{"id":231055,"date":"2024-03-18T06:30:00","date_gmt":"2024-03-18T06:30:00","guid":{"rendered":"https:\/\/datascientest.com\/?p=231055"},"modified":"2024-03-14T14:50:04","modified_gmt":"2024-03-14T14:50:04","slug":"regression-lineaire-tout-savoir","status":"publish","type":"post","link":"https:\/\/datascientest.com\/regression-lineaire-tout-savoir","title":{"rendered":"R\u00e9gression lin\u00e9aire : Qu&rsquo;est-ce que c&rsquo;est ? Comment \u00e7a fonctionne ?"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"231055\" class=\"elementor elementor-231055\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-83ae671 e-flex e-con-boxed e-con\" data-id=\"83ae671\" 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-cfb4208 elementor-widget elementor-widget-heading\" data-id=\"cfb4208\" 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\">C\u2019est l\u2019outil le plus utilis\u00e9 en statistiques\u2026 A partir d\u2019un ensemble de donn\u00e9es connues, la r\u00e9gression lin\u00e9aire d\u00e9finit une ligne droite ou bien une courbe qui par la suite, va aider \u00e0 pr\u00e9dire des ph\u00e9nom\u00e8nes. La r\u00e9gression lin\u00e9aire est employ\u00e9e dans de nombreux domaines dont le machine learning.<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-8d5c930 elementor-widget elementor-widget-text-editor\" data-id=\"8d5c930\" 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;\">\u00ab <a href=\"https:\/\/datascientest.com\/regression-lineaire-python\">R\u00e9gression lin\u00e9aire<\/a> \u00bb\u2026 Ce nom pourrait para\u00eetre intimidant. En r\u00e9alit\u00e9, il recouvre une fonction statistique fondamentale. <strong>\u00c0 partir d\u2019un nuage de points (issus de variables num\u00e9riques), la r\u00e9gression lin\u00e9aire trace une ligne ou une courbe qui est la plus proche de tous ces points.<\/strong> Cette figure g\u00e9om\u00e9trique se veut la plus fiable possible.<\/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-67266ca e-flex e-con-boxed e-con\" data-id=\"67266ca\" 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-5bfb120 elementor-widget elementor-widget-heading\" data-id=\"5bfb120\" 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\">Un outil de pr\u00e9diction<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-21524fb elementor-widget elementor-widget-text-editor\" data-id=\"21524fb\" 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;\">Nous avons l\u00e0 un outil de pr\u00e9diction car \u00e0 partir d\u2019une ou plusieurs variables que nous lui soumettons, la r\u00e9gression lin\u00e9aire aide \u00e0 d\u00e9finir d\u2019autres variables en relation logique.<\/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-eb447fc elementor-widget elementor-widget-heading\" data-id=\"eb447fc\" 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-medium\">Quelques exemples de r\u00e9gression lin\u00e9aire<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-0d651e8 elementor-widget elementor-widget-text-editor\" data-id=\"0d651e8\" 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;\">En tant que <strong>m\u00e9thode de pr\u00e9diction<\/strong> reposant sur des statistiques, la r\u00e9gression lin\u00e9aire est mise \u00e0 contribution dans un tr\u00e8s grand nombre d\u2019activit\u00e9s : \u00e9conomie, m\u00e9decine, environnement, sport\u2026<\/span><\/p><p><span style=\"font-weight: 400;\">Voici quelques cas d\u2019usage typiques :<\/span><\/p><ul><li><span style=\"font-weight: 400;\">Estimer le taux de vente d\u2019un produit donn\u00e9 en fonction du budget publicitaire investi et\/ou d\u2019une tranche d\u2019\u00e2ge des consommateurs.<\/span><\/li><li><span style=\"font-weight: 400;\">Pr\u00e9dire la r\u00e9sistance d&rsquo;un mat\u00e9riau selon diverses conditions externes.<\/span><\/li><li><span style=\"font-weight: 400;\">Evaluer l\u2019\u00e2ge d\u2019une \u00e9toile en fonction de sa luminosit\u00e9 et autres facteurs environnants.<\/span><\/li><li><span style=\"font-weight: 400;\">Pr\u00e9voir les \u00e9volutions d\u2019un type d\u2019action en Bourse selon l\u2019analyse du sentiment du public par rapport \u00e0 de nouveaux produits.<\/span><\/li><li><span style=\"font-weight: 400;\">etc.<\/span><\/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-ba923a4 e-flex e-con-boxed e-con\" data-id=\"ba923a4\" 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-13717e1 elementor-widget elementor-widget-heading\" data-id=\"13717e1\" 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\">Qui a invent\u00e9 la r\u00e9gression lin\u00e9aire ?<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f5b8695 elementor-widget elementor-widget-text-editor\" data-id=\"f5b8695\" 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;\">C\u2019est un math\u00e9maticien et statisticien britannique du nom de <strong>Francis Galton (1822 \u2013 1911)<\/strong> qui est \u00e0 l\u2019origine de ce concept. Etant cousin de Charles Darwin, il \u00e9tait fortement int\u00e9ress\u00e9 par des notions telles que l\u2019h\u00e9r\u00e9dit\u00e9 et la g\u00e9n\u00e9tique. Lui-m\u00eame cherchait \u00e0 r\u00e9soudre des probl\u00e8mes concrets tels que celui-ci : la taille des parents aide-t-elle \u00e0 pr\u00e9dire la taille qu\u2019auront les enfants une fois qu\u2019ils ont atteint l\u2019\u00e2ge adulte ?<\/span><\/p><p><span style=\"font-weight: 400;\">Par la suite, d\u2019autres chercheurs ont affin\u00e9 les m\u00e9thodes de r\u00e9gression lin\u00e9aire.<\/span><\/p><ul><li><span style=\"font-weight: 400;\"><strong>Karl Pearson<\/strong> est le cr\u00e9ateur du <a href=\"https:\/\/datascientest.com\/correlations-de-pearson-et-de-spearman\">coefficient de corr\u00e9lation de Pearson<\/a>, un outil fondamental dans <strong>l&rsquo;\u00e9tude des relations entre variables<\/strong>. Nous abordons ce qu\u2019est le <a href=\"https:\/\/datascientest.com\/coefficient-de-correlation-tout-savoir\">coefficient de corr\u00e9lation<\/a> plus bas.<\/span><\/li><li><span style=\"font-weight: 400;\"><strong>Ronald A. Fisher<\/strong> a contribu\u00e9 \u00e0 formaliser la r\u00e9gression lin\u00e9aire. L\u2019une des techniques qu\u2019il a mis au point permet de d\u00e9duire l\u2019<a href=\"https:\/\/datascientest.com\/ecart-type-excel\">\u00e9cart type<\/a>, un autre facteur fondamental explicit\u00e9 plus bas.<\/span><\/li><li><span style=\"font-weight: 400;\"><strong>John Turkey<\/strong> a \u00e9labor\u00e9 des techniques aidant \u00e0 diagnostiquer des probl\u00e8mes dans les mod\u00e8les de r\u00e9gression lin\u00e9aire<\/span><\/li><li><span style=\"font-weight: 400;\"><strong>Bradley Efron<\/strong> a d\u00e9fini des m\u00e9thodes pour \u00e9valuer la pr\u00e9cision des param\u00e8tres.<\/span><\/li><li><span style=\"font-weight: 400;\">etc.<\/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-dd1f9f7 elementor-widget elementor-widget-image\" data-id=\"dd1f9f7\" 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=\"600\" height=\"600\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2024\/02\/regression-lineaire.jpg\" class=\"attachment-full size-full wp-image-231079\" alt=\"\" \/>\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-0e49e69 elementor-align-center button-principale elementor-widget elementor-widget-button\" data-id=\"0e49e69\" 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=\"\/formation-data-analyst\">\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\">Apprendre \u00e0 utiliser la r\u00e9gression lin\u00e9raire<\/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-7a6e6f9 e-flex e-con-boxed e-con\" data-id=\"7a6e6f9\" 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-433d3d3 elementor-widget elementor-widget-heading\" data-id=\"433d3d3\" 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\">R\u00e9gression lin\u00e9aire simple et multiple<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f6bda9a elementor-widget elementor-widget-text-editor\" data-id=\"f6bda9a\" 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;\">On distingue deux types de r\u00e9gressions lin\u00e9aires :<\/span><\/p><ul><li><span style=\"font-weight: 400;\">Celle bas\u00e9e sur les <strong>relations entre deux variables X et Y<\/strong> (Y \u00e9tant d\u00e9duit de X), produit une droite et se voit appel\u00e9e r\u00e9gression lin\u00e9aire simple.<\/span><\/li><li>Celle bas\u00e9e sur <strong style=\"font-weight: 400;\">plusieurs variables X produit habituellement une courbe<\/strong>. Elle est appel\u00e9e <a href=\"https:\/\/datascientest.com\/regression-lineaire-multiple-tout-savoir\"><b>r\u00e9gression lin\u00e9aire multiple<\/b><\/a>.<\/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-b6891fe elementor-widget elementor-widget-heading\" data-id=\"b6891fe\" 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-medium\">R\u00e9gression lin\u00e9aire simple<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-d312842 elementor-widget elementor-widget-text-editor\" data-id=\"d312842\" 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;\">La r\u00e9gression lin\u00e9aire simple repose sur la formule suivante :<\/span><\/p><p style=\"padding-left: 80px;\"><strong>Y = \u03b20 + \u03b21 \u00d7 X + \u03f5<\/strong><\/p><ul><li><span style=\"font-weight: 400;\"><strong>Y<\/strong> est la variable que l\u2019on cherche \u00e0 pr\u00e9dire. Elle est appel\u00e9e \u00ab variable d\u00e9pendante \u00bb.<\/span><\/li><li><span style=\"font-weight: 400;\"><strong>\u03b20<\/strong> est la valeur de Y lorsque X est \u00e9gal \u00e0 z\u00e9ro.<\/span><\/li><li><span style=\"font-weight: 400;\"><strong>\u03b21<\/strong> repr\u00e9sente le \u00ab coefficient de r\u00e9gression \u00bb et produit la pente de la ligne, soit de combien change Y lorsque X augmente d\u2019une unit\u00e9<\/span><\/li><li><span style=\"font-weight: 400;\"><strong>X<\/strong> est la variable de base.<\/span><\/li><li><span style=\"font-weight: 400;\"><strong>\u03f5<\/strong> d\u00e9signe la marge d\u2019erreur in\u00e9vitable.<\/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-ae5fabc elementor-widget elementor-widget-text-editor\" data-id=\"ae5fabc\" 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;\">En gros, nous cherchons \u00e0 \u00e9valuer <strong>\u03b20<\/strong> et <strong>\u03b21<\/strong> en vue de minimiser \u03f5 et obtenir la courbe la plus fiable possible au croisement de <strong>X<\/strong> et <strong>Y<\/strong>.<\/span><\/p><p><span style=\"font-weight: 400;\">\u200bNous avons l\u00e0 une formule simple puisqu\u2019elle repose sur la relation de deux variables. Le probl\u00e8me pos\u00e9 par Francis Galton (\u00e9valuer la taille de l\u2019enfant devenu adulte en fonction de la taille cumul\u00e9e de ses parents) serait un bon exemple de r\u00e9gression lin\u00e9aire.<\/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-d9c0cee elementor-widget elementor-widget-heading\" data-id=\"d9c0cee\" 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-medium\">R\u00e9gression lin\u00e9aire multiple<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-28baf7c elementor-widget elementor-widget-text-editor\" data-id=\"28baf7c\" 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;\">La formule de la r\u00e9gression lin\u00e9aire multiple est une extension de sa forme simple :<\/span><\/p><p style=\"padding-left: 80px;\"><strong>Y = \u03b20 + \u03b21 \u00d7 X1 + \u03b22 \u00d7 X2 + \u2026 + \u03b2n \u00d7 Xn + \u03f5<\/strong><\/p><p><span style=\"font-weight: 400;\">L\u00e0 encore <strong>Y<\/strong> est la variable d\u00e9pendante &#8211; celle que l\u2019on tente de pr\u00e9dire &#8211; et <strong>\u03f5<\/strong> est la marge d\u2019erreur. Les couples <strong>\u03b2n \u00d7 Xn<\/strong> \u00e9voluent sur le m\u00eame mod\u00e8le que dans la r\u00e9gression simple si ce n\u2019est qu\u2019ils sont multiples. Cette fois, l\u2019objectif est de trouver les coefficients <strong>\u03b2n<\/strong> correspondant aux variables <strong>Xn<\/strong> qui ensemble, vont minimiser au mieux \u03f5, et ainsi produire la <\/span><span style=\"font-weight: 400;\">meilleure pr\u00e9diction possible.<\/span><\/p><p><span style=\"font-weight: 400;\">\u00c0 titre d\u2019exemple, des donn\u00e9es <strong>X<\/strong> telles que la taille d\u2019une maison, le nombre de pi\u00e8ces habitables, l&rsquo;\u00e2ge du b\u00e2timent, et la proximit\u00e9 de transports publics pourraient aider \u00e0\u00a0 pr\u00e9dire<strong> Y<\/strong>, soit le prix de vente du bien.<\/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-3c29d01 elementor-widget elementor-widget-image\" data-id=\"3c29d01\" 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=\"888\" height=\"500\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2024\/02\/regression-lineaire2.jpg\" class=\"attachment-full size-full wp-image-231089\" alt=\"\" srcset=\"https:\/\/datascientest.com\/wp-content\/uploads\/2024\/02\/regression-lineaire2.jpg 888w, https:\/\/datascientest.com\/wp-content\/uploads\/2024\/02\/regression-lineaire2-300x169.jpg 300w, https:\/\/datascientest.com\/wp-content\/uploads\/2024\/02\/regression-lineaire2-768x432.jpg 768w\" sizes=\"(max-width: 888px) 100vw, 888px\" \/>\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-571cfc1 elementor-align-center button-principale elementor-widget elementor-widget-button\" data-id=\"571cfc1\" 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=\"\/formation-data-analyst\">\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\">Se former en analyse de donn\u00e9es<\/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-b419ca3 e-flex e-con-boxed e-con\" data-id=\"b419ca3\" 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-51eed8c elementor-widget elementor-widget-heading\" data-id=\"51eed8c\" 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\">Deux concepts cl\u00e9s de la r\u00e9gression lin\u00e9aire<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-08a79ef elementor-widget elementor-widget-text-editor\" data-id=\"08a79ef\" 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;\">D\u2019autres \u00e9l\u00e9ments ont une importance dans le calcul d\u2019une courbe de r\u00e9gression lin\u00e9aire.<\/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-36c0a41 elementor-widget elementor-widget-heading\" data-id=\"36c0a41\" 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-medium\">Coefficient de corr\u00e9lation<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f1c8532 elementor-widget elementor-widget-text-editor\" data-id=\"f1c8532\" 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;\">Cette mesure d\u00e9crit le <strong>degr\u00e9 de relation lin\u00e9aire entre deux variables<\/strong> et varie entre -1 et 1.<\/span><\/p><p><span style=\"font-weight: 400;\">Si le coefficient de corr\u00e9lation est <strong>\u00e9gal \u00e0 1<\/strong>, il existe alors une <strong>relation lin\u00e9aire positive parfaite<\/strong>. Quand l&rsquo;une des variables augmente, l&rsquo;autre cro\u00eet de mani\u00e8re proportionnelle.<\/span><\/p><p><span style=\"font-weight: 400;\">S\u2019il est<strong> \u00e9gal \u00e0 -1<\/strong>, la <strong>relation est \u00e0 nouveau parfaite, mais n\u00e9gative<\/strong>.<\/span><\/p><p><span style=\"font-weight: 400;\">Il arrive ainsi que tous les points soient situ\u00e9s sur la droite \/ courbe mais ce cas est extr\u00eamement rare. Habituellement, la figure de r\u00e9gression lin\u00e9aire appara\u00eet vers le milieu d\u2019un ensemble de points situ\u00e9s de part et d\u2019autre.<\/span><\/p><p><span style=\"font-weight: 400;\">Enfin, si le coefficient de corr\u00e9lation <strong>s\u2019approche de 0<\/strong>, cela signifie qu\u2019il n\u2019existe <strong>aucune relation lin\u00e9aire<\/strong> entre les deux variables.<\/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-afa3158 elementor-widget elementor-widget-heading\" data-id=\"afa3158\" 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-medium\">\u00c9cart type<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5571548 elementor-widget elementor-widget-text-editor\" data-id=\"5571548\" 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;\">Cette mesure statistique, <strong>mesure combien les valeurs individuelles s&rsquo;\u00e9cartent de la moyenne de l&rsquo;ensemble<\/strong>. Si l\u2019\u00e9cart type est faible, les donn\u00e9es sont globalement proches de la moyenne. Un \u00e9cart type \u00e9lev\u00e9, \u00e0 l\u2019inverse, d\u00e9note d\u2019une forte dispersion des donn\u00e9es.<\/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-deaaa77 e-flex e-con-boxed e-con\" data-id=\"deaaa77\" 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-534fcdd elementor-widget elementor-widget-heading\" data-id=\"534fcdd\" 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\">La r\u00e9gression lin\u00e9aire dans le machine learning<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-b604382 elementor-widget elementor-widget-text-editor\" data-id=\"b604382\" 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;\">La r\u00e9gression lin\u00e9aire est mise \u00e0 profit dans le <a href=\"https:\/\/datascientest.com\/machine-learning-tout-savoir\">machine learning<\/a>.<\/span><\/p><p><span style=\"font-weight: 400;\">Par principe, le machine learning op\u00e8re \u00e0 partir d\u2019un <a href=\"https:\/\/datascientest.com\/dataset-definition\">dataset<\/a> (des donn\u00e9es pr\u00e9sent\u00e9es sous la forme de lignes et colonnes) \u00e0 partir duquel un <strong>algorithme <\/strong>va chercher \u00e0 d\u00e9finir un mod\u00e8le. Celui-ci va alors \u00eatre ajust\u00e9 afin de <strong>r\u00e9duire les \u00e9carts entre la courbe et les points<\/strong>, puis minimiser les erreurs.<\/span><\/p><p><span style=\"font-weight: 400;\">La r\u00e9gression lin\u00e9aire est le mod\u00e8le le plus simple pour ceux qui souhaitent <strong>d\u00e9buter dans le machine learning<\/strong>, par exemple, avec la biblioth\u00e8que math\u00e9matique <a href=\"https:\/\/datascientest.com\/numpy\">Numpy sous Python<\/a>.<\/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-fe2b400 elementor-widget elementor-widget-image\" data-id=\"fe2b400\" 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=\"750\" height=\"500\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2024\/02\/regression-lineaire1.jpg\" class=\"attachment-full size-full wp-image-231090\" alt=\"\" srcset=\"https:\/\/datascientest.com\/wp-content\/uploads\/2024\/02\/regression-lineaire1.jpg 750w, https:\/\/datascientest.com\/wp-content\/uploads\/2024\/02\/regression-lineaire1-300x200.jpg 300w\" sizes=\"(max-width: 750px) 100vw, 750px\" \/>\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-b62d653 elementor-align-center button-principale elementor-widget elementor-widget-button\" data-id=\"b62d653\" 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=\"\/formations-data\">\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\">D\u00e9couvrir nos formations<\/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-2c657d4 elementor-widget elementor-widget-html\" data-id=\"2c657d4\" 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\": \"Qu\u2019est-ce que la r\u00e9gression lin\u00e9aire ?\",\r\n    \"acceptedAnswer\": {\r\n      \"@type\": \"Answer\",\r\n      \"text\": \"il recouvre une fonction statistique fondamentale. A partir d\u2019un nuage de points (issus de variables num\u00e9riques), la r\u00e9gression lin\u00e9aire trace une ligne ou une courbe qui est la plus proche de tous ces points. Cette figure g\u00e9om\u00e9trique se veut la plus fiable possible.\"\r\n    }\r\n  },{\r\n    \"@type\": \"Question\",\r\n    \"name\": \"Qui a invent\u00e9 la r\u00e9gression lin\u00e9aire ?\",\r\n    \"acceptedAnswer\": {\r\n      \"@type\": \"Answer\",\r\n      \"text\": \"C\u2019est un math\u00e9maticien et statisticien britannique du nom de Francis Galton (1822 \u2013 1911) qui est \u00e0 l\u2019origine de ce concept. Etant cousin de Charles Darwin, il \u00e9tait fortement int\u00e9ress\u00e9 par des notions telles que l\u2019h\u00e9r\u00e9dit\u00e9 et la g\u00e9n\u00e9tique. Lui-m\u00eame cherchait \u00e0 r\u00e9soudre des probl\u00e8mes concrets tels que celui-ci : la taille des parents aide-t-elle \u00e0 pr\u00e9dire la taille qu\u2019auront les enfants une fois qu\u2019ils ont atteint l\u2019\u00e2ge adulte ?\"\r\n    }\r\n  },{\r\n    \"@type\": \"Question\",\r\n    \"name\": \"La r\u00e9gression lin\u00e9aire dans le machine learning\",\r\n    \"acceptedAnswer\": {\r\n      \"@type\": \"Answer\",\r\n      \"text\": \"La r\u00e9gression lin\u00e9aire est le mod\u00e8le le plus simple pour ceux qui souhaitent d\u00e9buter dans le machine learning, par exemple, avec la biblioth\u00e8que math\u00e9matique Numpy sous Python.\"\r\n    }\r\n  }]\r\n}\r\n<\/script>\r\n\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>C\u2019est l\u2019outil le plus utilis\u00e9 en statistiques\u2026 A partir d\u2019un ensemble de donn\u00e9es connues, la r\u00e9gression lin\u00e9aire d\u00e9finit une ligne droite ou bien une courbe qui par la suite, va aider \u00e0 pr\u00e9dire des ph\u00e9nom\u00e8nes. La r\u00e9gression lin\u00e9aire est employ\u00e9e dans de nombreux domaines dont le machine learning. \u00ab R\u00e9gression lin\u00e9aire \u00bb\u2026 Ce nom pourrait [&hellip;]<\/p>\n","protected":false},"author":77,"featured_media":231057,"comment_status":"open","ping_status":"open","sticky":false,"template":"elementor_theme","format":"standard","meta":{"content-type":"","inline_featured_image":false},"categories":[2497],"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>R\u00e9gression lin\u00e9aire : Qu&#039;est-ce que c&#039;est ? 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Comment \u00e7a fonctionne ?","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/datascientest.com\/regression-lineaire-tout-savoir","og_locale":"fr_FR","og_type":"article","og_title":"R\u00e9gression lin\u00e9aire : Qu'est-ce que c'est ? Comment \u00e7a fonctionne ?","og_url":"https:\/\/datascientest.com\/regression-lineaire-tout-savoir","og_site_name":"Formation Data Science | DataScientest.com","article_published_time":"2024-03-18T06:30:00+00:00","article_modified_time":"2024-03-14T14:50:04+00:00","og_image":[{"width":1200,"height":686,"url":"https:\/\/datascientest.com\/wp-content\/uploads\/2024\/02\/regression_lineaire_datascientest.jpg","type":"image\/jpeg"}],"author":"Raphael Kassel","twitter_card":"summary_large_image","twitter_misc":{"\u00c9crit par":"Raphael Kassel","Dur\u00e9e de lecture estim\u00e9e":"7 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/datascientest.com\/regression-lineaire-tout-savoir","url":"https:\/\/datascientest.com\/regression-lineaire-tout-savoir","name":"R\u00e9gression lin\u00e9aire : Qu'est-ce que c'est ? 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