> # Projet Econometrie - Regression lineaire multiple
> # Donnees : mtcars (R dataset)
> 
> # 1. Chargement des donnees
> data(mtcars)
> cat("========== Apercu des donnees ==========\n")
========== Apercu des donnees ==========
> print(head(mtcars))
                   mpg cyl disp  hp drat    wt  qsec vs am gear carb
Mazda RX4         21.0   6  160 110 3.90 2.620 16.46  0  1    4    4
Mazda RX4 Wag     21.0   6  160 110 3.90 2.875 17.02  0  1    4    4
Datsun 710        22.8   4  108  93 3.85 2.320 18.61  1  1    4    1
Hornet 4 Drive    21.4   6  258 110 3.08 3.215 19.44  1  0    3    1
Hornet Sportabout 18.7   8  360 175 3.15 3.440 17.02  0  0    3    2
Valiant           18.1   6  225 105 2.76 3.460 20.22  1  0    3    1
> 
> # 2. Statistiques descriptives
> cat("\n========== Statistiques descriptives ==========\n")

========== Statistiques descriptives ==========
> print(summary(mtcars))
      mpg             cyl             disp             hp             drat             wt             qsec             vs        
 Min.   :10.40   Min.   :4.000   Min.   : 71.1   Min.   : 52.0   Min.   :2.760   Min.   :1.513   Min.   :14.50   Min.   :0.0000  
 1st Qu.:15.43   1st Qu.:4.000   1st Qu.:120.8   1st Qu.: 96.5   1st Qu.:3.080   1st Qu.:2.581   1st Qu.:16.89   1st Qu.:0.0000  
 Median :19.20   Median :6.000   Median :196.3   Median :123.0   Median :3.695   Median :3.325   Median :17.71   Median :0.0000  
 Mean   :20.09   Mean   :6.188   Mean   :230.7   Mean   :146.7   Mean   :3.597   Mean   :3.217   Mean   :17.85   Mean   :0.4375  
 3rd Qu.:22.80   3rd Qu.:8.000   3rd Qu.:326.0   3rd Qu.:180.0   3rd Qu.:3.920   3rd Qu.:3.610   3rd Qu.:18.90   3rd Qu.:1.0000  
 Max.   :33.90   Max.   :8.000   Max.   :472.0   Max.   :335.0   Max.   :4.930   Max.   :5.424   Max.   :22.90   Max.   :1.0000  
       am              gear            carb      
 Min.   :0.0000   Min.   :3.000   Min.   :1.000  
 1st Qu.:0.0000   1st Qu.:3.000   1st Qu.:2.000  
 Median :0.0000   Median :4.000   Median :2.000  
 Mean   :0.4062   Mean   :3.688   Mean   :2.812  
 3rd Qu.:1.0000   3rd Qu.:4.000   3rd Qu.:4.000  
 Max.   :1.0000   Max.   :5.000   Max.   :8.000  
> 
> # 3. Matrice de correlation
> cat("\n========== Matrice de correlation ==========\n")

========== Matrice de correlation ==========
> cor_matrix <- cor(mtcars[, c("mpg", "cyl", "disp", "hp", "wt", "am")])
> print(cor_matrix)
            mpg        cyl       disp         hp         wt          am
mpg   1.0000000 -0.8521620 -0.8475514 -0.7761684 -0.8676594  0.59983243
cyl  -0.8521620  1.0000000  0.9020329  0.8324475  0.7824958 -0.52260706
disp -0.8475514  0.9020329  1.0000000  0.7909486  0.8879799 -0.59122707
hp   -0.7761684  0.8324475  0.7909486  1.0000000  0.6587479 -0.24320426
wt   -0.8676594  0.7824958  0.8879799  0.6587479  1.0000000 -0.69249534
am    0.5998324 -0.5226071 -0.5912271 -0.2432043 -0.6924953  1.00000000
> 
> # 4. Modele de regression lineaire multiple
> modele <- lm(mpg ~ cyl + hp + wt + am, data = mtcars)
> cat("\n========== Resume du modele ==========\n")

========== Resume du modele ==========
> print(summary(modele))

Call:
lm(formula = mpg ~ cyl + hp + wt + am, data = mtcars)

Residuals:
    Min      1Q  Median      3Q     Max 
-3.9387 -1.2560 -0.4013  1.1253  5.5493 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 36.14654    3.10478  11.642 4.94e-12 ***
cyl         -0.85717    0.56345  -1.521   0.1399    
hp          -0.01840    0.01162  -1.584   0.1248    
wt          -3.53198    0.71669  -4.928 3.86e-05 ***
am           2.20189    1.07402   2.050   0.0503 .  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 2.513 on 27 degrees of freedom
Multiple R-squared:  0.8431,    Adjusted R-squared:  0.8199 
F-statistic: 36.25 on 4 and 27 DF,  p-value: 1.717e-10

> 
> # 5. Diagnostic des hypotheses
> library(lmtest)
> cat("\n========== Test de Breusch-Pagan (homoscedasticite) ==========\n")

========== Test de Breusch-Pagan (homoscedasticite) ==========
> print(bptest(modele))

        studentized Breusch-Pagan test

data:  modele
BP = 2.487, df = 4, p-value = 0.6466

> cat("\n========== Test de Shapiro-Wilk (normalite des residus) ==========\n")

========== Test de Shapiro-Wilk (normalite des residus) ==========
> print(shapiro.test(residuals(modele)))

        Shapiro-Wilk normality test

data:  residuals(modele)
W = 0.94937, p-value = 0.1345

> cat("\n========== Test de Durbin-Watson (autocorrelation des erreurs) ==========\n")

========== Test de Durbin-Watson (autocorrelation des erreurs) ==========
> print(dwtest(modele))

        Durbin-Watson test

data:  modele
DW = 1.4968, p-value = 0.1002
alternative hypothesis: true autocorrelation is greater than 0

> 
> # 6. Export des donnees en CSV
> write.csv(mtcars, "mtcars.csv", row.names = TRUE)
> cat("\nLes donnees ont ete exportees dans le fichier 'mtcars.csv'.\n")

Les donnees ont ete exportees dans le fichier 'mtcars.csv'.