Temperature
Wissal Fridhi GPD
Tuesday, May 03, 2016
RESUME
Ce projet porte sur l'étude des performances de la température dans plusieurs pays européens.Ainsi, on a recourt à une base de données décrivant une comparaison intrinsèque entre les températures mensuelles et annuelles au sein de 35 pays.
Ayant réalisé ume méthode statistique multivariée qui est l'ACP(Analyse en Composantes Principales) nous avons traité le jeu de données "Temperature"
INTRODUCTION
La temperature demeure un thème indispensable dans la vie de tous les humains partout dans le monde. Particulièrement et avec les changement climatiques qui s'imposent à notre planète, L'europe s'est beaucoup influencé par ces changement, c'est pourquoi Il serait intéressant d'analyser les etats de la température dans l'Europe en faisant une ACP en relation avec des facteurs intérieurs étroitement liés à ce sujet.
PROBLEMATIQUE
Faire une comparaison entre les performances de la température dans les pays d'Europe en se basant sur les mêmes données.
DESCRIPTION DES DONNEES
On dispose d'un jeu de données contenant 35 individus (23 individus actifs et 12 individus supplémentaires) et 17 variables dont 12 sont quantitatives(january,february,march,april,may,june,july,august,september,october,november,december), 4 sont quantitatives supplémentaires(annual, amplitude,latitude,longitude) et une seule est qualitative supplémentaire (Area).LOGICIELS UTILISES
R 3.2.2 et RStudio
/Importation du jeu de données /
data=read.csv("C:/Users/user/Desktop/temperature.csv",sep=";",header=TRUE,dec=".",row.names=1)
View (data)/ Description des données /
str(data)## 'data.frame': 35 obs. of 17 variables:
## $ January : num 2.9 9.1 -0.2 3.3 -1.1 -0.4 4.8 -5.8 -5.9 -3.7 ...
## $ February : num 2.5 9.7 0.1 3.3 0.8 -0.4 5 -6.2 -5 -2 ...
## $ March : num 5.7 11.7 4.4 6.7 5.5 1.3 5.9 -2.7 -0.3 1.9 ...
## $ April : num 8.2 15.4 8.2 8.9 11.6 5.8 7.8 3.1 7.4 7.9 ...
## $ May : num 12.5 20.1 13.8 12.8 17 11.1 10.4 10.2 14.3 13.2 ...
## $ June : num 14.8 24.5 16 15.6 20.2 15.4 13.3 14 17.8 16.9 ...
## $ July : num 17.1 27.4 18.3 17.8 22 17.1 15 17.2 19.4 18.4 ...
## $ August : num 17.1 27.2 18 17.8 21.3 16.6 14.6 14.9 18.5 17.6 ...
## $ September: num 14.5 23.8 14.4 15 16.9 13.3 12.7 9.7 13.7 13.7 ...
## $ October : num 11.4 19.2 10 11.1 11.3 8.8 9.7 5.2 7.5 8.6 ...
## $ November : num 7 14.6 4.2 6.7 5.1 4.1 6.7 0.1 1.2 2.6 ...
## $ December : num 4.4 11 1.2 4.4 0.7 1.3 5.4 -2.3 -3.6 -1.7 ...
## $ Annual : num 9.9 17.8 9.1 10.3 10.9 7.8 9.3 4.8 7.1 7.7 ...
## $ Amplitude: num 14.6 18.3 18.5 14.4 23.1 17.5 10.2 23.4 25.3 22.1 ...
## $ Latitude : num 52.2 37.6 52.3 50.5 47.3 55.4 53.2 60.1 50.3 50 ...
## $ Longitude: num 4.5 23.5 13.2 4.2 19 12.3 6.1 25 30.3 19.6 ...
## $ Area : Factor w/ 4 levels "East","North",..: 4 3 4 4 1 2 2 2 1 1 ...summary(data)## January February March April
## Min. :-9.300 Min. :-7.900 Min. :-3.700 Min. : 2.900
## 1st Qu.:-1.550 1st Qu.:-0.150 1st Qu.: 1.600 1st Qu.: 7.250
## Median : 0.200 Median : 1.900 Median : 5.400 Median : 8.900
## Mean : 1.346 Mean : 2.217 Mean : 5.229 Mean : 9.283
## 3rd Qu.: 4.900 3rd Qu.: 5.800 3rd Qu.: 8.500 3rd Qu.:12.050
## Max. :10.700 Max. :11.800 Max. :14.100 Max. :16.900
## May June July August
## Min. : 6.50 Min. : 9.30 Min. :11.10 Min. :10.60
## 1st Qu.:12.15 1st Qu.:15.40 1st Qu.:17.30 1st Qu.:16.65
## Median :13.80 Median :16.90 Median :18.90 Median :18.30
## Mean :13.91 Mean :17.41 Mean :19.62 Mean :18.98
## 3rd Qu.:16.35 3rd Qu.:19.80 3rd Qu.:21.75 3rd Qu.:21.60
## Max. :20.90 Max. :24.50 Max. :27.40 Max. :27.20
## September October November December
## Min. : 7.90 Min. : 4.50 Min. :-1.100 Min. :-6.00
## 1st Qu.:13.00 1st Qu.: 8.65 1st Qu.: 3.200 1st Qu.: 0.25
## Median :14.80 Median :10.20 Median : 5.100 Median : 1.70
## Mean :15.63 Mean :11.00 Mean : 6.066 Mean : 2.88
## 3rd Qu.:18.25 3rd Qu.:13.30 3rd Qu.: 7.900 3rd Qu.: 5.40
## Max. :24.30 Max. :19.40 Max. :14.900 Max. :12.00
## Annual Amplitude Latitude Longitude
## Min. : 4.50 Min. :10.20 Min. :37.20 Min. : 0.00
## 1st Qu.: 7.75 1st Qu.:14.90 1st Qu.:43.90 1st Qu.: 5.05
## Median : 9.70 Median :18.50 Median :50.00 Median :10.50
## Mean :10.27 Mean :18.32 Mean :49.04 Mean :13.01
## 3rd Qu.:12.65 3rd Qu.:21.45 3rd Qu.:53.35 3rd Qu.:19.30
## Max. :18.20 Max. :27.60 Max. :64.10 Max. :37.60
## Area
## East : 8
## North: 8
## South:10
## West : 9
##
## / Réalisation de l’ACP /
library(FactoMineR)
res.pca=PCA(data,ncp=2,quanti.sup=13:16,quali.sup=17,ind.sup=24:35)
Interprétation du cercle de corrélation
La 1ere composante principale est prédominante car elle resume pour elle seule 82.90 % de l’inertie totale;
La 2eme composante est relativement importante résumant 15,4 de l’inertie totale;
Ces 2 composantes donnent 98,3 comme inertie totale.
toutes les variables actives sont du même coté que la 1ere composante, nous notons que les mois “septembre” “octobre” et “avril” sont plus étroitement liés avec cette composante que les autres variables et ils representent des temperatures annuelles élevées.
Par analogie avec le nuage des indiv les villes qui sont situés au sud et qui ont des coordonnées elevés sur la 1ere composante (res\(ind\)coord[,1] ) presentent les températures annuelles elevées sont donc des villes chaudes et donc de latitudes faibles.
L’apmlitude est fortement liée à la 2ème composante et les valeurs les plus elevées de cette mesure ont été observées pour des villes de l’Est et les valeurs les plus basses ont été observées pour les villes européennes de l’ouest et le nord.
La longitude est liée à cet axe mais la relation n’est pas forte avec une corrélation de 0,41
/Caractérisation des variables/
Il existe une corrélation positive entre les températures mensuelles et annuelles et plus précisément dans deux périodes importantes : la saison estivale et la saison hivernale.
Par analogie au graphe des individus on peut considérer deux typologies des villes : les villes du sud caractérisées par des températures mensuelles et annuelles elevées et des latitudes faibles, et les villes du nord froides avec des hautes latitudes.
res.pca$var## $coord
## Dim.1 Dim.2
## January 0.8424506 -0.53135762
## February 0.8842848 -0.45583250
## March 0.9450521 -0.28731281
## April 0.9738876 0.09956500
## May 0.8698517 0.45781159
## June 0.8333141 0.54532195
## July 0.8441626 0.50866195
## August 0.9092443 0.40192442
## September 0.9856254 0.15253617
## October 0.9916246 -0.08476471
## November 0.9523567 -0.28941418
## December 0.8731191 -0.47286559
##
## $cor
## Dim.1 Dim.2
## January 0.8424506 -0.53135762
## February 0.8842848 -0.45583250
## March 0.9450521 -0.28731281
## April 0.9738876 0.09956500
## May 0.8698517 0.45781159
## June 0.8333141 0.54532195
## July 0.8441626 0.50866195
## August 0.9092443 0.40192442
## September 0.9856254 0.15253617
## October 0.9916246 -0.08476471
## November 0.9523567 -0.28941418
## December 0.8731191 -0.47286559
##
## $cos2
## Dim.1 Dim.2
## January 0.7097230 0.282340915
## February 0.7819596 0.207783268
## March 0.8931235 0.082548649
## April 0.9484570 0.009913188
## May 0.7566419 0.209591455
## June 0.6944124 0.297376030
## July 0.7126106 0.258736979
## August 0.8267252 0.161543240
## September 0.9714575 0.023267284
## October 0.9833194 0.007185057
## November 0.9069833 0.083760565
## December 0.7623370 0.223601871
##
## $contrib
## Dim.1 Dim.2
## January 7.134508 15.2810946
## February 7.860668 11.2458224
## March 8.978146 4.4677680
## April 9.534387 0.5365300
## May 7.606161 11.3436865
## June 6.980597 16.0948378
## July 7.163535 14.0035823
## August 8.310674 8.7431803
## September 9.765600 1.2592917
## October 9.884842 0.3888757
## November 9.117472 4.5333604
## December 7.663411 12.1019702res.pca$var$cor## Dim.1 Dim.2
## January 0.8424506 -0.53135762
## February 0.8842848 -0.45583250
## March 0.9450521 -0.28731281
## April 0.9738876 0.09956500
## May 0.8698517 0.45781159
## June 0.8333141 0.54532195
## July 0.8441626 0.50866195
## August 0.9092443 0.40192442
## September 0.9856254 0.15253617
## October 0.9916246 -0.08476471
## November 0.9523567 -0.28941418
## December 0.8731191 -0.47286559library(factoextra)## Loading required package: ggplot2## Warning: package 'ggplot2' was built under R version 3.2.4## Loading required package: gridfviz_pca_ind(res.pca,habillage=17)
Inertie des composantes principales
round(res.pca$eig,3)## eigenvalue percentage of variance
## comp 1 9.948 82.898
## comp 2 1.848 15.397
## comp 3 0.126 1.052
## comp 4 0.038 0.319
## comp 5 0.017 0.139
## comp 6 0.013 0.107
## comp 7 0.006 0.049
## comp 8 0.002 0.017
## comp 9 0.001 0.009
## comp 10 0.001 0.008
## comp 11 0.001 0.004
## comp 12 0.000 0.001
## cumulative percentage of variance
## comp 1 82.898
## comp 2 98.295
## comp 3 99.347
## comp 4 99.666
## comp 5 99.805
## comp 6 99.912
## comp 7 99.961
## comp 8 99.978
## comp 9 99.986
## comp 10 99.994
## comp 11 99.999
## comp 12 100.000fviz_screeplot(res.pca)
Coordonnées, contribution, cos2 des individus
res.pca$ind## $coord
## Dim.1 Dim.2
## Amsterdam 0.22693852 -1.371378702
## Athens 7.60067204 0.930375742
## Berlin -0.28785832 0.016454075
## Brussels 0.63117358 -1.177217640
## Budapest 1.66802839 1.712697730
## Copenhagen -1.46239513 -0.492056307
## Dublin -0.50524137 -2.673496925
## Elsinki -4.03629712 0.462039367
## Kiev -1.71222008 2.007597607
## Krakow -1.25865727 0.874989077
## Lisbon 5.59928833 -1.554345838
## London 0.05764006 -1.573766723
## Madrid 4.06406743 0.697664862
## Minsk -3.23789748 1.391289730
## Moscow -3.46261171 2.182015808
## Oslo -3.30598698 0.310053024
## Paris 1.41971350 -0.897598545
## Prague -0.10900287 0.698041163
## Reykjavik -4.70406435 -2.957197699
## Rome 5.38200124 0.293698723
## Sarajevo 0.16345193 0.319489453
## Sofia 0.41781097 0.795074460
## Stockholm -3.14855331 0.005577557
##
## $cos2
## Dim.1 Dim.2
## Amsterdam 0.02474831 9.037408e-01
## Athens 0.97830645 1.465844e-02
## Berlin 0.32789958 1.071347e-03
## Brussels 0.21639751 7.527801e-01
## Budapest 0.46337591 4.885264e-01
## Copenhagen 0.80588015 9.123692e-02
## Dublin 0.03411320 9.551775e-01
## Elsinki 0.95654320 1.253419e-02
## Kiev 0.41732984 5.737380e-01
## Krakow 0.64509341 3.117546e-01
## Lisbon 0.92554429 7.132255e-02
## London 0.00131785 9.824220e-01
## Madrid 0.93424771 2.753176e-02
## Minsk 0.84071389 1.552234e-01
## Moscow 0.71081284 2.822692e-01
## Oslo 0.97838231 8.605543e-03
## Paris 0.69481859 2.777373e-01
## Prague 0.01987080 8.148950e-01
## Reykjavik 0.71527677 2.826756e-01
## Rome 0.99549987 2.964543e-03
## Sarajevo 0.07819664 2.987590e-01
## Sofia 0.18627345 6.745387e-01
## Stockholm 0.92423563 2.900338e-06
##
## $contrib
## Dim.1 Dim.2
## Amsterdam 0.022509389 4.425554e+00
## Athens 25.249412071 2.036899e+00
## Berlin 0.036216364 6.370885e-04
## Brussels 0.174118494 3.261117e+00
## Budapest 1.216057639 6.902625e+00
## Copenhagen 0.934709699 5.697475e-01
## Dublin 0.111569397 1.681947e+01
## Elsinki 7.120549993 5.023550e-01
## Kiev 1.281346111 9.484319e+00
## Krakow 0.692408290 1.801599e+00
## Lisbon 13.702914482 5.685231e+00
## London 0.001452098 5.828188e+00
## Madrid 7.218867870 1.145372e+00
## Minsk 4.582193987 4.554996e+00
## Moscow 5.240284554 1.120388e+01
## Oslo 4.776937527 2.262167e-01
## Paris 0.880944827 1.895907e+00
## Prague 0.005193057 1.146608e+00
## Reykjavik 9.671498999 2.057849e+01
## Rome 12.660033938 2.029817e-01
## Sarajevo 0.011676896 2.401960e-01
## Sofia 0.076296912 1.487539e+00
## Stockholm 4.332807405 7.320502e-05
##
## $dist
## Amsterdam Athens Berlin Brussels Budapest Copenhagen
## 1.4425652 7.6844809 0.5026994 1.3568214 2.4503985 1.6290316
## Dublin Elsinki Kiev Krakow Lisbon London
## 2.7355058 4.1269655 2.6504515 1.5670981 5.8201507 1.5877837
## Madrid Minsk Moscow Oslo Paris Prague
## 4.2046503 3.5313355 4.1070138 3.3423109 1.7031974 0.7732683
## Reykjavik Rome Sarajevo Sofia Stockholm
## 5.5620667 5.3941521 0.5845155 0.9680646 3.2750633res.pca$ind.sup## $coord
## Dim.1 Dim.2
## Antwerp 0.5892648 -1.16201065
## Barcelona 5.9892460 -0.38329986
## Bordeaux 2.8501570 -0.73131707
## Edinburgh -1.2889857 -2.34463780
## Frankfurt 0.3890032 0.15364874
## Geneva 0.3248580 0.17052566
## Genoa 5.8482798 -0.12707972
## Milan 3.1561321 1.55567808
## Palermo 7.2922522 -0.20543700
## Seville 7.8644835 0.25777733
## St. Petersburg -4.0229276 1.58587572
## Zurich -0.6082877 -0.05761394
##
## $cos2
## Dim.1 Dim.2
## Antwerp 0.1954400 0.7599985442
## Barcelona 0.9938250 0.0040704547
## Bordeaux 0.9233629 0.0607919740
## Edinburgh 0.2296285 0.7597680759
## Frankfurt 0.3296074 0.0514219671
## Geneva 0.3639175 0.1002755755
## Genoa 0.9933376 0.0004690218
## Milan 0.7906782 0.1921006780
## Palermo 0.9689404 0.0007690083
## Seville 0.9975864 0.0010717650
## St. Petersburg 0.8295199 0.1289082379
## Zurich 0.6401597 0.0057428226
##
## $dist
## Antwerp Barcelona Bordeaux Edinburgh
## 1.3329189 6.0078239 2.9660781 2.6898945
## Frankfurt Geneva Genoa Milan
## 0.6775708 0.5385080 5.8678595 3.5494028
## Palermo Seville St. Petersburg Zurich
## 7.4082076 7.8739915 4.4170144 0.7602648res.pca$ind$coord## Dim.1 Dim.2
## Amsterdam 0.22693852 -1.371378702
## Athens 7.60067204 0.930375742
## Berlin -0.28785832 0.016454075
## Brussels 0.63117358 -1.177217640
## Budapest 1.66802839 1.712697730
## Copenhagen -1.46239513 -0.492056307
## Dublin -0.50524137 -2.673496925
## Elsinki -4.03629712 0.462039367
## Kiev -1.71222008 2.007597607
## Krakow -1.25865727 0.874989077
## Lisbon 5.59928833 -1.554345838
## London 0.05764006 -1.573766723
## Madrid 4.06406743 0.697664862
## Minsk -3.23789748 1.391289730
## Moscow -3.46261171 2.182015808
## Oslo -3.30598698 0.310053024
## Paris 1.41971350 -0.897598545
## Prague -0.10900287 0.698041163
## Reykjavik -4.70406435 -2.957197699
## Rome 5.38200124 0.293698723
## Sarajevo 0.16345193 0.319489453
## Sofia 0.41781097 0.795074460
## Stockholm -3.14855331 0.005577557sort(round(res.pca$ind$contrib[,1],3))## London Prague Sarajevo Amsterdam Berlin Sofia
## 0.001 0.005 0.012 0.023 0.036 0.076
## Dublin Brussels Krakow Paris Copenhagen Budapest
## 0.112 0.174 0.692 0.881 0.935 1.216
## Kiev Stockholm Minsk Oslo Moscow Elsinki
## 1.281 4.333 4.582 4.777 5.240 7.121
## Madrid Reykjavik Rome Lisbon Athens
## 7.219 9.671 12.660 13.703 25.249sort(round(res.pca$ind$contrib[,2],3))## Stockholm Berlin Rome Oslo Sarajevo Elsinki
## 0.000 0.001 0.203 0.226 0.240 0.502
## Copenhagen Madrid Prague Sofia Krakow Paris
## 0.570 1.145 1.147 1.488 1.802 1.896
## Athens Brussels Amsterdam Minsk Lisbon London
## 2.037 3.261 4.426 4.555 5.685 5.828
## Budapest Kiev Moscow Dublin Reykjavik
## 6.903 9.484 11.204 16.819 20.578sort(res.pca$ind$cos2)## [1] 2.900338e-06 1.071347e-03 1.317850e-03 2.964543e-03 8.605543e-03
## [6] 1.253419e-02 1.465844e-02 1.987080e-02 2.474831e-02 2.753176e-02
## [11] 3.411320e-02 7.132255e-02 7.819664e-02 9.123692e-02 1.552234e-01
## [16] 1.862735e-01 2.163975e-01 2.777373e-01 2.822692e-01 2.826756e-01
## [21] 2.987590e-01 3.117546e-01 3.278996e-01 4.173298e-01 4.633759e-01
## [26] 4.885264e-01 5.737380e-01 6.450934e-01 6.745387e-01 6.948186e-01
## [31] 7.108128e-01 7.152768e-01 7.527801e-01 8.058802e-01 8.148950e-01
## [36] 8.407139e-01 9.037408e-01 9.242356e-01 9.255443e-01 9.342477e-01
## [41] 9.551775e-01 9.565432e-01 9.783065e-01 9.783823e-01 9.824220e-01
## [46] 9.954999e-01fviz_pca_contrib(res.pca, choice = "ind" , axes = 1)## Warning in fviz_pca_contrib(res.pca, choice = "ind", axes = 1): The
## function fviz_pca_contrib() is deprecated. Please use the function
## fviz_contrib() which can handle outputs of PCA, CA and MCA functions.
fviz_pca_contrib(res.pca, choice = "ind" , axes = 2)## Warning in fviz_pca_contrib(res.pca, choice = "ind", axes = 2): The
## function fviz_pca_contrib() is deprecated. Please use the function
## fviz_contrib() which can handle outputs of PCA, CA and MCA functions.
fviz_cos2(res.pca)## Warning in if (!element %in% c("row", "col", "var", "ind", "quanti.var", :
## the condition has length > 1 and only the first element will be used
res.pca$var$coord[1:23]## [1] 0.84245060 0.88428481 0.94505214 0.97388757 0.86985167
## [6] 0.83331408 0.84416264 0.90924428 0.98562545 0.99162463
## [11] 0.95235673 0.87311910 -0.53135762 -0.45583250 -0.28731281
## [16] 0.09956500 0.45781159 0.54532195 0.50866195 0.40192442
## [21] 0.15253617 -0.08476471 -0.28941418res.pca$var$cor## Dim.1 Dim.2
## January 0.8424506 -0.53135762
## February 0.8842848 -0.45583250
## March 0.9450521 -0.28731281
## April 0.9738876 0.09956500
## May 0.8698517 0.45781159
## June 0.8333141 0.54532195
## July 0.8441626 0.50866195
## August 0.9092443 0.40192442
## September 0.9856254 0.15253617
## October 0.9916246 -0.08476471
## November 0.9523567 -0.28941418
## December 0.8731191 -0.47286559names(which.max(res.pca$var$cor[,1]))## [1] "October"La variable “October” est la plus corrélée avec le premier axe ( une corrélation de 0.991)
names(which.max(res.pca$var$cor[,2])) ## [1] "June"La variable “June” est la plus corrélée avec le 2ème axe ( une corrélation de 0.545)
res.pca$quanti.sup## $coord
## Dim.1 Dim.2
## Annual 0.9975483 -0.06845254
## Amplitude -0.3140756 0.94441398
## Latitude -0.9099106 -0.21543731
## Longitude -0.3644584 0.64497259
##
## $cor
## Dim.1 Dim.2
## Annual 0.9975483 -0.06845254
## Amplitude -0.3140756 0.94441398
## Latitude -0.9099106 -0.21543731
## Longitude -0.3644584 0.64497259
##
## $cos2
## Dim.1 Dim.2
## Annual 0.99510271 0.00468575
## Amplitude 0.09864347 0.89191777
## Latitude 0.82793735 0.04641323
## Longitude 0.13282993 0.41598964res.pca$quali.sup## $coord
## Dim.1 Dim.2
## East -1.0992214 1.3802437
## North -2.4435569 -0.9884068
## South 4.5618962 0.1373766
## West 0.4974918 -0.8574352
##
## $cos2
## Dim.1 Dim.2
## East 0.3797241 0.5987000663
## North 0.8499535 0.1390662460
## South 0.9981689 0.0009051878
## West 0.2323311 0.6901414045
##
## $v.test
## Dim.1 Dim.2
## East -1.0812425 3.1502604
## North -2.4035900 -2.2559342
## South 3.5755516 0.2498407
## West 0.3394596 -1.3575510
##
## $dist
## East North South West
## 1.783820 2.650482 4.566079 1.032125
##
## $eta2
## Dim 1 Dim 2
## Area 0.6787608 0.5461533/Effectuer un habillage selon la variable catégorielle : Area/
plot(res.pca,choix='ind',habillage=17,cex=0.7)
/Realiser un biplot/
library(ade4)## Warning: package 'ade4' was built under R version 3.2.3##
## Attaching package: 'ade4'
##
## The following object is masked from 'package:FactoMineR':
##
## reconstXpca=dudi.pca(data[,-c(17)],scannf=F,scale=T,nf=2)
biplot(Xpca)
/Extraire les coordonnées des individus sur dim 1 et dim2 ( nommer respectivement PC1 et PC2)/
PC1 <- res.pca$ind$coord[,1]
PC2 <- res.pca$ind$coord[,2]/Créer dataframe nommée PCs qui fait concaténer PC1 et PC2/
labs <- rownames(res.pca$ind$coord)
PCs <- data.frame(cbind(PC1,PC2))
rownames(PCs) <- rownames(res.pca$ind$coord)attach(data)
colnames(data)## [1] "January" "February" "March" "April" "May"
## [6] "June" "July" "August" "September" "October"
## [11] "November" "December" "Annual" "Amplitude" "Latitude"
## [16] "Longitude" "Area"/Nuage de points/
library(ggplot2)
p1<-ggplot(PCs,aes(PC1,PC2,label=rownames(PCs)))+geom_point()
p1
p2<-ggplot(PCs,aes(x=PC1,y=PC2,label=rownames(PCs)))+geom_point()
p2
cPC1 <- res.pca$quali.sup$coord[,1]
cPC2 <- res.pca$quali.sup$coord[,2]
clabs <- rownames(res.pca$quali.sup$coord)
cPCs <- data.frame(cbind(cPC1,cPC2))
rownames(cPCs) <- clabs
colnames(cPCs) <- colnames(PCs)p <- ggplot() + theme_bw(base_size = 20)
p
p <- p + geom_text(data=PCs, aes(x=PC1,y=PC2,label=rownames(PCs)), size=4)
p
vPC1 <- res.pca$var$coord[,1]
vPC2 <- res.pca$var$coord[,2]
vlabs <- rownames(res.pca$var$coord)
vPCs <- data.frame(cbind(vPC1,vPC2))
rownames(vPCs) <- vlabs
colnames(vPCs) <- colnames(PCs)
angle <- seq(-pi, pi, length = 50)
angle## [1] -3.14159265 -3.01336438 -2.88513611 -2.75690784 -2.62867957
## [6] -2.50045130 -2.37222302 -2.24399475 -2.11576648 -1.98753821
## [11] -1.85930994 -1.73108167 -1.60285339 -1.47462512 -1.34639685
## [16] -1.21816858 -1.08994031 -0.96171204 -0.83348377 -0.70525549
## [21] -0.57702722 -0.44879895 -0.32057068 -0.19234241 -0.06411414
## [26] 0.06411414 0.19234241 0.32057068 0.44879895 0.57702722
## [31] 0.70525549 0.83348377 0.96171204 1.08994031 1.21816858
## [36] 1.34639685 1.47462512 1.60285339 1.73108167 1.85930994
## [41] 1.98753821 2.11576648 2.24399475 2.37222302 2.50045130
## [46] 2.62867957 2.75690784 2.88513611 3.01336438 3.14159265df <- data.frame(x = sin(angle), y = cos(angle))
df## x y
## 1 -1.224606e-16 -1.00000000
## 2 -1.278772e-01 -0.99179001
## 3 -2.536546e-01 -0.96729486
## 4 -3.752670e-01 -0.92691676
## 5 -4.907176e-01 -0.87131870
## 6 -5.981105e-01 -0.80141362
## 7 -6.956826e-01 -0.71834935
## 8 -7.818315e-01 -0.62348980
## 9 -8.551428e-01 -0.51839257
## 10 -9.144126e-01 -0.40478334
## 11 -9.586679e-01 -0.28452759
## 12 -9.871818e-01 -0.15959990
## 13 -9.994862e-01 -0.03205158
## 14 -9.953791e-01 0.09602303
## 15 -9.749279e-01 0.22252093
## 16 -9.384684e-01 0.34536505
## 17 -8.865993e-01 0.46253829
## 18 -8.201723e-01 0.57211666
## 19 -7.402780e-01 0.67230089
## 20 -6.482284e-01 0.76144596
## 21 -5.455349e-01 0.83808810
## 22 -4.338837e-01 0.90096887
## 23 -3.151082e-01 0.94905575
## 24 -1.911586e-01 0.98155916
## 25 -6.407022e-02 0.99794539
## 26 6.407022e-02 0.99794539
## 27 1.911586e-01 0.98155916
## 28 3.151082e-01 0.94905575
## 29 4.338837e-01 0.90096887
## 30 5.455349e-01 0.83808810
## 31 6.482284e-01 0.76144596
## 32 7.402780e-01 0.67230089
## 33 8.201723e-01 0.57211666
## 34 8.865993e-01 0.46253829
## 35 9.384684e-01 0.34536505
## 36 9.749279e-01 0.22252093
## 37 9.953791e-01 0.09602303
## 38 9.994862e-01 -0.03205158
## 39 9.871818e-01 -0.15959990
## 40 9.586679e-01 -0.28452759
## 41 9.144126e-01 -0.40478334
## 42 8.551428e-01 -0.51839257
## 43 7.818315e-01 -0.62348980
## 44 6.956826e-01 -0.71834935
## 45 5.981105e-01 -0.80141362
## 46 4.907176e-01 -0.87131870
## 47 3.752670e-01 -0.92691676
## 48 2.536546e-01 -0.96729486
## 49 1.278772e-01 -0.99179001
## 50 1.224606e-16 -1.00000000pv <- ggplot() + theme_bw(base_size = 20)
pv
pv <- pv + geom_path(aes(x, y), data = df, colour="grey70")
pv
pv <- pv + geom_text(data=vPCs, aes(x=vPC1,y=vPC2,label=rownames(vPCs)), size=4) + xlab("PC1") + ylab("PC2")
pv
pv <- pv + geom_segment(data=vPCs, aes(x = 0, y = 0, xend = vPC1*0.9, yend = vPC2*0.9), arrow = arrow(length = unit(1/2, 'picas')), color = "grey30")
pv
library(gridExtra)## Warning: package 'gridExtra' was built under R version 3.2.4grid.arrange(p,pv,nrow=1)
CONCLUSION
En effectuant la méthode de l'ACP , on a réussi à réduire l'information sur les changementS du températures à partir de 35 individus et 17 variables en deux dimensions avec une précision de 98.3% de l'information totale.