1. Charger le fichier “jouet3.txt”. Faire la régression de \(y\) sur \(x2, x3\).
load("jouet2.Rdata")
summary(jouet2)
##        x1                x2               y          
##  Min.   :-3.5011   Min.   :0.0140   Min.   :-2.9514  
##  1st Qu.:-1.6569   1st Qu.:0.2485   1st Qu.:-0.8356  
##  Median :-0.8041   Median :0.5127   Median : 0.1708  
##  Mean   :-0.8420   Mean   :0.5131   Mean   : 0.3207  
##  3rd Qu.:-0.1245   3rd Qu.:0.7802   3rd Qu.: 1.4039  
##  Max.   : 1.9076   Max.   :0.9963   Max.   : 4.3604
library(ggplot2)
## Warning: package 'ggplot2' was built under R version 3.5.3
ggplot(jouet2) + geom_point(aes(x = x2, y = y))

ggplot(jouet2) + geom_point(aes(x = x1, y = y))

reg <- lm(y ~ x1 + x2, data=jouet2)
summary(reg)
## 
## Call:
## lm(formula = y ~ x1 + x2, data = jouet2)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -3.13860 -0.68004  0.07635  0.63161  2.34730 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -1.78690    0.20580  -8.683 9.32e-14 ***
## x1          -0.90288    0.09107  -9.914  < 2e-16 ***
## x2           2.62564    0.32531   8.071 1.89e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9668 on 97 degrees of freedom
## Multiple R-squared:  0.6342, Adjusted R-squared:  0.6267 
## F-statistic: 84.09 on 2 and 97 DF,  p-value: < 2.2e-16
  1. Afficher le graphique de \(\hat{y}\) en ordonnée contre \(\hat{\e}\) en abscisse
data2 <- jouet2
data2$yc <- predict(reg)
data2$ec <- data2$y - data2$yc
ggplot(data2) + geom_point(aes(x = yc, y = ec))

  1. Quelle conclusion tirer de ce graphique?

Réponse : pas de structure particulière. Le modèle semble réaliste en terme de moyenne.