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| </p><p>Pendant longtemps, la régression d'une <a href="/wiki/Variable_al%C3%A9atoire" title="Variable aléatoire">variable aléatoire</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y}">
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| <semantics>
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| <mrow class="MJX-TeXAtom-ORD">
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| <mi>y</mi>
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| </mrow>
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| <annotation encoding="application/x-tex">{\displaystyle y}</annotation>
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| </semantics>
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| </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b8a6208ec717213d4317e666f1ae872e00620a0d" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:1.155ex; height:2.009ex;" alt="y"/></span> sur le vecteur de variables aléatoires <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x}">
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| <semantics>
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| </mrow>
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| <annotation encoding="application/x-tex">{\displaystyle x}</annotation>
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| </semantics>
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| </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="x"/></span> désignait la moyenne conditionnelle de <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y}">
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| <annotation encoding="application/x-tex">{\displaystyle y}</annotation>
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| </semantics>
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| </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b8a6208ec717213d4317e666f1ae872e00620a0d" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:1.155ex; height:2.009ex;" alt="y"/></span> sachant <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x}">
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| <semantics>
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| <mrow class="MJX-TeXAtom-ORD">
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| </mrow>
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| <annotation encoding="application/x-tex">{\displaystyle x}</annotation>
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| </semantics>
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| </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="x"/></span>. Aujourd'hui, le terme de régression désigne tout élément de la distribution conditionnelle de <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y}">
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| <annotation encoding="application/x-tex">{\displaystyle y}</annotation>
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| </semantics>
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| </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b8a6208ec717213d4317e666f1ae872e00620a0d" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:1.155ex; height:2.009ex;" alt="y"/></span> sachant <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x}">
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| </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="x"/></span>, considérée comme une fonction de <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x}">
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| <annotation encoding="application/x-tex">{\displaystyle x}</annotation>
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| </semantics>
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| </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="x"/></span>. On peut par exemple s'intéresser à la moyenne conditionnelle, à la médiane conditionnelle, au mode conditionnel, à la variance conditionnelle<sup id="cite_ref-manski91_1-0" class="reference"><a href="#cite_note-manski91-1"><span class="cite_crochet">[</span>1<span class="cite_crochet">]</span></a></sup>...
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| </p><p>Le terme « régression » a été introduit par <a href="/wiki/Francis_Galton" title="Francis Galton">Francis Galton</a> à la suite d'une étude sur la taille des descendants de personnes de grande taille, qui diminue de générations en générations vers une taille moyenne (donc leur taille régresse)<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite_crochet">[</span>2<span class="cite_crochet">]</span></a></sup><sup class="reference cite_virgule">,</sup><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite_crochet">[</span>3<span class="cite_crochet">]</span></a></sup>.
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| </p>
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| ==Français== | | ==Français== |
| '''régression''' n.f. | | '''régression''' n.f. |
Domaine
Définition
La régression est un ensemble de méthodes statistiques très utilisées pour analyser la relation d'une variable par rapport à une ou plusieurs autres. Pendant longtemps, la régression d'une variable aléatoire sur le vecteur de variables aléatoires désignait la moyenne conditionnelle de sachant . Aujourd'hui, le terme de régression désigne tout élément de la distribution conditionnelle de sachant , considérée comme une fonction de . On peut par exemple s'intéresser à la moyenne conditionnelle, à la médiane conditionnelle, au mode conditionnel, à la variance conditionnelle.
Le terme régression a été introduit par Francis Galton à la suite d'une étude sur la taille des descendants de personnes de grande taille, qui diminue de générations en générations vers une taille moyenne (donc leur taille régresse).
Français
régression n.f.
Anglais
Regression
Source : Wikipedia IA
