################################################
## Exercice 1 
################################################
# imoprter le fichierEx1_Sommeil

#2
r<-round(cor(Ex1_Sommeil$HeuresSommeil, Ex1_Sommeil$Note),3)
r

#3-4-6
modele <- lm(Note ~ HeuresSommeil, data = Ex1_Sommeil)
summary(modele)

#graphique(bonus)
library(ggplot2)

ggplot(Ex1_Sommeil, aes(x = HeuresSommeil, y = Note)) +
  geom_point() +
  geom_smooth(method = "lm", col = "green", se = FALSE) +
  labs(title = "Lien entre sommeil et note à l'examen",
       x = "Heures de sommeil", y = "Note à l'examen") +
  theme_minimal()
#7Rc    
RC<-round(qt(1-0.05, df =48), 2)
RC

## prediction
prediction<-predict(modele, newdata = data.frame(HeuresSommeil = 8))
prediction

# 11.Intervalle de prédiction pour un étudiant ayant dormi 8 heures
predict(modele, 
        newdata = data.frame(HeuresSommeil = 8), 
        interval = "prediction", 
        level = 0.95)


################################################
## Exercice 2 
################################################
# importer le fichier Ex2_productivite.csv

#1
r2<-round(cor(Ex2_productivite$jours_absence, Ex2_productivite$productivite),2)
r2

#2
modele2 <- lm(productivite ~ jours_absence, data = Ex2_productivite)
summary(modele2)
#graphique(bonus)
library(ggplot2)

ggplot(Ex2_productivite, aes(x = jours_absence, y = productivite)) +
  geom_point() +
  geom_smooth(method = "lm", col = "red", se = FALSE) +
  labs(title = "Lien entre productivite et jours_absence",
       x = "jours_absence", y = "productivite") +
  theme_minimal()
prediction<-predict(modele2, newdata = data.frame(jours_absence= 10))
prediction
predict(modele2, 
        newdata = data.frame(jours_absence= 10), 
        interval = "prediction", 
        level = 0.95)
#3
predict(modele2, 
        newdata = data.frame(jours_absence= 30))
        
################################################
## Exercice 3 
################################################
# importer le fichier Ex3_consomation.csv


modele3 <- lm(consommation ~ inflation, data = Ex3_consomation)
summary(modele3)
#graphique(bonus)
library(ggplot2)

ggplot(Ex3_consomation, aes(x = temperature, y = consommation)) +
  geom_point() +
  geom_smooth(method = "lm", col = "red", se = FALSE) +
  labs(title = "Lien entre temperature et consommation",
       x = "temperature", y = "consommation") +
  theme_minimal()
#1
prediction<-round(predict(modele3, newdata = data.frame(temperature= 25)),2)
prediction
#3
prediction3<- round(predict(modele3, 
        newdata = data.frame(temperature= -18)),2)
prediction3
        

################################################
## Exercice 4 
################################################
# importer le fichier Ex4_vente

#1
Test.cor<- cor.test(Ex4_vente$ventes, Ex4_vente$inflation,"less")
Test.cor
 
Test.cor
modele4 <- lm(ventes ~ inflation, data = Ex4_vente)
summary(modele4)
#graphique(bonus)
library(ggplot2)

ggplot(Ex4_vente, aes(x = inflation, y = ventes)) +
  geom_point() +
  geom_smooth(method = "lm", col = "red", se = FALSE) +
  labs(title = "Lien entre inflation et ventes",
       x = "inflation", y = "ventes") +
  theme_minimal()

#2
prediction4<-round(predict(modele4, newdata = data.frame(inflation= c(3.896, 9.778 ))),3)
prediction4

#3
Valeur.reelle <- subset(Ex4_vente, subset=(inflation >= 3.895 & inflation <= 3.897) | 
               (inflation >= 9.777 & inflation <= 9.779))
Valeur.reelle