import numpy as np
from sklearn.linear_model import LinearRegression

modele = LinearRegression().fit(X_train, np.log(y_train))
residus = np.log(y_train) - modele.predict(X_train)

direct = np.exp(modele.predict(X_test))                 # valeur typique (médiane)
corrige = direct * np.mean(np.exp(residus))              # smearing de Duan : corrige le biais

print(direct.sum() / y_test.sum())                      # total retrouvé : 0.72 ici
print(corrige.sum() / y_test.sum())                     # 0.97 après correction