\n<\/math>\n<\/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<div class=\"elementor-element elementor-element-0fe7bbb e-flex e-con-boxed e-con\" data-id=\"0fe7bbb\" 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-b56a373 elementor-widget elementor-widget-text-editor\" data-id=\"b56a373\" 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>To calculate the <strong>Pearson correlation coefficient,<\/strong> start by calculating the covariance. In other words, the mean of the product of the deviations from the mean.<\/p><p>Then divide this covariance by the product of the standard deviations of X and Y.<\/p><p>Depending on the result, you can interpret the relationship between the two variables. For example:<\/p><ul><li>if r is close to 0: the linear relationship is zero. Note that just because there&#8217;s no linear relationship between two variables doesn&#8217;t mean there&#8217;s no relationship at all.<\/li><li>if r is close to -1: there&#8217;s a strong linear relationship between the two variables, but<\/li><li>it&#8217;s negative. They are therefore moving in opposite directions.<\/li><li>if r is close to 1: there is a strong positive linear relationship between the two variables. They are moving in the same direction.<\/li><\/ul>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-bdf492a elementor-widget elementor-widget-text-editor\" data-id=\"bdf492a\" 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>Good to know:<\/strong> while this<strong> correlation coefficient<\/strong> formula is effective for better understanding the relationship between two variables, it only works if the distribution is free of outliers. Otherwise, the results of the calculation may lead to totally erroneous conclusions.<\/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-90b3b53 elementor-widget elementor-widget-heading\" data-id=\"90b3b53\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">Spearman's correlation coefficient<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-466d30d elementor-widget elementor-widget-text-editor\" data-id=\"466d30d\" 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>This formula (also known as the rank correlation coefficient) is used to analyze monotonic relationships. Regardless of the form of the relationship (linear, exponential, &#8230;.). As such, <strong>Spearman&#8217;s coefficient<\/strong> is best suited when there are outliers or skewed distributions. Through this calculation, the latter are less likely to distort the result.<\/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-cbce871 e-flex e-con-boxed e-con\" data-id=\"cbce871\" 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-68b7c15 elementor-widget elementor-widget-heading\" data-id=\"68b7c15\" 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\">What are the limits of the correlation coefficient?<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-29aa641 elementor-widget elementor-widget-text-editor\" data-id=\"29aa641\" 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> correlation coefficient<\/strong> formula is only the first step in determining the relationships between several variables. For a more comprehensive view, it is essential to carry out other mathematical calculations, such as significance testing and checking for the absence of bias.<\/p><p>Used together, these different statistical tools enable you to take a few extra steps in building a machine learning model.<\/p><p>But to better understand the connections between data and <a href=\"https:\/\/datascientest.com\/en\/convolutional-neural-network-everything-you-need-to-know\">neural networks,<\/a> it&#8217;s best to get fully trained in the science of data. Join our Datascientest training course.<\/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-88fec8d e-flex e-con-boxed e-con\" data-id=\"88fec8d\" 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-75a36fa elementor-widget elementor-widget-heading\" data-id=\"75a36fa\" 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\">Key points to remember<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f125919 elementor-widget elementor-widget-text-editor\" data-id=\"f125919\" 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<ul><li style=\"font-weight: 400;\" aria-level=\"1\">The correlation coefficient indicates the relationship between several variables.<\/li><li style=\"font-weight: 400;\" aria-level=\"1\">It gives an indication of the intensity, form and direction of the relationship.<\/li><li style=\"font-weight: 400;\" aria-level=\"1\">Depending on the type of relationship, <strong>Spearman&#8217;s or Pearson&#8217;s<\/strong> correlation coefficients can be used.<\/li><\/ul>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-0832871 elementor-widget elementor-widget-image\" data-id=\"0832871\" 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\/2023\/07\/coefficient-de-correlation1.jpg\" title=\"\" alt=\"\" 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-eca1e62 elementor-align-center button-principale elementor-widget elementor-widget-button\" data-id=\"eca1e62\" 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-scientist-course\">\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\">Mastering the correlation coefficient<\/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<div class=\"elementor-element elementor-element-c0d56bb e-flex e-con-boxed e-con\" data-id=\"c0d56bb\" 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-18fffe6 elementor-widget elementor-widget-html\" data-id=\"18fffe6\" data-element_type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"FAQPage\",\n  \"mainEntity\": [{\n    \"@type\": \"Question\",\n    \"name\": \"What is the correlation coefficient?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"Before understanding the correlation coefficient, it's important to understand the relationships between the different variables in a dataset. Thus, if the values of a variable Y depend on the value x (or vice versa), there is a relationship between these two variables. Knowledge of X (or Y) should then make it possible to predict the other variable Y (or X).\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"The correlation coefficient formula\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correlation coefficient is used to study monotonic relationships (whether linear or not). But depending on their linearity, two types of correlation coefficient are used (Pearson or Spearman), which we'll look at in the next paragraph. The formula used then differs according to the type of relationship. But it is always written in this form : \"r\\\".\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"Spearman's correlation coefficient\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"This formula (also known as the rank correlation coefficient) is used to analyze monotonic relationships. Regardless of the form of the relationship (linear, exponential, ....). As such, Spearman's coefficient is best suited when there are outliers or skewed distributions. Through this calculation, the latter are less likely to distort the result.\"\n    }\n  },{\n    \"@type\": \"Question\",\n    \"name\": \"What are the limits of the correlation coefficient?\",\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correlation coefficient formula is only the first step in determining the relationships between several variables. To get a more comprehensive view, it's essential to perform other mathematical calculations, such as testing for significance and verifying the absence of bias.\"\n    }\n  }]\n}\n<\/script>\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>To better understand data, it&#8217;s essential to analyze its relationships. And to facilitate this analysis when faced with tens of thousands of lines of data, there are mathematical formulas. In particular, the correlation coefficient. What is the correlation coefficient? Relationship and dependence between two variables Before we can understand the correlation coefficient, we need to [&hellip;]<\/p>\n","protected":false},"author":67,"featured_media":179857,"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>Understanding Correlation Coefficient: Definition and Applications<\/title>\n<meta name=\"description\" content=\"Delve into the concept of correlation coefficient, a statistical measure used to quantify the strength and direction of the\" \/>\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\/understanding-correlation-coefficient-definition-and-applications\" \/>\n<meta property=\"og:locale\" content=\"en_GB\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Understanding Correlation Coefficient: Definition and Applications\" \/>\n<meta property=\"og:description\" content=\"To better understand data, it&#039;s essential to analyze its relationships. 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