14. Régression linéaire multiple
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5
1 0
1 5
2 0
5
1 0
1 5
2 0
2 5
âge (années)
temps (sec)
2.5 %
10 %
25 %
50 %
75 %
90 %
97.5 %
Figure 14.11 – Exemple de normes calculées à l’aide d’un modèle de régression.
97.5 % de la variable Y à l’âge x 1 = 10 ans (en secondes) par :
exp(3.745 − 0.239 · 10 + 0.00706 · 10
2
− 1.96 ·
√
0.0676) = 4.7
exp(3.745 − 0.239 · 10 + 0.00706 · 10
2
− 1.28 ·
√
0.0676) = 5.6
exp(3.745 − 0.239 · 10 + 0.00706 · 10
2
− 0.67 ·
√
0.0676) = 6.6
exp(3.745 − 0.239 · 10 + 0.00706 · 10
2 + 0.00 ·
√
0.0676) = 7.9
exp(3.745 − 0.239 · 10 + 0.00706 · 10
2 + 0.67 ·
√
0.0676) = 9.3
exp(3.745 − 0.239 · 10 + 0.00706 · 10
2 + 1.28 ·
√
0.0676) = 11.0
exp(3.745 − 0.239 · 10 + 0.00706 · 10
2 + 1.96 ·
√
0.0676) = 13.1.
De tels quantiles calculés entre 5 et 18 ans sont présentés dans la figure 14.11
(on y voit également les données utilisées pour cette modélisation). Il sera ainsi
possible de comparer via ces normes les performances de deux enfants d’âge
différent ou celles d’un même enfant à deux âges différents (afin de pouvoir
juger si par exemple un enfant en retard dans son développement a fait des
progrès ou non).
Nous terminerons cette section en mentionnant que la formule d’un intervalle de prédiction au niveau 95 % donnée ci-dessus n’est en fait qu’une approxi-