class: center, middle, inverse, title-slide # Bases du modèle linéaire ## Chapitre VI - Analyse en composantes principales ### Antoine Bichat - Émilie Lebarbier<br>AgroParisTech --- # Chargement des données ```r budget <- read.table("Etat.don", row.names = 1, sep = "") colnames(budget) <- c("PVP", "AGR", "CMI", "TRA", "LOG", "EDU", "ACS", "ANC", "DEF", "DET", "DIV") head(budget) ``` ``` PVP AGR CMI TRA LOG EDU ACS ANC DEF DET DIV 1872 18.0 0.5 0.1 6.7 0.5 2.1 2.0 0 26.4 41.5 2.1 1880 14.1 0.8 0.1 15.3 1.9 3.7 0.5 0 29.8 31.3 2.5 1890 13.6 0.7 0.7 6.8 0.6 7.1 0.7 0 33.8 34.4 1.7 1900 14.3 1.7 1.7 6.9 1.2 7.4 0.8 0 37.7 26.2 2.2 1903 10.3 1.5 0.4 9.3 0.6 8.5 0.9 0 38.4 27.2 3.0 1906 13.4 1.4 0.5 8.1 0.7 8.6 1.8 0 38.5 25.3 1.9 ``` ```r str(budget) ``` ``` 'data.frame': 24 obs. of 11 variables: $ PVP: num 18 14.1 13.6 14.3 10.3 13.4 13.5 12.9 12.3 7.6 ... $ AGR: num 0.5 0.8 0.7 1.7 1.5 1.4 1.1 1.4 0.3 1.2 ... $ CMI: num 0.1 0.1 0.7 1.7 0.4 0.5 0.5 0.3 0.1 3.2 ... $ TRA: num 6.7 15.3 6.8 6.9 9.3 8.1 9 9.4 11.9 5.1 ... $ LOG: num 0.5 1.9 0.6 1.2 0.6 0.7 0.6 0.6 2.4 0.6 ... $ EDU: num 2.1 3.7 7.1 7.4 8.5 8.6 9 9.3 3.7 5.6 ... $ ACS: num 2 0.5 0.7 0.8 0.9 1.8 3.4 4.3 1.7 1.8 ... $ ANC: num 0 0 0 0 0 0 0 0 1.9 10 ... $ DEF: num 26.4 29.8 33.8 37.7 38.4 38.5 36.8 41.1 42.4 29 ... $ DET: num 41.5 31.3 34.4 26.2 27.2 25.3 23.5 19.4 23.1 35 ... $ DIV: num 2.1 2.5 1.7 2.2 3 1.9 2.6 1.3 0.2 0.9 ... ``` --- # Étude descriptive simple ```r Moyenne <- apply(budget, 2, mean) EcartType <- apply(budget, 2, sd) data.frame(Moyenne, EcartType) ``` ``` Moyenne EcartType PVP 12.212500 2.238267 AGR 1.995833 1.681221 CMI 3.941667 4.585603 TRA 8.320833 2.520866 LOG 3.958333 4.271841 EDU 9.941667 5.335600 ACS 4.816667 3.482087 ANC 4.275000 4.244203 DEF 30.258333 7.466733 DET 19.141667 12.455972 DIV 1.183333 1.047841 ``` --- # Corrélations ```r cor(budget) ``` ``` PVP AGR CMI TRA LOG PVP 1.0000000000 -0.08456147 -0.0003918372 0.23274025 0.03561605 AGR -0.0845614667 1.00000000 0.6001369948 -0.27583846 0.43573158 CMI -0.0003918372 0.60013699 1.0000000000 0.09297364 0.89103331 TRA 0.2327402544 -0.27583846 0.0929736369 1.00000000 0.16610414 LOG 0.0356160473 0.43573158 0.8910333053 0.16610414 1.00000000 EDU -0.1500396685 0.73132063 0.4670513945 -0.21315407 0.23236075 ACS -0.1314025825 0.80568293 0.6211906273 -0.20307154 0.48776783 ANC -0.6869011667 0.04428292 0.0225073627 -0.31322317 0.04471192 DEF 0.1010501404 -0.44836614 -0.5363480862 0.15797549 -0.37856133 DET 0.0335563384 -0.69491720 -0.8042078286 -0.14834035 -0.75803796 DIV 0.1493242957 -0.27720187 -0.3480384333 0.11436882 -0.43793515 EDU ACS ANC DEF DET DIV PVP -0.1500397 -0.1314026 -0.68690117 0.10105014 0.03355634 0.14932430 AGR 0.7313206 0.8056829 0.04428292 -0.44836614 -0.69491720 -0.27720187 CMI 0.4670514 0.6211906 0.02250736 -0.53634809 -0.80420783 -0.34803843 TRA -0.2131541 -0.2030715 -0.31322317 0.15797549 -0.14834035 0.11436882 LOG 0.2323607 0.4877678 0.04471192 -0.37856133 -0.75803796 -0.43793515 EDU 1.0000000 0.8749779 0.15696654 -0.52405752 -0.67024982 -0.24864596 ACS 0.8749779 1.0000000 0.28819417 -0.56715016 -0.80819753 -0.52959488 ANC 0.1569665 0.2881942 1.00000000 -0.41685323 -0.04936630 -0.37746819 DEF -0.5240575 -0.5671502 -0.41685323 1.00000000 0.26163585 0.02041298 DET -0.6702498 -0.8081975 -0.04936630 0.26163585 1.00000000 0.55393211 DIV -0.2486460 -0.5295949 -0.37746819 0.02041298 0.55393211 1.00000000 ``` --- # Analyse descriptive _tidy_ ```r library(tidyverse) budget_tidy <- budget %>% rownames_to_column(var = "Année") %>% mutate(Année = as.numeric(Année)) %>% gather(key = "Poste", value = "Pourcentage", -Année) budget_tidy ``` ``` Année Poste Pourcentage 1 1872 PVP 18.0 2 1880 PVP 14.1 3 1890 PVP 13.6 4 1900 PVP 14.3 5 1903 PVP 10.3 6 1906 PVP 13.4 7 1909 PVP 13.5 8 1912 PVP 12.9 9 1920 PVP 12.3 10 1923 PVP 7.6 11 1926 PVP 10.5 12 1929 PVP 10.0 13 1932 PVP 10.6 14 1935 PVP 8.8 15 1938 PVP 10.1 16 1947 PVP 15.6 17 1950 PVP 11.2 18 1953 PVP 12.9 19 1956 PVP 10.9 20 1959 PVP 13.1 21 1962 PVP 12.8 22 1965 PVP 12.4 23 1968 PVP 11.4 24 1971 PVP 12.8 25 1872 AGR 0.5 26 1880 AGR 0.8 27 1890 AGR 0.7 28 1900 AGR 1.7 29 1903 AGR 1.5 30 1906 AGR 1.4 31 1909 AGR 1.1 32 1912 AGR 1.4 33 1920 AGR 0.3 34 1923 AGR 1.2 35 1926 AGR 0.3 36 1929 AGR 0.6 37 1932 AGR 0.8 38 1935 AGR 2.6 39 1938 AGR 1.1 40 1947 AGR 1.6 41 1950 AGR 1.3 42 1953 AGR 1.5 43 1956 AGR 5.3 44 1959 AGR 4.4 45 1962 AGR 4.7 46 1965 AGR 4.3 47 1968 AGR 6.0 48 1971 AGR 2.8 49 1872 CMI 0.1 50 1880 CMI 0.1 51 1890 CMI 0.7 52 1900 CMI 1.7 53 1903 CMI 0.4 54 1906 CMI 0.5 55 1909 CMI 0.5 56 1912 CMI 0.3 57 1920 CMI 0.1 58 1923 CMI 3.2 59 1926 CMI 0.4 60 1929 CMI 0.6 61 1932 CMI 0.3 62 1935 CMI 1.4 63 1938 CMI 1.2 64 1947 CMI 10.1 65 1950 CMI 16.5 66 1953 CMI 7.0 67 1956 CMI 9.7 68 1959 CMI 7.3 69 1962 CMI 7.5 70 1965 CMI 8.4 71 1968 CMI 9.5 72 1971 CMI 7.1 73 1872 TRA 6.7 74 1880 TRA 15.3 75 1890 TRA 6.8 76 1900 TRA 6.9 77 1903 TRA 9.3 78 1906 TRA 8.1 79 1909 TRA 9.0 80 1912 TRA 9.4 81 1920 TRA 11.9 82 1923 TRA 5.1 83 1926 TRA 4.5 84 1929 TRA 9.0 85 1932 TRA 8.9 86 1935 TRA 7.8 87 1938 TRA 5.9 88 1947 TRA 11.4 89 1950 TRA 12.4 90 1953 TRA 7.9 91 1956 TRA 7.6 92 1959 TRA 5.7 93 1962 TRA 6.6 94 1965 TRA 9.1 95 1968 TRA 5.9 96 1971 TRA 8.5 97 1872 LOG 0.5 98 1880 LOG 1.9 99 1890 LOG 0.6 100 1900 LOG 1.2 101 1903 LOG 0.6 102 1906 LOG 0.7 103 1909 LOG 0.6 104 1912 LOG 0.6 105 1920 LOG 2.4 106 1923 LOG 0.6 107 1926 LOG 1.8 108 1929 LOG 1.0 109 1932 LOG 3.0 110 1935 LOG 1.4 111 1938 LOG 1.4 112 1947 LOG 7.6 113 1950 LOG 15.8 114 1953 LOG 12.1 115 1956 LOG 9.6 116 1959 LOG 9.8 117 1962 LOG 6.8 118 1965 LOG 6.0 119 1968 LOG 5.0 120 1971 LOG 4.0 121 1872 EDU 2.1 122 1880 EDU 3.7 123 1890 EDU 7.1 124 1900 EDU 7.4 125 1903 EDU 8.5 126 1906 EDU 8.6 127 1909 EDU 9.0 128 1912 EDU 9.3 129 1920 EDU 3.7 130 1923 EDU 5.6 131 1926 EDU 6.6 132 1929 EDU 8.1 133 1932 EDU 10.0 134 1935 EDU 12.4 135 1938 EDU 9.5 136 1947 EDU 8.8 137 1950 EDU 8.1 138 1953 EDU 8.1 139 1956 EDU 9.4 140 1959 EDU 12.5 141 1962 EDU 15.7 142 1965 EDU 19.5 143 1968 EDU 21.1 144 1971 EDU 23.8 145 1872 ACS 2.0 146 1880 ACS 0.5 147 1890 ACS 0.7 148 1900 ACS 0.8 149 1903 ACS 0.9 150 1906 ACS 1.8 151 1909 ACS 3.4 152 1912 ACS 4.3 153 1920 ACS 1.7 154 1923 ACS 1.8 155 1926 ACS 2.1 156 1929 ACS 3.2 157 1932 ACS 6.4 158 1935 ACS 6.2 159 1938 ACS 6.0 160 1947 ACS 4.8 161 1950 ACS 4.9 162 1953 ACS 5.3 163 1956 ACS 8.5 164 1959 ACS 8.0 165 1962 ACS 9.7 166 1965 ACS 10.6 167 1968 ACS 10.7 168 1971 ACS 11.3 169 1872 ANC 0.0 170 1880 ANC 0.0 171 1890 ANC 0.0 172 1900 ANC 0.0 173 1903 ANC 0.0 174 1906 ANC 0.0 175 1909 ANC 0.0 176 1912 ANC 0.0 177 1920 ANC 1.9 178 1923 ANC 10.0 179 1926 ANC 10.1 180 1929 ANC 11.8 181 1932 ANC 13.4 182 1935 ANC 11.3 183 1938 ANC 5.9 184 1947 ANC 3.4 185 1950 ANC 3.4 186 1953 ANC 3.9 187 1956 ANC 4.6 188 1959 ANC 5.0 189 1962 ANC 5.3 190 1965 ANC 4.7 191 1968 ANC 4.2 192 1971 ANC 3.7 193 1872 DEF 26.4 194 1880 DEF 29.8 195 1890 DEF 33.8 196 1900 DEF 37.7 197 1903 DEF 38.4 198 1906 DEF 38.5 199 1909 DEF 36.8 200 1912 DEF 41.1 201 1920 DEF 42.4 202 1923 DEF 29.0 203 1926 DEF 19.9 204 1929 DEF 28.0 205 1932 DEF 27.4 206 1935 DEF 29.3 207 1938 DEF 40.7 208 1947 DEF 32.2 209 1950 DEF 20.7 210 1953 DEF 36.1 211 1956 DEF 28.2 212 1959 DEF 26.7 213 1962 DEF 24.5 214 1965 DEF 19.8 215 1968 DEF 20.0 216 1971 DEF 18.8 217 1872 DET 41.5 218 1880 DET 31.3 219 1890 DET 34.4 220 1900 DET 26.2 221 1903 DET 27.2 222 1906 DET 25.3 223 1909 DET 23.5 224 1912 DET 19.4 225 1920 DET 23.1 226 1923 DET 35.0 227 1926 DET 41.6 228 1929 DET 25.8 229 1932 DET 19.2 230 1935 DET 18.5 231 1938 DET 18.2 232 1947 DET 4.6 233 1950 DET 4.2 234 1953 DET 5.2 235 1956 DET 6.2 236 1959 DET 7.5 237 1962 DET 6.4 238 1965 DET 3.5 239 1968 DET 4.4 240 1971 DET 7.2 241 1872 DIV 2.1 242 1880 DIV 2.5 243 1890 DIV 1.7 244 1900 DIV 2.2 245 1903 DIV 3.0 246 1906 DIV 1.9 247 1909 DIV 2.6 248 1912 DIV 1.3 249 1920 DIV 0.2 250 1923 DIV 0.9 251 1926 DIV 2.3 252 1929 DIV 2.0 253 1932 DIV 0.0 254 1935 DIV 0.4 255 1938 DIV 0.0 256 1947 DIV 0.0 257 1950 DIV 1.5 258 1953 DIV 0.0 259 1956 DIV 0.0 260 1959 DIV 0.0 261 1962 DIV 0.1 262 1965 DIV 1.8 263 1968 DIV 1.9 264 1971 DIV 0.0 ``` --- ```r budget_tidy %>% group_by(Poste) %>% summarise(Min = min(Pourcentage), Moyenne = mean(Pourcentage), Max = max(Pourcentage), `Écart-type` = sd(Pourcentage)) ``` ``` # A tibble: 11 x 5 Poste Min Moyenne Max `Écart-type` <chr> <dbl> <dbl> <dbl> <dbl> 1 ACS 0.5 4.82 11.3 3.48 2 AGR 0.3 2.00 6 1.68 3 ANC 0 4.28 13.4 4.24 4 CMI 0.1 3.94 16.5 4.59 5 DEF 18.8 30.3 42.4 7.47 6 DET 3.5 19.1 41.6 12.5 7 DIV 0 1.18 3 1.05 8 EDU 2.1 9.94 23.8 5.34 9 LOG 0.5 3.96 15.8 4.27 10 PVP 7.6 12.2 18 2.24 11 TRA 4.5 8.32 15.3 2.52 ``` --- ```r budget_tidy %>% group_by(Année) %>% summarise(Total = sum(Pourcentage)) ``` ``` # A tibble: 24 x 2 Année Total <dbl> <dbl> 1 1872 99.9 2 1880 100 3 1890 100. 4 1900 100. 5 1903 100. 6 1906 100. 7 1909 100 8 1912 100 9 1920 100 10 1923 100 # … with 14 more rows ``` --- # Boîtes à moustaches ```r ggplot(budget_tidy) + aes(x = Poste, y = Pourcentage, fill = Poste) + geom_boxplot() + scale_fill_viridis_d() + theme_minimal() + theme(legend.position = "none") ``` <img src="chap6_files/figure-html/boxplot-1.png" width="720" style="display: block; margin: auto;" /> --- # Série temporelle ```r ggplot(budget_tidy) + aes(x = Année, y = Pourcentage, color = Poste) + geom_line(aes(linetype = Poste, group = Poste)) + scale_color_viridis_d() + scale_x_continuous(breaks = seq(1870, 1975, 5)) + theme_minimal() ``` <img src="chap6_files/figure-html/textplot-1.png" width="720" style="display: block; margin: auto;" /> --- # Analyse en composantes principales ```r library(FactoMineR) par(mfrow = c(1, 2)) res_acp <- PCA(budget, scale.unit = TRUE, ncp = 11) ``` <img src="chap6_files/figure-html/acp-1.png" width="792" style="display: block; margin: auto;" /> --- # Valeurs propres ```r round(res_acp$eig, 4) ``` ``` eigenvalue percentage of variance comp 1 4.9724 45.2033 comp 2 2.0506 18.6422 comp 3 1.2902 11.7288 comp 4 0.9931 9.0278 comp 5 0.7084 6.4396 comp 6 0.5581 5.0741 comp 7 0.2043 1.8568 comp 8 0.1252 1.1382 comp 9 0.0628 0.5710 comp 10 0.0350 0.3182 comp 11 0.0000 0.0000 cumulative percentage of variance comp 1 45.2033 comp 2 63.8455 comp 3 75.5743 comp 4 84.6020 comp 5 91.0416 comp 6 96.1157 comp 7 97.9726 comp 8 99.1108 comp 9 99.6818 comp 10 100.0000 comp 11 100.0000 ``` --- # Scree plot ```r barplot(res_acp$eig[, 1]) ``` <img src="chap6_files/figure-html/screeplot-1.png" width="720" style="display: block; margin: auto;" /> --- # Coordonnées des anciennes variables ```r res_acp$var$coord[, 1:3] ``` ``` Dim.1 Dim.2 Dim.3 PVP -0.1733014 0.739752960 0.3417977 AGR 0.8184263 0.005456946 0.3666890 CMI 0.8330641 0.341250794 -0.1415737 TRA -0.1369586 0.630760525 -0.3756538 LOG 0.7216397 0.397737441 -0.3849194 EDU 0.7867728 -0.136952321 0.4248170 ACS 0.9332323 -0.100841264 0.1663739 ANC 0.2889227 -0.807313867 -0.3750564 DEF -0.6122032 0.216338862 -0.2595352 DET -0.8888848 -0.301344901 0.1603550 DIV -0.5483342 0.112143846 0.5363494 ``` --- # Contributions des anciennes variables ```r res_acp$var$contrib[, 1:3] ``` ``` Dim.1 Dim.2 Dim.3 PVP 0.6040060 26.686053774 9.055070 AGR 13.4708947 0.001452146 10.421958 CMI 13.9570659 5.678822239 1.553527 TRA 0.3772386 19.401707169 10.937781 LOG 10.4731694 7.714430711 11.484003 EDU 12.4490430 0.914639027 13.988056 ACS 17.5152669 0.495892444 2.145479 ANC 1.6788062 31.783063684 10.903019 DEF 7.5375205 2.282338278 5.220911 DET 15.8901574 4.428316253 1.993052 DIV 6.0468314 0.613284274 22.297143 ``` ```r colSums(res_acp$var$contrib[, 1:3]) ``` ``` Dim.1 Dim.2 Dim.3 100 100 100 ``` --- # Nouvelles coordonnées des individus ```r res_acp$ind$coord[, 1:5] ``` ``` Dim.1 Dim.2 Dim.3 Dim.4 Dim.5 1872 -2.9004412 1.02429446 1.56419591 0.48725211 -2.05733909 1880 -2.7671380 2.01204170 -0.16867655 1.48363180 1.23604848 1890 -2.4163977 0.22399375 0.76549836 -0.26771722 -0.70960627 1900 -2.0567917 0.75485866 1.00708899 -0.52319863 -0.50305662 1903 -2.3380494 0.16694324 0.62262603 0.18085933 1.21337857 1906 -1.9850718 0.62578832 0.69302799 -0.70999852 0.15170297 1909 -1.9073089 0.81166027 0.98733211 -0.20092543 0.59515926 1912 -1.4307977 0.76797327 0.19556195 -1.29023611 0.78144538 1920 -2.1387261 0.95660042 -1.74582201 -1.06391843 0.62703005 1923 -1.1436834 -2.88291614 -0.86815228 0.43626965 -0.54206310 1926 -1.6745515 -2.61049990 0.49637656 1.76239443 -1.19394276 1929 -1.1735873 -1.83067994 -0.61190346 1.15625184 0.69458371 1932 0.2708924 -1.95888681 -1.46253819 0.04132425 0.34436726 1935 0.6589576 -2.29627848 -0.66335015 -0.30717135 0.82323609 1938 -0.4023531 -1.34280394 -0.84991874 -1.84912354 0.06308464 1947 1.0889415 2.25682864 -1.27788255 -0.22652682 -0.37665118 1950 2.3708351 2.17612638 -1.91767059 2.65983353 -0.18484080 1953 1.2033631 1.13453601 -1.66116711 -0.75364490 -0.96023691 1956 2.9269811 0.23012624 -0.58914533 -0.44520746 -0.50939381 1959 2.6856088 0.13932205 0.07215077 -0.69076426 -1.21132090 1962 3.0540897 -0.11197408 0.58714272 -0.64513145 -0.41926068 1965 3.1421286 0.30959773 1.41290865 0.76374426 0.93076828 1968 3.6943677 -0.46869676 2.29717813 0.28211486 0.47549988 1971 3.2387319 -0.08795507 1.11513879 -0.28011195 0.73140752 ``` --- # Qualité de la resprésentation des individus ```r res_acp$ind$cos2[, 1:5] ``` ``` Dim.1 Dim.2 Dim.3 Dim.4 Dim.5 1872 0.465171295 0.0580142168 0.1352904313 0.0131278089 0.2340434785 1880 0.450978329 0.2384338938 0.0016757277 0.1296421734 0.0899839482 1890 0.785391875 0.0067487190 0.0788203008 0.0096405578 0.0677305256 1900 0.604890304 0.0814755431 0.1450212626 0.0391407528 0.0361850951 1903 0.572626562 0.0029194552 0.0406086629 0.0034264625 0.1542257114 1906 0.710002588 0.0705606218 0.0865384357 0.0908285492 0.0041466338 1909 0.601302046 0.1088928084 0.1611302724 0.0066729896 0.0585486675 1912 0.406684090 0.1171636637 0.0075974778 0.3307037469 0.1213103885 1920 0.439305553 0.0878855553 0.2927226265 0.1087108847 0.0377600946 1923 0.107119154 0.6806432562 0.0617230462 0.0155871074 0.0240633016 1926 0.192670583 0.4682370142 0.0169293743 0.2134148336 0.0979457043 1929 0.183003318 0.4453003135 0.0497501013 0.1776368371 0.0641028508 1932 0.008779696 0.4590969322 0.2559175916 0.0002043128 0.0141882692 1935 0.060749797 0.7376985643 0.0615623916 0.0132005257 0.0948153448 1938 0.024553266 0.2734763421 0.1095593288 0.5185927066 0.0006035898 1947 0.124026485 0.5327242776 0.1707997370 0.0053671606 0.0148382943 1950 0.250426973 0.2109825910 0.1638424412 0.3152007965 0.0015222082 1953 0.183253021 0.1628899700 0.3492081927 0.0718772256 0.1166848746 1956 0.734688601 0.0045414624 0.0297651676 0.0169976281 0.0222520885 1959 0.754563902 0.0020307207 0.0005446185 0.0499195007 0.1535072662 1962 0.887974643 0.0011936362 0.0328189236 0.0396217274 0.0167342113 1965 0.726838616 0.0070564393 0.1469664645 0.0429423684 0.0637783415 1968 0.679824664 0.0109420974 0.2628488137 0.0039643192 0.0112620511 1971 0.646126659 0.0004765291 0.0765994251 0.0048331575 0.0329523589 ``` --- # Contributions des individus ```r res_acp$ind$contrib[, 1:5] ``` ``` Dim.1 Dim.2 Dim.3 Dim.4 Dim.5 1872 7.04943236 2.13181412 7.90177621 0.996145506 24.89716762 1880 6.41634442 8.22571481 0.09188653 9.235652723 8.98688530 1890 4.89286093 0.10194630 1.89247853 0.300723888 2.96191828 1900 3.54492190 1.15779314 3.27550400 1.148546330 1.48857913 1903 4.58071615 0.05662880 1.25197883 0.137245201 8.66025805 1906 3.30201065 0.79570960 1.55111494 2.115096613 0.13537123 1909 3.04837289 1.33859214 3.14824814 0.169388981 2.08355315 1912 1.71546744 1.19837269 0.12351256 6.984795702 3.59199273 1920 3.83297828 1.85934863 9.84333720 4.749326109 2.31267656 1923 1.09606835 16.88743576 2.43407670 0.798592682 1.72837460 1926 2.34975760 13.84672460 0.79572859 13.032314416 8.38504125 1929 1.15413560 6.80964602 1.20922815 5.609448973 2.83783654 1932 0.06149217 7.79683555 6.90807218 0.007165148 0.69756054 1935 0.36386563 10.71392998 1.42111130 0.395892001 3.98645615 1938 0.13565655 3.66374217 2.33290604 14.346540219 0.02340914 1947 0.99365391 10.34896359 5.27380795 0.215305237 0.83448176 1950 4.71008496 9.62205687 11.87655410 29.684124108 0.20097122 1953 1.21344305 2.61538879 8.91187491 2.383136152 5.42369147 1956 7.17903180 0.10760488 1.12095276 0.831649238 1.52631971 1959 6.04382020 0.03944022 0.01681219 2.002050555 8.63091038 1962 7.81609123 0.02547620 1.11334508 1.746271463 1.03396649 1965 8.27320806 0.19475796 6.44719201 2.447435427 5.09590512 1968 11.43684600 0.44635828 17.04244032 0.333939093 1.32996131 1971 8.78973987 0.01571888 4.01606078 0.329214234 3.14671225 ``` --- # Cercle des corrélations ```r par(mfrow = c(1, 2)) plot.PCA(res_acp, choix = "var") plot.PCA(res_acp, choix = "var", axes = c(1, 3)) ``` <img src="chap6_files/figure-html/cercle-1.png" width="792" style="display: block; margin: auto;" /> --- # Projection des individus ```r par(mfrow = c(1, 2)) plot.PCA(res_acp, choix = "ind") plot.PCA(res_acp, choix = "ind", axes = c(1, 3)) ``` <img src="chap6_files/figure-html/proj-1.png" width="792" style="display: block; margin: auto;" /> --- class: center, middle, inverse # Des questions ? .footnote[Slides créées avec le package <b><a href="https://github.com/yihui/xaringan" target="_blank">xaringan</a></b>.]