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Le logiciel R - Effectuer des analyses statistiques
12.3.9 Analyse des r´ esidus
Nous pr´ esentons ici quelques ´ el´ ements sur l’analyse des r´ esidus permettant
de v´ erifier les hypoth` eses du mod` ele et de d´ etecter des valeurs possiblement
atypiques ou aberrantes. Pour plus de d´ etails, nous vous conseillons la lecture
de [3].
Validation des hypoth` eses du mod` ele
En r´ egression lin´ eaire simple, nous avons d´ ej` a ´ evoqu´ e l’analyse des r´ esidus
pour ´ eprouver les hypoth` eses du mod` ele de r´ egression. Deux graphiques ont ´ et´ e
pr´ esent´ es permettant d’invalider l’hypoth` ese de normalit´ e des erreurs et l’hypoth` ese d’homosc´ edasticit´ e des erreurs.
Exemple fil rouge : ´
Etude « Poids de naissance de l’enfant ».
Nous ´ etudions la validit´ e des hypoth` eses pour le mod` ele suivant :
BWT = β 0 +β 1 SMOKE+β 2 AGE+β 3 LWT+β 4 RACE2+β 5 RACE3+β 6 UI+β 7 HT+β 8 SMOKE×AGE+.
> modelefinal<-lm(BWT∼SMOKE+AGE+LWT+factor(RACE)+UI+HT+SMOKE:AGE)
> par(mfrow=c(1:2))
> plot(modelefinal,1:2,col.smooth="red")
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−2000 −1000 0
1000
Fitted values
Residuals
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Residuals vs Fitted
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−3 −2 −1 0 1 2 3
Theoretical Quantiles
Standardized residuals
Normal Q−Q
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Figure 12.10 – Inspection de l’hypoth` ese d’homosc´ edasticit´ e (` a gauche) et de
normalit´ e (` a droite).