Analyse de Données avec PCA et Régression Linéaire
GROUPE 4 PROJET RTI
2024-12-07
Chargement des Données
setwd("C:/Users/LENOVO/Desktop/Donnees projet RTI/")
donnees <- read.csv(file = "kone.csv",
header = TRUE,
sep = ";",
dec = ",",
row.names = 1)
# Afficher les premières lignes des données
head(donnees)## AEP AE PSAAA MI TA Tcorrpt Tchom IDF MVIH
## Burkina Faso 49.86 16.08 54.59 10.11 37.75 11 4.32 28.0 4522
## Niger 54.52 16.60 79.35 12.02 19.10 10 0.53 29.0 2120
## Cote d Ivoire 65.10 62.60 47.07 9.05 43.27 34 3.15 27.4 22957
## Senegal 21.39 60.50 32.32 5.10 55.62 8 6.76 18.2 2438
## Ghana 66.92 74.08 32.00 5.54 76.58 36 6.81 16.9 17114
## Mali 25.60 37.60 45.16 11.56 33.07 18 7.73 24.7 5969Analyse des Composantes Principales (ACP)
library(psych)
library(FactoMineR)
library(factoextra)
# Extraction d'un sous-ensemble de colonnes
base <- donnees[c(1:9)]
# Matrice de corrélation
mat_cor <- cor(base)
# ACP avec FactoMineR
ResACP <- PCA(base, graph = FALSE)
ResACP$eig## eigenvalue percentage of variance cumulative percentage of variance
## comp 1 4.13072465 45.8969406 45.89694
## comp 2 1.71496936 19.0552151 64.95216
## comp 3 1.32964923 14.7738803 79.72604
## comp 4 0.77914172 8.6571302 88.38317
## comp 5 0.56700419 6.3000466 94.68321
## comp 6 0.28595654 3.1772949 97.86051
## comp 7 0.10782687 1.1980763 99.05858
## comp 8 0.06212006 0.6902229 99.74881
## comp 9 0.02260739 0.2511932 100.00000ResACP$var$contrib## Dim.1 Dim.2 Dim.3 Dim.4 Dim.5
## AEP 0.001378201 34.26468125 16.2191029 0.9032130 30.4209743
## AE 20.795796216 1.04991363 5.2437074 0.1491811 0.4581436
## PSAAA 16.904629049 1.90648570 1.0626943 18.4935011 0.4015112
## MI 16.867147418 0.09695867 1.5024287 28.0365042 5.4945277
## TA 12.474556751 18.79700813 0.1242270 7.5183306 0.7299920
## Tcorrpt 0.068447269 38.53613492 10.3641796 0.9247986 27.2688933
## Tchom 10.748419893 0.33593009 19.3230840 27.9893122 6.8660934
## IDF 17.242675450 4.87811286 0.3056236 8.1352257 11.3603506
## MVIH 4.896949754 0.13477475 45.8549525 7.8499336 16.9995139# Visualisation des résultats avec factoextra
fviz_pca_biplot(ResACP, col.ind = "red", col.var = "blue", repel = TRUE)
Analyse Factorielle avec Rotation Varimax
resultats1 <- principal(r = mat_cor, nfactors = 9, residuals = FALSE, rotate = "none")
resultats1$values## [1] 4.13072465 1.71496936 1.32964923 0.77914172 0.56700419 0.28595654 0.10782687
## [8] 0.06212006 0.02260739resultats1$loadings##
## Loadings:
## PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8 PC9
## AEP 0.767 0.464 -0.415 -0.113
## AE 0.927 -0.134 0.264 0.106 -0.137 0.112
## PSAAA -0.836 0.181 0.119 -0.380 0.305 0.107
## MI -0.835 0.141 0.467 -0.177 0.161
## TA 0.718 0.568 -0.242 -0.248 0.175
## Tcorrpt 0.813 -0.371 0.393 0.174
## Tchom 0.666 -0.507 0.467 -0.197 0.135 0.101
## IDF -0.844 0.289 0.252 0.254 -0.246
## MVIH 0.450 0.781 0.247 0.310 0.122
##
## PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8 PC9
## SS loadings 4.131 1.715 1.330 0.779 0.567 0.286 0.108 0.062 0.023
## Proportion Var 0.459 0.191 0.148 0.087 0.063 0.032 0.012 0.007 0.003
## Cumulative Var 0.459 0.650 0.797 0.884 0.947 0.979 0.991 0.997 1.000resultats2 <- principal(r = mat_cor, nfactors = 2, residuals = FALSE, rotate = "varimax")
resultats2$loadings##
## Loadings:
## RC1 RC2
## AEP 0.763
## AE 0.936
## PSAAA -0.850
## MI -0.825 -0.130
## TA 0.653 0.642
## Tcorrpt 0.814
## Tchom 0.654 0.147
## IDF -0.870 0.197
## MVIH 0.452
##
## RC1 RC2
## SS loadings 4.103 1.743
## Proportion Var 0.456 0.194
## Cumulative Var 0.456 0.650Visualisation de la Régression multiple
library(car)
library(GGally)
# Modèle de régression
modele <- lm(MI ~ PSAAA + IDF, data = donnees)
summary(modele)##
## Call:
## lm(formula = MI ~ PSAAA + IDF, data = donnees)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.3416 -0.9533 -0.0696 1.0013 2.9580
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.97621 2.74307 -0.356 0.7293
## PSAAA 0.02937 0.04458 0.659 0.5250
## IDF 0.33409 0.12609 2.650 0.0243 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.878 on 10 degrees of freedom
## Multiple R-squared: 0.5901, Adjusted R-squared: 0.5081
## F-statistic: 7.199 on 2 and 10 DF, p-value: 0.01157# Variance inflation factor
vif(modele)## PSAAA IDF
## 1.516786 1.516786# Visualisation des corrélations entre les variables
ggpairs(donnees, columns = c("PSAAA", "IDF", "MI"))
# Matrice de corrélation pour les six premières variables
mat_cor <- cor(donnees[1:9])
# Vérification de certaines colonnes spécifiques
base <- donnees[c(1:9)]
# Charger le package psych pour l'analyse factorielle
library(psych)
library(FactoMineR)
ResACP <- PCA(base)
ResACP$eig## eigenvalue percentage of variance cumulative percentage of variance
## comp 1 4.13072465 45.8969406 45.89694
## comp 2 1.71496936 19.0552151 64.95216
## comp 3 1.32964923 14.7738803 79.72604
## comp 4 0.77914172 8.6571302 88.38317
## comp 5 0.56700419 6.3000466 94.68321
## comp 6 0.28595654 3.1772949 97.86051
## comp 7 0.10782687 1.1980763 99.05858
## comp 8 0.06212006 0.6902229 99.74881
## comp 9 0.02260739 0.2511932 100.00000ResACP$var$contrib## Dim.1 Dim.2 Dim.3 Dim.4 Dim.5
## AEP 0.001378201 34.26468125 16.2191029 0.9032130 30.4209743
## AE 20.795796216 1.04991363 5.2437074 0.1491811 0.4581436
## PSAAA 16.904629049 1.90648570 1.0626943 18.4935011 0.4015112
## MI 16.867147418 0.09695867 1.5024287 28.0365042 5.4945277
## TA 12.474556751 18.79700813 0.1242270 7.5183306 0.7299920
## Tcorrpt 0.068447269 38.53613492 10.3641796 0.9247986 27.2688933
## Tchom 10.748419893 0.33593009 19.3230840 27.9893122 6.8660934
## IDF 17.242675450 4.87811286 0.3056236 8.1352257 11.3603506
## MVIH 4.896949754 0.13477475 45.8549525 7.8499336 16.9995139Visualisation de la Régression Linéaire
y <- donnees$MI
x <- donnees$IDF
# Diagramme de dispersion avec ligne de régression
plot(x, y, main = "Régression Linéaire",
xlab = "IDF",
ylab = "MI",
pch = 19, col = "blue")
abline(lm(y ~ x), col = "red", lwd = 2)
install.packages(“shiny”) install.packages(“rsconnect”)