{"id":478465,"date":"2023-08-09T09:33:12","date_gmt":"2023-08-09T09:33:12","guid":{"rendered":""},"modified":"2023-09-05T11:16:48","modified_gmt":"2023-09-05T11:16:48","slug":"polynomial-regression","status":"publish","type":"wiki","link":"https:\/\/oneproxy.pro\/fr\/wiki\/polynomial-regression\/","title":{"rendered":"R\u00e9gression polynomiale"},"content":{"rendered":"

La r\u00e9gression polynomiale est un type d'analyse de r\u00e9gression en statistique qui consiste \u00e0 mod\u00e9liser une relation entre une variable ind\u00e9pendante X<\/mi><\/mrow>X<\/annotation><\/semantics><\/math><\/span><\/span>X<\/span><\/span><\/span><\/span><\/span> et une variable d\u00e9pendante oui<\/mi><\/mrow>oui<\/annotation><\/semantics><\/math><\/span><\/span>oui<\/span><\/span><\/span><\/span><\/span> comme un polyn\u00f4me du ni\u00e8me degr\u00e9. Contrairement \u00e0 la r\u00e9gression lin\u00e9aire, qui mod\u00e9lise la relation sous forme de ligne droite, la r\u00e9gression polynomiale ajuste une courbe aux points de donn\u00e9es, offrant ainsi un ajustement plus flexible.<\/p>\n

L'histoire de l'origine de la r\u00e9gression polynomiale et sa premi\u00e8re mention<\/h2>\n

La r\u00e9gression polynomiale trouve ses racines dans le domaine plus large de l'interpolation polynomiale, qui remonte aux travaux math\u00e9matiques d'Isaac Newton et de Carl Friedrich Gauss. La m\u00e9thode d'interpolation polynomiale de Newton a \u00e9t\u00e9 d\u00e9velopp\u00e9e \u00e0 la fin du XVIIe si\u00e8cle et a fourni l'une des premi\u00e8res techniques d'ajustement de courbes polynomiales \u00e0 des points de donn\u00e9es.<\/p>\n

Dans le contexte de l'analyse de r\u00e9gression, la r\u00e9gression polynomiale a commenc\u00e9 \u00e0 gagner du terrain au XXe si\u00e8cle \u00e0 mesure que les outils informatiques progressaient, permettant une mod\u00e9lisation plus complexe des relations entre les variables.<\/p>\n

Informations d\u00e9taill\u00e9es sur la r\u00e9gression polynomiale. Extension du sujet R\u00e9gression polynomiale<\/h2>\n

La r\u00e9gression polynomiale d\u00e9veloppe la r\u00e9gression lin\u00e9aire simple en permettant de mod\u00e9liser la relation entre la variable ind\u00e9pendante et la variable d\u00e9pendante sous la forme d'une \u00e9quation polynomiale de la forme\u00a0:
\noui<\/mi>=<\/mo>\u03b2<\/mi>0<\/mn><\/msub>+<\/mo>\u03b2<\/mi>1<\/mn><\/msub>X<\/mi>+<\/mo>\u03b2<\/mi>2<\/mn><\/msub>X<\/mi>2<\/mn><\/msup>+<\/mo>\u2026<\/mo>+<\/mo>\u03b2<\/mi>n<\/mi><\/msub>X<\/mi>n<\/mi><\/msup>+<\/mo>\u03f5<\/mi><\/mrow>y = b\u00eata_0 + b\u00eata_1 x + b\u00eata_2 x^2 + ldots + b\u00eata_n x^n + epsilon<\/annotation><\/semantics><\/math><\/span><\/span>oui<\/span><\/span>=<\/span><\/span><\/span><\/span>\u03b2<\/span><\/span>0<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>\u03b2<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>X<\/span><\/span>+<\/span><\/span><\/span><\/span>\u03b2<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>X<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>\u2026<\/span><\/span>+<\/span><\/span><\/span><\/span>\u03b2<\/span><\/span>n<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>X<\/span><\/span>n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span><\/span><\/span>\u03f5<\/span><\/span><\/span><\/span><\/span><\/p>\n

Explication de l'\u00e9quation\u00a0:<\/h3>\n