Analyse de donnée

Get Started

Include Library

#ETL
library(tidyverse)

## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
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## ✔ forcats   1.0.0     ✔ stringr   1.5.1
## ✔ ggplot2   3.4.4     ✔ tibble    3.2.1
## ✔ lubridate 1.9.3     ✔ tidyr     1.3.1
## ✔ purrr     1.0.2     
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
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## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors

library(readxl)
library("scatterplot3d")

Include Data

df1 <- read_excel("Données_comparatives_voitures.xlsx")

Get Tidy data

# replace missing values (NA) by zero in all the dataset
df1[is.na(df1)] <- 0

Partie 1 : ACP

Matrice de correlation

cor(df1)

##                         Autonomie (km) Capacité batterie (kWh) Puissance (kW)
## Autonomie (km)              1.00000000              0.32981064     0.37425186
## Capacité batterie (kWh)     0.32981064              1.00000000     0.73355662
## Puissance (kW)              0.37425186              0.73355662     1.00000000
## Volume coffre (L)           0.46123753              0.64532311     0.94218437
## Places                      0.02432215              0.01828766     0.02619381
## Prix (€)                    0.27309591              0.94116747     0.66608631
##                         Volume coffre (L)     Places  Prix (€)
## Autonomie (km)                 0.46123753 0.02432215 0.2730959
## Capacité batterie (kWh)        0.64532311 0.01828766 0.9411675
## Puissance (kW)                 0.94218437 0.02619381 0.6660863
## Volume coffre (L)              1.00000000 0.02756115 0.5774464
## Places                         0.02756115 1.00000000 0.0211141
## Prix (€)                       0.57744642 0.02111410 1.0000000

ACP et Information output

princomp

## function (x, ...) 
## UseMethod("princomp")
## <bytecode: 0x0000024199fbe3d0>
## <environment: namespace:stats>

princomp

## function (x, ...) 
## UseMethod("princomp")
## <bytecode: 0x0000024199fbe3d0>
## <environment: namespace:stats>

princomp(df1,cor = TRUE)

## Call:
## princomp(x = df1, cor = TRUE)
## 
## Standard deviations:
##    Comp.1    Comp.2    Comp.3    Comp.4    Comp.5    Comp.6 
## 1.8616819 0.9999954 0.9275310 0.7585284 0.2374058 0.2052055 
## 
##  6  variables and  50 observations.

acp<-princomp(df1,cor=TRUE)

names(acp)

## [1] "sdev"     "loadings" "center"   "scale"    "n.obs"    "scores"   "call"

Vecteurs propres

eigenvector <- acp$loadings 
lambda <- acp$sdev*acp$sdev #variance = écrat-type^2
sum(lambda) 

## [1] 6

Eboulis des valeurs propres

Importance des composants : Deviation standart, proportion de la variance, proportion cumulative

summary(acp)

## Importance of components:
##                           Comp.1    Comp.2    Comp.3     Comp.4      Comp.5
## Standard deviation     1.8616819 0.9999954 0.9275310 0.75852841 0.237405838
## Proportion of Variance 0.5776432 0.1666651 0.1433856 0.09589423 0.009393589
## Cumulative Proportion  0.5776432 0.7443084 0.8876940 0.98358819 0.992981783
##                             Comp.6
## Standard deviation     0.205205512
## Proportion of Variance 0.007018217
## Cumulative Proportion  1.000000000

plot(1:6,lambda,type="b",ylab="Valeurspropres",xlab="Composantes
Principales",main="Eboulis des Valeurs Propres")

plot(acp)

#Coordonnées des individus dans la nouvelle base
acp$score #C=XP

##            Comp.1      Comp.2      Comp.3      Comp.4       Comp.5       Comp.6
##  [1,] -3.74550143 -1.25754858 -0.59873704 -0.30344694  0.060999969 -0.039727945
##  [2,] -3.62826619  0.20411002 -0.67343426 -0.27755664  0.001234103 -0.064082588
##  [3,] -3.44970864  1.17844799 -0.70233170 -0.32119568 -0.019734554  0.009595170
##  [4,] -2.86438461 -1.12908154  1.09546439  0.50452853 -0.049590320  0.193497972
##  [5,] -2.72209326  0.32951381  0.99056152  0.47857454 -0.089592344  0.214585993
##  [6,] -2.37838866  1.29345683  0.89575289  0.57111462  0.066439831  0.083790022
##  [7,] -2.30073411 -1.13864738  1.12986414  0.60740509  0.074975900  0.121432593
##  [8,] -2.13640034  0.31463938  0.97169349  0.58662640  0.077558456  0.114046838
##  [9,] -1.94465220  1.28756488  0.93306559  0.59557897  0.086353820  0.131303224
## [10,] -1.85296903 -1.14016790  1.22122234  0.66162599  0.082722048  0.146963718
## [11,] -0.83342998  0.32081843  1.33605920 -0.19248416 -0.045699725  0.044395128
## [12,] -1.22525177  1.17180001 -0.25637222 -0.96664941 -0.074966976 -0.136364312
## [13,] -1.18273046 -1.25877650 -0.01672396 -0.98490339 -0.161201238 -0.179740710
## [14,] -0.91173258  0.20326974 -0.05269676 -1.07875328 -0.139489003 -0.006318904
## [15,] -0.66187100  1.16994948 -0.14381475 -1.02969353 -0.057692321 -0.067992150
## [16,] -0.56658117 -1.26185864  0.09741322 -1.01285555 -0.061543559 -0.052128222
## [17,] -1.23275061  0.19467226 -0.20071437 -0.11532877  0.041345817 -0.021948978
## [18,] -1.07610230  1.16478247 -0.27758656 -0.05169186  0.089507078  0.008733315
## [19,] -1.04001543 -1.26468932 -0.02567528 -0.02837786  0.061167674  0.082537828
## [20,] -0.80010030  0.19622830 -0.08088109 -0.10326307 -0.006364470  0.007076123
## [21,] -0.65730651  1.17110139 -0.11148228 -0.11258522 -0.047581515  0.032110059
## [22,] -0.45350813 -1.30640447 -0.37556227  0.68817054 -0.811075231 -0.329426002
## [23,]  0.21845140  0.10378505 -0.86478784  1.01928393 -0.140921208 -0.728537365
## [24,] -0.10734733  1.08018391 -0.97413604  1.64419369  0.179031857 -0.059118134
## [25,] -0.07126046 -1.34928788 -0.72222475  1.66750769  0.150692454  0.014686380
## [26,]  0.25179004  0.10636490 -0.81303062  1.61857541  0.156911256 -0.133099209
## [27,]  0.42733389  1.07845752 -0.86499019  1.63195598  0.158763338 -0.133337893
## [28,]  0.41087599 -1.48043896 -2.13311398  0.42026666  0.348192467  0.253063187
## [29,]  0.03967671  0.02288717 -1.88322123  0.10126512 -0.273482128  0.567490626
## [30,]  0.21890056  1.04158733 -1.39383322 -0.73555597 -0.039121772 -0.258120958
## [31,]  0.28724428 -1.38953762 -1.15075065 -0.69412735 -0.069415052 -0.301790174
## [32,]  0.54753452  0.06998049 -1.21863286 -0.80550463 -0.048187364 -0.131569526
## [33,]  1.04193840  1.03501167 -1.27832081 -1.04395651  0.158720953  0.232069751
## [34,]  1.12463060 -1.40170465 -1.09735329 -1.07189958  0.147706967  0.230642041
## [35,]  1.28896436  0.05158211 -1.25552394 -1.09267826  0.150289523  0.223256285
## [36,]  1.67801635  1.15489716  0.27265291  0.10592436 -0.005866545 -0.054718912
## [37,]  1.32506256 -1.24433979  0.80346858 -0.25945531  0.643360480 -0.368218313
## [38,]  0.99670550  0.25411118  0.99998289 -0.70058463 -0.037699706  0.106252589
## [39,]  1.26033767  1.24101582  1.14061557 -0.60491760 -0.019441417  0.157650067
## [40,]  1.36444514 -1.19064425  1.38540189 -0.59780587 -0.029486309  0.162624673
## [41,]  1.24266891  0.26692348  1.21360123 -0.34404939 -0.188890861 -0.233911664
## [42,]  1.37475507  1.23926845  1.15109063 -0.37089894 -0.230592453 -0.212078887
## [43,]  1.39585124 -1.19374272  1.35832875 -0.37212330 -0.259610222 -0.142755994
## [44,]  2.37205834  0.20841418  0.84922596 -0.23557506  0.662103033 -0.145787956
## [45,]  2.91608117  1.13410016  0.33448884  0.21034119  0.058376001  0.084218055
## [46,]  2.92773906 -1.30267323  0.49951919  0.25562000  0.051888242  0.077703810
## [47,]  3.02103852  0.15055647  0.32541136  0.30806320  0.058997025  0.065231518
## [48,]  3.10413278  1.11753577  0.19369581  0.35961084  0.064406240  0.053503983
## [49,]  3.11579068 -1.31923762  0.35872615  0.40488965  0.057918481  0.046989738
## [50,]  3.89106275  0.07176323 -0.39137455  1.06679533 -0.782416719  0.335324110

var(acp$score)

##               Comp.1        Comp.2        Comp.3        Comp.4        Comp.5
## Comp.1  3.536591e+00 -1.102252e-16 -6.910572e-16  5.498896e-16 -6.910616e-16
## Comp.2 -1.102252e-16  1.020399e+00  1.467833e-16 -5.547865e-17  5.065043e-17
## Comp.3 -6.910572e-16  1.467833e-16  8.778711e-01  1.550852e-17  9.763296e-17
## Comp.4  5.498896e-16 -5.547865e-17  1.550852e-17  5.871075e-01  8.239494e-17
## Comp.5 -6.910616e-16  5.065043e-17  9.763296e-17  8.239494e-17  5.751177e-02
## Comp.6  1.370870e-15 -1.705530e-17 -2.239998e-16 -3.907664e-17  7.419655e-16
##               Comp.6
## Comp.1  1.370870e-15
## Comp.2 -1.705530e-17
## Comp.3 -2.239998e-16
## Comp.4 -3.907664e-17
## Comp.5  7.419655e-16
## Comp.6  4.296868e-02

plot(acp$score[,1],acp$score[,2],type="n",xlab="C1",ylab="C2")
abline(h=0.0,v=0.0)
text(acp$score[,1],acp$score[,2],row.names(df1))

Cercle de corrélation

C1 <-acp$loadings[,1]*acp$sdev[1]
C2 <-acp$loadings[,2]*acp$sdev[2]
correlation<-cbind(C1,C2)
print(correlation,digits=2)

##                            C1      C2
## Autonomie (km)          0.522  0.0662
## Capacité batterie (kWh) 0.904 -0.0412
## Puissance (kW)          0.920 -0.0074
## Volume coffre (L)       0.888  0.0080
## Places                  0.039  0.9960
## Prix (€)                0.860 -0.0423

print(correlation^2,digits=2)

##                             C1      C2
## Autonomie (km)          0.2727 4.4e-03
## Capacité batterie (kWh) 0.8178 1.7e-03
## Puissance (kW)          0.8466 5.5e-05
## Volume coffre (L)       0.7880 6.4e-05
## Places                  0.0015 9.9e-01
## Prix (€)                0.7392 1.8e-03

uncricle=cbind(cos((0:360)/180*pi),sin((0:360)/180*pi))
plot(uncricle,type="l",lty="solid",col="blue",lwd="2",xlab="C1",ylab="C2",cex.lab=1.2,cex.axis=1.2,cex.main=1.8)
abline(h=0.0,v=0.0)
text(C1,C2,labels=colnames(df1),cex=1)

cor(df1,acp$scores) #covarinace entre variables initial et variables composant principales

##                             Comp.1       Comp.2      Comp.3       Comp.4
## Autonomie (km)          0.52224858  0.066233077  0.77539901  0.348311238
## Capacité batterie (kWh) 0.90432478 -0.041240388 -0.29383516  0.255421018
## Puissance (kW)          0.92011989 -0.007395150  0.02183889 -0.359729250
## Volume coffre (L)       0.88769097  0.008005754  0.17847680 -0.398952456
## Places                  0.03891561  0.995990036 -0.08054010  0.001391419
## Prix (€)                0.85975703 -0.042287755 -0.36594175  0.316598493
##                                Comp.5        Comp.6
## Autonomie (km)           0.0030137371  0.0172097374
## Capacité batterie (kWh)  0.1516576977 -0.0769212414
## Puissance (kW)           0.0664320684  0.1379471189
## Volume coffre (L)       -0.0795137681 -0.1208353116
## Places                   0.0008264696 -0.0003130401
## Prix (€)                -0.1503863351  0.0475980209

Coordonnées des individus dans la nouvelle base + Cercle de corrélation

biplot(acp)

Complément de Statistiques descriptive

names(df1) #variables initial

## [1] "Autonomie (km)"          "Capacité batterie (kWh)"
## [3] "Puissance (kW)"          "Volume coffre (L)"      
## [5] "Places"                  "Prix (€)"

row.names(df1) #individus

##  [1] "1"  "2"  "3"  "4"  "5"  "6"  "7"  "8"  "9"  "10" "11" "12" "13" "14" "15"
## [16] "16" "17" "18" "19" "20" "21" "22" "23" "24" "25" "26" "27" "28" "29" "30"
## [31] "31" "32" "33" "34" "35" "36" "37" "38" "39" "40" "41" "42" "43" "44" "45"
## [46] "46" "47" "48" "49" "50"

n<-nrow(df1) #nombre d'individus
print(n)

## [1] 50

apply(df1,2,min) # valeuer min pour chaque variable

##          Autonomie (km) Capacité batterie (kWh)          Puissance (kW) 
##                     200                      50                      70 
##       Volume coffre (L)                  Places                Prix (€) 
##                     180                       2                   18550

apply(df1,2,function(x)(1:50)[x==min(x)]) # xmin pour chaque variable

## $`Autonomie (km)`
## [1] 1
## 
## $`Capacité batterie (kWh)`
## [1] 1 2 3 4 5
## 
## $`Puissance (kW)`
## [1] 1 2
## 
## $`Volume coffre (L)`
## [1] 1
## 
## $Places
##  [1]  1  4  7 10 13 16 19 22 25 28 31 34 37 40 43 46 49
## 
## $`Prix (€)`
## [1] 1

#apply(nomfichier,2,function(x)(1:derniére ligne)[x==min(x)]) <- xmin pour chaque variable
apply(df1,2,max) #valeuer max pour chaque variable

##          Autonomie (km) Capacité batterie (kWh)          Puissance (kW) 
##                     600                     150                     200 
##       Volume coffre (L)                  Places                Prix (€) 
##                    1000                       7                   83018

apply(df1,2,function(x)(1:50)[x==max(x)]) # xmax pour chaque variable

## $`Autonomie (km)`
## [1] 44 45 46 47 48 49 50
## 
## $`Capacité batterie (kWh)`
## [1] 50
## 
## $`Puissance (kW)`
## [1] 45 46 47 48 49 50
## 
## $`Volume coffre (L)`
## [1] 42 43 44 45 46 47 48 49 50
## 
## $Places
##  [1]  3  6  9 12 15 18 21 24 27 30 33 36 39 42 45 48
## 
## $`Prix (€)`
## [1] 50

Histograms pour chaque variables

hist(df1[[1]])

Distance chaque individu avec les variables initial

stars(USArrests[, 1:4], key.loc = c(14, 2), main = "USARRESTS : fullstars()",flip.labels=FALSE)

apply(df1,2,mean)

##          Autonomie (km) Capacité batterie (kWh)          Puissance (kW) 
##                  432.70                   98.24                  141.38 
##       Volume coffre (L)                  Places                Prix (€) 
##                  652.80                    4.62                41271.36

apply(df1,2,var)

##          Autonomie (km) Capacité batterie (kWh)          Puissance (kW) 
##            1.750936e+04            8.979412e+02            1.753914e+03 
##       Volume coffre (L)                  Places                Prix (€) 
##            7.459710e+04            4.281224e+00            2.020132e+08

summary(df1)

##  Autonomie (km)  Capacité batterie (kWh) Puissance (kW)  Volume coffre (L)
##  Min.   :200.0   Min.   : 50.00          Min.   : 70.0   Min.   : 180.0   
##  1st Qu.:318.8   1st Qu.: 72.00          1st Qu.:106.8   1st Qu.: 425.0   
##  Median :445.0   Median : 99.00          Median :143.5   Median : 665.0   
##  Mean   :432.7   Mean   : 98.24          Mean   :141.4   Mean   : 652.8   
##  3rd Qu.:540.0   3rd Qu.:125.00          3rd Qu.:177.2   3rd Qu.: 915.0   
##  Max.   :600.0   Max.   :150.00          Max.   :200.0   Max.   :1000.0   
##      Places        Prix (€)    
##  Min.   :2.00   Min.   :18550  
##  1st Qu.:2.00   1st Qu.:29722  
##  Median :5.00   Median :40894  
##  Mean   :4.62   Mean   :41271  
##  3rd Qu.:7.00   3rd Qu.:52066  
##  Max.   :7.00   Max.   :83018

boxplot(df1)

Partie 2 : ACP en 3D

Matrice de correlation

cor(df1)

##                         Autonomie (km) Capacité batterie (kWh) Puissance (kW)
## Autonomie (km)              1.00000000              0.32981064     0.37425186
## Capacité batterie (kWh)     0.32981064              1.00000000     0.73355662
## Puissance (kW)              0.37425186              0.73355662     1.00000000
## Volume coffre (L)           0.46123753              0.64532311     0.94218437
## Places                      0.02432215              0.01828766     0.02619381
## Prix (€)                    0.27309591              0.94116747     0.66608631
##                         Volume coffre (L)     Places  Prix (€)
## Autonomie (km)                 0.46123753 0.02432215 0.2730959
## Capacité batterie (kWh)        0.64532311 0.01828766 0.9411675
## Puissance (kW)                 0.94218437 0.02619381 0.6660863
## Volume coffre (L)              1.00000000 0.02756115 0.5774464
## Places                         0.02756115 1.00000000 0.0211141
## Prix (€)                       0.57744642 0.02111410 1.0000000

Statistiques descriptive

names(df1) #variables initial

## [1] "Autonomie (km)"          "Capacité batterie (kWh)"
## [3] "Puissance (kW)"          "Volume coffre (L)"      
## [5] "Places"                  "Prix (€)"

row.names(df1) #individus

##  [1] "1"  "2"  "3"  "4"  "5"  "6"  "7"  "8"  "9"  "10" "11" "12" "13" "14" "15"
## [16] "16" "17" "18" "19" "20" "21" "22" "23" "24" "25" "26" "27" "28" "29" "30"
## [31] "31" "32" "33" "34" "35" "36" "37" "38" "39" "40" "41" "42" "43" "44" "45"
## [46] "46" "47" "48" "49" "50"

n<-nrow(df) #nombre d'individus
print(n)

## NULL

apply(df1,2,min) # valeuer min pour chaque variable

##          Autonomie (km) Capacité batterie (kWh)          Puissance (kW) 
##                     200                      50                      70 
##       Volume coffre (L)                  Places                Prix (€) 
##                     180                       2                   18550

apply(df1,2,function(x)(1:38)[x==min(x)]) # xmin pour chaque variable

## $`Autonomie (km)`
## [1] 1
## 
## $`Capacité batterie (kWh)`
## [1] 1 2 3 4 5
## 
## $`Puissance (kW)`
## [1] 1 2
## 
## $`Volume coffre (L)`
## [1] 1
## 
## $Places
##  [1]  1  4  7 10 13 16 19 22 25 28 31 34 37 NA NA NA NA
## 
## $`Prix (€)`
## [1] 1

#apply(nomfichier,2,function(x)(1:derniére ligne)[x==min(x)]) <- xmin pour chaque variable
apply(df1,2,max) #valeuer max pour chaque variable

##          Autonomie (km) Capacité batterie (kWh)          Puissance (kW) 
##                     600                     150                     200 
##       Volume coffre (L)                  Places                Prix (€) 
##                    1000                       7                   83018

apply(df1,2,function(x)(1:38)[x==max(x)]) # xmax pour chaque variable

## $`Autonomie (km)`
## [1] NA NA NA NA NA NA NA
## 
## $`Capacité batterie (kWh)`
## [1] NA
## 
## $`Puissance (kW)`
## [1] NA NA NA NA NA NA
## 
## $`Volume coffre (L)`
## [1] NA NA NA NA NA NA NA NA NA
## 
## $Places
##  [1]  3  6  9 12 15 18 21 24 27 30 33 36 NA NA NA NA
## 
## $`Prix (€)`
## [1] NA

Histogramme

#Histograms pour x1
hist(df1[[1]])

#Histograms pour X2
hist(df1[[2]])

#Histograms pour X3
hist(df1[[3]])

#Histograms pour X4
hist(df1[[4]])

#Histograms pour X5
hist(df1[[5]])

#Histograms pour X6
hist(df1[[6]])

Distance chaque individu avec les variables initial

stars(df1[, 1:5], key.loc = c(14, 2), main = "Notes : full stars()",flip.labels=FALSE)

apply(df1,2,mean)

##          Autonomie (km) Capacité batterie (kWh)          Puissance (kW) 
##                  432.70                   98.24                  141.38 
##       Volume coffre (L)                  Places                Prix (€) 
##                  652.80                    4.62                41271.36

apply(df1,2,var)

##          Autonomie (km) Capacité batterie (kWh)          Puissance (kW) 
##            1.750936e+04            8.979412e+02            1.753914e+03 
##       Volume coffre (L)                  Places                Prix (€) 
##            7.459710e+04            4.281224e+00            2.020132e+08

summary(df1)

##  Autonomie (km)  Capacité batterie (kWh) Puissance (kW)  Volume coffre (L)
##  Min.   :200.0   Min.   : 50.00          Min.   : 70.0   Min.   : 180.0   
##  1st Qu.:318.8   1st Qu.: 72.00          1st Qu.:106.8   1st Qu.: 425.0   
##  Median :445.0   Median : 99.00          Median :143.5   Median : 665.0   
##  Mean   :432.7   Mean   : 98.24          Mean   :141.4   Mean   : 652.8   
##  3rd Qu.:540.0   3rd Qu.:125.00          3rd Qu.:177.2   3rd Qu.: 915.0   
##  Max.   :600.0   Max.   :150.00          Max.   :200.0   Max.   :1000.0   
##      Places        Prix (€)    
##  Min.   :2.00   Min.   :18550  
##  1st Qu.:2.00   1st Qu.:29722  
##  Median :5.00   Median :40894  
##  Mean   :4.62   Mean   :41271  
##  3rd Qu.:7.00   3rd Qu.:52066  
##  Max.   :7.00   Max.   :83018

boxplot(df1)

Nuages des points des individus dans chaque pair variables (xi,xj)

plot(df1)
pairs(df1)

R-package pour ACP

princomp

## function (x, ...) 
## UseMethod("princomp")
## <bytecode: 0x0000024199fbe3d0>
## <environment: namespace:stats>

princomp(df1,cor = TRUE)

## Call:
## princomp(x = df1, cor = TRUE)
## 
## Standard deviations:
##    Comp.1    Comp.2    Comp.3    Comp.4    Comp.5    Comp.6 
## 1.8616819 0.9999954 0.9275310 0.7585284 0.2374058 0.2052055 
## 
##  6  variables and  50 observations.

acp<-princomp(df1,cor=TRUE)

Information output

names(acp)

## [1] "sdev"     "loadings" "center"   "scale"    "n.obs"    "scores"   "call"

Vecteurs propres (norme) et valuers propers

summary(acp)

## Importance of components:
##                           Comp.1    Comp.2    Comp.3     Comp.4      Comp.5
## Standard deviation     1.8616819 0.9999954 0.9275310 0.75852841 0.237405838
## Proportion of Variance 0.5776432 0.1666651 0.1433856 0.09589423 0.009393589
## Cumulative Proportion  0.5776432 0.7443084 0.8876940 0.98358819 0.992981783
##                             Comp.6
## Standard deviation     0.205205512
## Proportion of Variance 0.007018217
## Cumulative Proportion  1.000000000

plot(1:6,lambda,type="b",ylab="Valeurspropres",xlab="Composantes Principales",main="Eboulis
des Valeurs Propres")

plot(acp)

Coordonnées des individus dans la nouvelle base

acp$score #C=XP

##            Comp.1      Comp.2      Comp.3      Comp.4       Comp.5       Comp.6
##  [1,] -3.74550143 -1.25754858 -0.59873704 -0.30344694  0.060999969 -0.039727945
##  [2,] -3.62826619  0.20411002 -0.67343426 -0.27755664  0.001234103 -0.064082588
##  [3,] -3.44970864  1.17844799 -0.70233170 -0.32119568 -0.019734554  0.009595170
##  [4,] -2.86438461 -1.12908154  1.09546439  0.50452853 -0.049590320  0.193497972
##  [5,] -2.72209326  0.32951381  0.99056152  0.47857454 -0.089592344  0.214585993
##  [6,] -2.37838866  1.29345683  0.89575289  0.57111462  0.066439831  0.083790022
##  [7,] -2.30073411 -1.13864738  1.12986414  0.60740509  0.074975900  0.121432593
##  [8,] -2.13640034  0.31463938  0.97169349  0.58662640  0.077558456  0.114046838
##  [9,] -1.94465220  1.28756488  0.93306559  0.59557897  0.086353820  0.131303224
## [10,] -1.85296903 -1.14016790  1.22122234  0.66162599  0.082722048  0.146963718
## [11,] -0.83342998  0.32081843  1.33605920 -0.19248416 -0.045699725  0.044395128
## [12,] -1.22525177  1.17180001 -0.25637222 -0.96664941 -0.074966976 -0.136364312
## [13,] -1.18273046 -1.25877650 -0.01672396 -0.98490339 -0.161201238 -0.179740710
## [14,] -0.91173258  0.20326974 -0.05269676 -1.07875328 -0.139489003 -0.006318904
## [15,] -0.66187100  1.16994948 -0.14381475 -1.02969353 -0.057692321 -0.067992150
## [16,] -0.56658117 -1.26185864  0.09741322 -1.01285555 -0.061543559 -0.052128222
## [17,] -1.23275061  0.19467226 -0.20071437 -0.11532877  0.041345817 -0.021948978
## [18,] -1.07610230  1.16478247 -0.27758656 -0.05169186  0.089507078  0.008733315
## [19,] -1.04001543 -1.26468932 -0.02567528 -0.02837786  0.061167674  0.082537828
## [20,] -0.80010030  0.19622830 -0.08088109 -0.10326307 -0.006364470  0.007076123
## [21,] -0.65730651  1.17110139 -0.11148228 -0.11258522 -0.047581515  0.032110059
## [22,] -0.45350813 -1.30640447 -0.37556227  0.68817054 -0.811075231 -0.329426002
## [23,]  0.21845140  0.10378505 -0.86478784  1.01928393 -0.140921208 -0.728537365
## [24,] -0.10734733  1.08018391 -0.97413604  1.64419369  0.179031857 -0.059118134
## [25,] -0.07126046 -1.34928788 -0.72222475  1.66750769  0.150692454  0.014686380
## [26,]  0.25179004  0.10636490 -0.81303062  1.61857541  0.156911256 -0.133099209
## [27,]  0.42733389  1.07845752 -0.86499019  1.63195598  0.158763338 -0.133337893
## [28,]  0.41087599 -1.48043896 -2.13311398  0.42026666  0.348192467  0.253063187
## [29,]  0.03967671  0.02288717 -1.88322123  0.10126512 -0.273482128  0.567490626
## [30,]  0.21890056  1.04158733 -1.39383322 -0.73555597 -0.039121772 -0.258120958
## [31,]  0.28724428 -1.38953762 -1.15075065 -0.69412735 -0.069415052 -0.301790174
## [32,]  0.54753452  0.06998049 -1.21863286 -0.80550463 -0.048187364 -0.131569526
## [33,]  1.04193840  1.03501167 -1.27832081 -1.04395651  0.158720953  0.232069751
## [34,]  1.12463060 -1.40170465 -1.09735329 -1.07189958  0.147706967  0.230642041
## [35,]  1.28896436  0.05158211 -1.25552394 -1.09267826  0.150289523  0.223256285
## [36,]  1.67801635  1.15489716  0.27265291  0.10592436 -0.005866545 -0.054718912
## [37,]  1.32506256 -1.24433979  0.80346858 -0.25945531  0.643360480 -0.368218313
## [38,]  0.99670550  0.25411118  0.99998289 -0.70058463 -0.037699706  0.106252589
## [39,]  1.26033767  1.24101582  1.14061557 -0.60491760 -0.019441417  0.157650067
## [40,]  1.36444514 -1.19064425  1.38540189 -0.59780587 -0.029486309  0.162624673
## [41,]  1.24266891  0.26692348  1.21360123 -0.34404939 -0.188890861 -0.233911664
## [42,]  1.37475507  1.23926845  1.15109063 -0.37089894 -0.230592453 -0.212078887
## [43,]  1.39585124 -1.19374272  1.35832875 -0.37212330 -0.259610222 -0.142755994
## [44,]  2.37205834  0.20841418  0.84922596 -0.23557506  0.662103033 -0.145787956
## [45,]  2.91608117  1.13410016  0.33448884  0.21034119  0.058376001  0.084218055
## [46,]  2.92773906 -1.30267323  0.49951919  0.25562000  0.051888242  0.077703810
## [47,]  3.02103852  0.15055647  0.32541136  0.30806320  0.058997025  0.065231518
## [48,]  3.10413278  1.11753577  0.19369581  0.35961084  0.064406240  0.053503983
## [49,]  3.11579068 -1.31923762  0.35872615  0.40488965  0.057918481  0.046989738
## [50,]  3.89106275  0.07176323 -0.39137455  1.06679533 -0.782416719  0.335324110

a<-acp$score
s3d <- scatterplot3d(a[,1:3], type="h", angle= 60, grid=TRUE, box = FALSE, pch=16, color ="steelblue",
              main="3D Scatter Plot",
              xlab = "text",
              ylab = "text",
              zlab = "text")

#text (s3d$xyz.convert(C[, 1:3]), labels = rownames(C),cex= 0.7)

corrélation des anciennes variables avec les composantes principales

cor(df1,acp$scores)

##                             Comp.1       Comp.2      Comp.3       Comp.4
## Autonomie (km)          0.52224858  0.066233077  0.77539901  0.348311238
## Capacité batterie (kWh) 0.90432478 -0.041240388 -0.29383516  0.255421018
## Puissance (kW)          0.92011989 -0.007395150  0.02183889 -0.359729250
## Volume coffre (L)       0.88769097  0.008005754  0.17847680 -0.398952456
## Places                  0.03891561  0.995990036 -0.08054010  0.001391419
## Prix (€)                0.85975703 -0.042287755 -0.36594175  0.316598493
##                                Comp.5        Comp.6
## Autonomie (km)           0.0030137371  0.0172097374
## Capacité batterie (kWh)  0.1516576977 -0.0769212414
## Puissance (kW)           0.0664320684  0.1379471189
## Volume coffre (L)       -0.0795137681 -0.1208353116
## Places                   0.0008264696 -0.0003130401
## Prix (€)                -0.1503863351  0.0475980209

C<-cor(df1,acp$scores)
C1<-C[,1]
C2<-C[,2]
C3<-C[,3]
barplot(C1)

barplot(C2)

barplot(C3)