{"id":185167,"date":"2024-05-09T06:30:00","date_gmt":"2024-05-09T05:30:00","guid":{"rendered":"https:\/\/datascientest.com\/en\/?p=185167"},"modified":"2024-05-09T01:40:11","modified_gmt":"2024-05-09T00:40:11","slug":"all-about-the-power-law","status":"publish","type":"post","link":"https:\/\/datascientest.com\/en\/all-about-the-power-law","title":{"rendered":"Power law: understanding the relationships between variables"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"185167\" class=\"elementor elementor-185167\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-2e6d4a1 e-flex e-con-boxed e-con\" data-id=\"2e6d4a1\" 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-e66fae3 elementor-widget elementor-widget-heading\" data-id=\"e66fae3\" 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\">What if everything was connected? Well, maybe not everything. But a large part of natural phenomena. This is at least what the power law reveals. This mathematical concept establishes dynamic relationships between variables that do not follow the same models. Discover this law in more detail.<\/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-79f65c7 e-flex e-con-boxed e-con\" data-id=\"79f65c7\" 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-f11599d elementor-widget elementor-widget-heading\" data-id=\"f11599d\" 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 power law?<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-638bdac elementor-widget elementor-widget-text-editor\" data-id=\"638bdac\" 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><span style=\"font-weight: 400;\">The power law (or exponent law) reveals the <a href=\"https:\/\/datascientest.com\/en\/calculate-correlation-between-two-variables-how-do-you-measure-dependence\">relationships between two variables<\/a>, <b>where one is a function of the other raised to some power.<\/b><\/span><\/p><p><span style=\"font-weight: 400;\">Mathematically, this is expressed as follows:<\/span><\/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-f45271f elementor-widget elementor-widget-text-editor\" data-id=\"f45271f\" 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<pre style=\"padding-left: 440px;\"><span style=\"font-weight: 400;\">y = ax \u2227 b<\/span><\/pre>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-bcf3e76 elementor-widget elementor-widget-text-editor\" data-id=\"bcf3e76\" 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><span style=\"font-weight: 400;\">Where:<\/span><\/p><ul><li><b>y<\/b><span> is the dependent variable,<\/span><\/li><li><b>x<\/b><span style=\"font-weight: 400;\"> is the independent variable,<\/span><\/li><li><b>a<\/b><span style=\"font-weight: 400;\"> is the coefficient that influences the relationship between these two variables,<\/span><\/li><li><b>b<\/b><span style=\"font-weight: 400;\"> is the exponent that determines how <\/span><b>x<\/b><span style=\"font-weight: 400;\"> affects <\/span><b>y<\/b><span style=\"font-weight: 400;\">.<\/span><\/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-869007e elementor-widget elementor-widget-text-editor\" data-id=\"869007e\" 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><span style=\"font-weight: 400;\">To help you better understand this power law, here is <\/span><b>a concrete example:<\/b><\/p><p><span style=\"font-weight: 400;\">The growth of a plant which evolves according to the amount of light it receives.<\/span><\/p><p><span style=\"font-weight: 400;\">In this example:<\/span><\/p><ul><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">y is the height of the plant,<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">x is the amount of light received each day,<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">a is the coefficient that may influence the relationship between the plant&#8217;s height and the amount of light,<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">b is the exponent that determines how the amount of light affects the plant&#8217;s height.<\/span><\/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-1c8c41f elementor-widget elementor-widget-text-editor\" data-id=\"1c8c41f\" 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><span style=\"font-weight: 400;\">In this equation, the relationship between the plant&#8217;s height and the amount of light varies greatly depending on the exponent b.<\/span><\/p><ul><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">If b is greater than 1, it means that small increases in light will lead to significant increases in plant height,<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">If b is between 0 and 1, it means that the plant&#8217;s height increases as it receives more light. However, each increase in light has less impact on its growth,<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">If b is negative, this signifies an inverse relationship between light and plant height. Thus, the more light the plant receives, the slower its growth.<\/span><\/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-ce1b236 elementor-widget elementor-widget-image\" data-id=\"ce1b236\" 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\" width=\"748\" height=\"600\" src=\"https:\/\/datascientest.com\/en\/files\/2024\/05\/power_law_data_science1.jpg\" class=\"attachment-large size-large wp-image-185176\" alt=\"\" srcset=\"https:\/\/datascientest.com\/en\/files\/2024\/05\/power_law_data_science1.jpg 748w, https:\/\/datascientest.com\/en\/files\/2024\/05\/power_law_data_science1-300x241.jpg 300w\" sizes=\"(max-width: 748px) 100vw, 748px\" \/>\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-34de4ad elementor-align-center button-principal elementor-widget elementor-widget-button\" data-id=\"34de4ad\" 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-md\" href=\"https:\/\/datascientest.com\/en\/data-analyst-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\">Become a Data Analyst<\/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-b682d42 e-flex e-con-boxed e-con\" data-id=\"b682d42\" 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-805b952 elementor-widget elementor-widget-heading\" data-id=\"805b952\" 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 power laws?<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7c2da45 elementor-widget elementor-widget-text-editor\" data-id=\"7c2da45\" 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><span style=\"font-weight: 400;\">There is not just one power law, but several. Here are the main ones:<\/span><\/p><ul><li><b>Zipf&#8217;s Law<\/b><span style=\"font-weight: 400;\">: it describes the distribution of word frequencies in a text, the size of cities in a region, individual incomes, etc. According to this law, the frequency of an element is inversely proportional to its rank,<\/span><\/li><li><b>Pareto&#8217;s Law<\/b><span style=\"font-weight: 400;\">: this is the 80\/20 rule, which stipulates that about 80% of effects come from 20% of causes. For example, in a company, 80% of revenues are generated by 20% of clients,<\/span><\/li><li><b>Ohm&#8217;s Law<\/b><span style=\"font-weight: 400;\">: applicable to electricity, this law describes the relationship between voltage, current intensity, and resistance,\u00a0<\/span><\/li><li><b>Newton&#8217;s Law of Universal Gravitation<\/b><span style=\"font-weight: 400;\">: it describes the <a href=\"https:\/\/www.britannica.com\/science\/Newtons-law-of-gravitation\">force of attraction between two masses<\/a>,\u00a0<\/span><\/li><li><a href=\"https:\/\/www.ncbi.nlm.nih.gov\/pmc\/articles\/PMC3933913\/\"><b>Gompertz Law of Growth<\/b><\/a><span style=\"font-weight: 400;\">: it is used to model the growth of biological populations or the evolution of diseases.<\/span><\/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-343fbda elementor-widget elementor-widget-text-editor\" data-id=\"343fbda\" 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><span style=\"font-weight: 400;\">As these laws are notably varied, the power law applies to various fields.<\/span><\/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-42f1b95 e-flex e-con-boxed e-con\" data-id=\"42f1b95\" 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-f62c1f1 elementor-widget elementor-widget-heading\" data-id=\"f62c1f1\" 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 power law used for?<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-25158e8 elementor-widget elementor-widget-text-editor\" data-id=\"25158e8\" 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><span style=\"font-weight: 400;\">Whenever there is a need to describe nonlinear relationships between two variables, the power law can apply. It can be used to model phenomena in:<\/span><\/p><ul><li><b>Economics<\/b><span style=\"font-weight: 400;\">: economic growth models often use the power law with variables such as GDP, profits, company size, etc.,<\/span><\/li><li><b>Biology<\/b><span style=\"font-weight: 400;\">: the power law establishes the relationship between the size of an organism and its basal metabolism,<\/span><\/li><li><b>Transportation<\/b><span style=\"font-weight: 400;\">: transport networks are often modeled using power laws that describe the distribution of the number of roads in relation to the size of cities,<\/span><\/li><li><b>Computer Science<\/b><span style=\"font-weight: 400;\">: the Internet is modeled based on the distribution of the number of links to web pages. This is referred to as a scale-free network.<\/span><\/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-b74a3f8 elementor-widget elementor-widget-text-editor\" data-id=\"b74a3f8\" 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><span style=\"font-weight: 400;\">Due to its omnipresence at all scales of society, the power law is a mathematical concept that is absolutely essential to master. Especially if you are looking to design machine learning models. That&#8217;s why it is essential to get trained. And why not <strong>with <a href=\"https:\/\/datascientest.com\/en\/\">DataScientest<\/a>!<\/strong><\/span><\/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-4181eba elementor-widget elementor-widget-image\" data-id=\"4181eba\" 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\" width=\"744\" height=\"600\" src=\"https:\/\/datascientest.com\/en\/files\/2024\/05\/power_law_data_science2.jpg\" class=\"attachment-large size-large wp-image-185189\" alt=\"\" srcset=\"https:\/\/datascientest.com\/en\/files\/2024\/05\/power_law_data_science2.jpg 744w, https:\/\/datascientest.com\/en\/files\/2024\/05\/power_law_data_science2-300x242.jpg 300w\" sizes=\"(max-width: 744px) 100vw, 744px\" \/>\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-d9e5c38 elementor-align-center button-principal elementor-widget elementor-widget-button\" data-id=\"d9e5c38\" 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-md\" 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\">Become a Data Scientist<\/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<div class=\"elementor-element elementor-element-6be0949 elementor-widget elementor-widget-html\" data-id=\"6be0949\" 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\">\r\n{\r\n  \"@context\": \"https:\/\/schema.org\",\r\n  \"@type\": \"FAQPage\",\r\n  \"mainEntity\": [{\r\n    \"@type\": \"Question\",\r\n    \"name\": \"What is the power law?\",\r\n    \"acceptedAnswer\": {\r\n      \"@type\": \"Answer\",\r\n      \"text\": \"The power law (or exponent law) reveals the relationships between two variables, where one is a function of the other raised to some power.\"\r\n    }\r\n  },{\r\n    \"@type\": \"Question\",\r\n    \"name\": \"What are the different power laws?\",\r\n    \"acceptedAnswer\": {\r\n      \"@type\": \"Answer\",\r\n      \"text\": \"There is not just one power law, but several. 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The power law (or [&hellip;]<\/p>\n","protected":false},"author":45,"featured_media":185169,"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>Power law: understanding the relationships between variables<\/title>\n<meta name=\"description\" content=\"The power law establishes relationships between seemingly different variables, and it applies to all areas of activity.\" \/>\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\/all-about-the-power-law\" \/>\n<meta property=\"og:locale\" content=\"en_GB\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Power law: understanding the relationships between variables\" \/>\n<meta property=\"og:description\" content=\"What if everything was connected? 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