14. Régression linéaire multiple
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60
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−10
−5
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10
X1=poids (kg)
résidu
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X2=âge (années)
résidu
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165 175 185 195
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X3=taille (cm)
résidu
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70 80 90
110
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−5
0
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X4=abdomen (cm)
résidu
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26
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0
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X5=biceps (cm)
résidu
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X6=poignet (cm)
résidu
Figure 14.5 – Résidus versus prédicteurs.
Exemple 14.6 On reprend l’exemple de la prédiction de graisse corporelle. La
figure 14.5 nous montre les résidus estimés en fonction des m = 6 différents
prédicteurs. Il s’agit de vérifier les points suivants :
• la moyenne des résidus doit être nulle partout (linéarité)
• la variance des résidus autour de 0 doit être la même partout (homoscédasticité)
• la distribution des résidus autour de 0 doit être partout symétrique et avec
peu de valeurs extrêmes (normalité).
Le terme « partout » veut dire ici « aux alentours de chaque valeur possible
de chacun des prédicteurs ». Autrement dit, afin de ne pas contredire les hypotemps ne soient pas en moyenne plus semblables que les résidus de deux observations récoltées
loin dans le temps. Dans le cas contraire, on pourra essayer de modéliser cette dépendance. De
même, on pourra essayer de modéliser la dépendance que l’on aura dans les cas où plusieurs
observations sont faites sur un même individu. Ces méthodes de détection et de modélisation
de la dépendance entre observations dépassent cependant le cadre de ce texte.