swiss
## Fertility Agriculture Examination Education Catholic
## Courtelary 80.2 17.0 15 12 9.96
## Delemont 83.1 45.1 6 9 84.84
## Franches-Mnt 92.5 39.7 5 5 93.40
## Moutier 85.8 36.5 12 7 33.77
## Neuveville 76.9 43.5 17 15 5.16
## Porrentruy 76.1 35.3 9 7 90.57
## Broye 83.8 70.2 16 7 92.85
## Glane 92.4 67.8 14 8 97.16
## Gruyere 82.4 53.3 12 7 97.67
## Sarine 82.9 45.2 16 13 91.38
## Veveyse 87.1 64.5 14 6 98.61
## Aigle 64.1 62.0 21 12 8.52
## Aubonne 66.9 67.5 14 7 2.27
## Avenches 68.9 60.7 19 12 4.43
## Cossonay 61.7 69.3 22 5 2.82
## Echallens 68.3 72.6 18 2 24.20
## Grandson 71.7 34.0 17 8 3.30
## Lausanne 55.7 19.4 26 28 12.11
## La Vallee 54.3 15.2 31 20 2.15
## Lavaux 65.1 73.0 19 9 2.84
## Morges 65.5 59.8 22 10 5.23
## Moudon 65.0 55.1 14 3 4.52
## Nyone 56.6 50.9 22 12 15.14
## Orbe 57.4 54.1 20 6 4.20
## Oron 72.5 71.2 12 1 2.40
## Payerne 74.2 58.1 14 8 5.23
## Paysd'enhaut 72.0 63.5 6 3 2.56
## Rolle 60.5 60.8 16 10 7.72
## Vevey 58.3 26.8 25 19 18.46
## Yverdon 65.4 49.5 15 8 6.10
## Conthey 75.5 85.9 3 2 99.71
## Entremont 69.3 84.9 7 6 99.68
## Herens 77.3 89.7 5 2 100.00
## Martigwy 70.5 78.2 12 6 98.96
## Monthey 79.4 64.9 7 3 98.22
## St Maurice 65.0 75.9 9 9 99.06
## Sierre 92.2 84.6 3 3 99.46
## Sion 79.3 63.1 13 13 96.83
## Boudry 70.4 38.4 26 12 5.62
## La Chauxdfnd 65.7 7.7 29 11 13.79
## Le Locle 72.7 16.7 22 13 11.22
## Neuchatel 64.4 17.6 35 32 16.92
## Val de Ruz 77.6 37.6 15 7 4.97
## ValdeTravers 67.6 18.7 25 7 8.65
## V. De Geneve 35.0 1.2 37 53 42.34
## Rive Droite 44.7 46.6 16 29 50.43
## Rive Gauche 42.8 27.7 22 29 58.33
## Infant.Mortality
## Courtelary 22.2
## Delemont 22.2
## Franches-Mnt 20.2
## Moutier 20.3
## Neuveville 20.6
## Porrentruy 26.6
## Broye 23.6
## Glane 24.9
## Gruyere 21.0
## Sarine 24.4
## Veveyse 24.5
## Aigle 16.5
## Aubonne 19.1
## Avenches 22.7
## Cossonay 18.7
## Echallens 21.2
## Grandson 20.0
## Lausanne 20.2
## La Vallee 10.8
## Lavaux 20.0
## Morges 18.0
## Moudon 22.4
## Nyone 16.7
## Orbe 15.3
## Oron 21.0
## Payerne 23.8
## Paysd'enhaut 18.0
## Rolle 16.3
## Vevey 20.9
## Yverdon 22.5
## Conthey 15.1
## Entremont 19.8
## Herens 18.3
## Martigwy 19.4
## Monthey 20.2
## St Maurice 17.8
## Sierre 16.3
## Sion 18.1
## Boudry 20.3
## La Chauxdfnd 20.5
## Le Locle 18.9
## Neuchatel 23.0
## Val de Ruz 20.0
## ValdeTravers 19.5
## V. De Geneve 18.0
## Rive Droite 18.2
## Rive Gauche 19.3
boxplot (swiss)
boxplot (swiss)
cor (swiss)
## Fertility Agriculture Examination Education Catholic
## Fertility 1.0000000 0.35307918 -0.6458827 -0.66378886 0.4636847
## Agriculture 0.3530792 1.00000000 -0.6865422 -0.63952252 0.4010951
## Examination -0.6458827 -0.68654221 1.0000000 0.69841530 -0.5727418
## Education -0.6637889 -0.63952252 0.6984153 1.00000000 -0.1538589
## Catholic 0.4636847 0.40109505 -0.5727418 -0.15385892 1.0000000
## Infant.Mortality 0.4165560 -0.06085861 -0.1140216 -0.09932185 0.1754959
## Infant.Mortality
## Fertility 0.41655603
## Agriculture -0.06085861
## Examination -0.11402160
## Education -0.09932185
## Catholic 0.17549591
## Infant.Mortality 1.00000000
pcr <- prcomp(swiss)
pcr
## Standard deviations (1, .., p=6):
## [1] 43.835630 21.602248 12.053416 4.759160 3.657544 2.488222
##
## Rotation (n x k) = (6 x 6):
## PC1 PC2 PC3 PC4 PC5
## Fertility -0.15163143 0.14270789 0.81454413 -0.49552828 0.12247267
## Agriculture -0.28121756 0.85914886 -0.35256541 -0.24078519 0.02235164
## Examination 0.12207834 -0.17688621 -0.18767793 -0.57042350 -0.76887882
## Education 0.06329733 -0.32260928 -0.40096045 -0.58075837 0.61904343
## Catholic -0.93748965 -0.32543441 -0.07870742 0.04104832 -0.08547871
## Infant.Mortality -0.01131739 -0.01498883 0.10014161 -0.17923725 0.05296062
## PC6
## Fertility 0.1805890073
## Agriculture -0.0006755062
## Examination 0.0450281625
## Education 0.1032102386
## Catholic -0.0043788222
## Infant.Mortality -0.9770814149
variab<-pcr$sdev^2/sum(pcr$sdev^2)
plot(variab,type= "o", col = "blue",lwd=2 )
summary(pcr)
## Importance of components:
## PC1 PC2 PC3 PC4 PC5 PC6
## Standard deviation 43.836 21.6022 12.05342 4.75916 3.65754 2.4882
## Proportion of Variance 0.746 0.1812 0.05641 0.00879 0.00519 0.0024
## Cumulative Proportion 0.746 0.9272 0.98361 0.99240 0.99760 1.0000
round(cor(swiss),2)
## Fertility Agriculture Examination Education Catholic
## Fertility 1.00 0.35 -0.65 -0.66 0.46
## Agriculture 0.35 1.00 -0.69 -0.64 0.40
## Examination -0.65 -0.69 1.00 0.70 -0.57
## Education -0.66 -0.64 0.70 1.00 -0.15
## Catholic 0.46 0.40 -0.57 -0.15 1.00
## Infant.Mortality 0.42 -0.06 -0.11 -0.10 0.18
## Infant.Mortality
## Fertility 0.42
## Agriculture -0.06
## Examination -0.11
## Education -0.10
## Catholic 0.18
## Infant.Mortality 1.00
pairs(swiss)
det(cor(swiss))
## [1] 0.03496976
acp=prcomp(swiss,scale=TRUE)
acp
## Standard deviations (1, .., p=6):
## [1] 1.7887865 1.0900955 0.9206573 0.6625169 0.4522540 0.3476529
##
## Rotation (n x k) = (6 x 6):
## PC1 PC2 PC3 PC4 PC5
## Fertility -0.4569876 0.3220284 -0.17376638 0.53555794 -0.38308893
## Agriculture -0.4242141 -0.4115132 0.03834472 -0.64291822 -0.37495215
## Examination 0.5097327 0.1250167 -0.09123696 -0.05446158 -0.81429082
## Education 0.4543119 0.1790495 0.53239316 -0.09738818 0.07144564
## Catholic -0.3501111 0.1458730 0.80680494 0.09947244 -0.18317236
## Infant.Mortality -0.1496668 0.8111645 -0.16010636 -0.52677184 0.10453530
## PC6
## Fertility 0.47295441
## Agriculture 0.30870058
## Examination -0.22401686
## Education 0.68081610
## Catholic -0.40219666
## Infant.Mortality -0.07457754
acp$sdev
## [1] 1.7887865 1.0900955 0.9206573 0.6625169 0.4522540 0.3476529
acp$sdev^2
## [1] 3.1997570 1.1883082 0.8476098 0.4389287 0.2045337 0.1208626
variab2<-acp$sdev^2/sum(acp$sdev^2)
X11()
plot(variab2,type= "o", col = "red",lwd=2 )
summary(acp)
## Importance of components:
## PC1 PC2 PC3 PC4 PC5 PC6
## Standard deviation 1.7888 1.0901 0.9207 0.66252 0.45225 0.34765
## Proportion of Variance 0.5333 0.1981 0.1413 0.07315 0.03409 0.02014
## Cumulative Proportion 0.5333 0.7313 0.8726 0.94577 0.97986 1.00000
acp$rotation
## PC1 PC2 PC3 PC4 PC5
## Fertility -0.4569876 0.3220284 -0.17376638 0.53555794 -0.38308893
## Agriculture -0.4242141 -0.4115132 0.03834472 -0.64291822 -0.37495215
## Examination 0.5097327 0.1250167 -0.09123696 -0.05446158 -0.81429082
## Education 0.4543119 0.1790495 0.53239316 -0.09738818 0.07144564
## Catholic -0.3501111 0.1458730 0.80680494 0.09947244 -0.18317236
## Infant.Mortality -0.1496668 0.8111645 -0.16010636 -0.52677184 0.10453530
## PC6
## Fertility 0.47295441
## Agriculture 0.30870058
## Examination -0.22401686
## Education 0.68081610
## Catholic -0.40219666
## Infant.Mortality -0.07457754
summary(acp)
## Importance of components:
## PC1 PC2 PC3 PC4 PC5 PC6
## Standard deviation 1.7888 1.0901 0.9207 0.66252 0.45225 0.34765
## Proportion of Variance 0.5333 0.1981 0.1413 0.07315 0.03409 0.02014
## Cumulative Proportion 0.5333 0.7313 0.8726 0.94577 0.97986 1.00000
X11()
plot(acp)
X11()
plot(acp$sdev^2)
acp$x
## PC1 PC2 PC3 PC4 PC5
## Courtelary 0.35966320 1.38445294 -0.85051250 0.901220398 0.62485501
## Delemont -1.61669718 1.01507287 0.54200749 0.500510824 0.63944520
## Franches-Mnt -2.08169474 0.73804451 0.46762748 1.485847610 0.40329414
## Moutier -0.73961186 0.58951830 -0.57296512 1.060829924 0.22746839
## Neuveville 0.37744699 0.44404417 -0.62154168 0.243445489 0.07036727
## Porrentruy -1.35457456 2.26736561 0.34677833 -0.304490831 0.82759212
## Broye -1.70588478 1.11569053 0.42755045 -0.462117868 -0.81689334
## Glane -2.15919258 1.74527576 0.39402942 -0.246773891 -0.80171700
## Gruyere -1.50143716 0.61591364 0.70040053 0.465293939 -0.20115598
## Sarine -0.95127129 1.87485258 0.65766071 -0.001952872 -0.29680368
## Veveyse -1.98977728 1.52487142 0.40148471 -0.284527045 -0.62028283
## Aigle 0.79645531 -1.34438945 -0.33373145 -0.076442876 -0.43498539
## Aubonne -0.17333509 -0.87244232 -0.82401299 -0.498793337 0.18643461
## Avenches 0.23310414 0.48391431 -0.79975220 -0.951245812 -0.11611103
## Cossonay 0.41586227 -1.06046222 -0.91823904 -0.733391216 -0.53199203
## Echallens -0.59249012 -0.29764382 -0.84865076 -0.887294641 -0.40707537
## Grandson 0.46083396 0.17817635 -0.95582929 0.464409328 0.32130229
## Lausanne 2.75464368 0.63021848 0.40597944 -0.087421447 0.25149480
## La Vallee 3.39241613 -2.05305600 0.24225300 1.694613627 -0.49963197
## Lavaux 0.15271431 -0.65027049 -0.77457628 -0.947459432 -0.31485139
## Morges 0.70627127 -0.88377615 -0.62519400 -0.219839553 -0.49024369
## Moudon -0.24966208 0.15566824 -1.17786188 -0.780165186 0.52825321
## Nyone 1.27620439 -1.24208575 -0.14250524 -0.110975582 -0.14568957
## Orbe 0.93966875 -1.85066669 -0.59225596 0.134260798 -0.06569470
## Oron -0.95731037 -0.40859623 -1.30693030 -0.632333638 0.18078555
## Payerne -0.48392114 0.82395905 -1.08715051 -0.772801139 0.28086226
## Paysd'enhaut -0.93124651 -1.17366513 -0.96561988 0.127849798 0.84214339
## Rolle 0.55359958 -1.58954300 -0.34371862 -0.108163848 0.18704679
## Vevey 1.94290010 0.59705666 -0.02021011 -0.198903657 0.08201694
## Yverdon 0.12203721 0.40960015 -0.90240418 -0.676274034 0.54017227
## Conthey -2.38317443 -2.02276611 1.04128495 0.430598800 0.13299510
## Entremont -1.93436729 -0.71850262 1.04264011 -0.724809501 0.12990280
## Herens -2.55908086 -1.12168536 0.82950051 -0.191494657 -0.07550697
## Martigwy -1.50705630 -0.60173085 0.96551279 -0.447204193 -0.31782028
## Monthey -2.08032844 -0.04531614 0.65203813 0.228938170 0.14882965
## St Maurice -1.23144667 -1.13822925 1.32843662 -0.338197959 0.15945698
## Sierre -2.98214753 -1.21675728 0.79135414 0.955631678 -0.30609367
## Sion -1.06762998 -0.32474201 1.22400362 0.509840403 -0.42575724
## Boudry 1.15534712 0.37211856 -0.78337665 0.133442264 -0.59979032
## La Chauxdfnd 1.96628970 0.91988564 -0.71244741 0.773971084 -0.29115130
## Le Locle 1.29313296 0.41023891 -0.56560353 1.130072588 0.02879514
## Neuchatel 3.04976701 1.89923565 0.33960819 -0.260340420 -0.79512594
## Val de Ruz -0.01130497 0.22092431 -1.03201259 0.643215149 0.27030163
## ValdeTravers 1.34128486 0.33591622 -0.94050348 0.780451248 -0.16578592
## V. De Geneve 5.59516797 0.55731309 2.62736774 -0.318001744 0.03805959
## Rive Droite 1.83839091 -0.70723653 1.62590990 -0.817770415 0.92780802
## Rive Gauche 2.52144140 0.01423545 1.64417740 -0.585256326 0.69047649
## PC6
## Courtelary 0.28033964
## Delemont 0.09025482
## Franches-Mnt 0.08627169
## Moutier 0.30665938
## Neuveville 0.75910816
## Porrentruy -0.70174843
## Broye -0.07757248
## Glane 0.26752807
## Gruyere -0.22788401
## Sarine -0.03293721
## Veveyse -0.12334422
## Aigle 0.27378194
## Aubonne 0.29079022
## Avenches 0.37470333
## Cossonay -0.24293294
## Echallens -0.31848413
## Grandson -0.02923246
## Lausanne 0.23982711
## La Vallee -0.24037010
## Lavaux 0.27006772
## Morges 0.12051748
## Moudon -0.33910446
## Nyone -0.25809836
## Orbe -0.41163208
## Oron 0.13453598
## Payerne 0.36132900
## Paysd'enhaut 0.39630123
## Rolle 0.13279485
## Vevey -0.24947330
## Yverdon -0.09193142
## Conthey -0.01592934
## Entremont -0.21341405
## Herens -0.03701734
## Martigwy -0.38226288
## Monthey -0.31143720
## St Maurice -0.28510792
## Sierre 0.64117811
## Sion 0.26705293
## Boudry -0.01819963
## La Chauxdfnd -0.85239150
## Le Locle -0.06110993
## Neuchatel 0.45717792
## Val de Ruz 0.21233262
## ValdeTravers -0.72666398
## V. De Geneve 0.43474730
## Rive Droite 0.22632172
## Rive Gauche -0.37534182
predict(acp)
## PC1 PC2 PC3 PC4 PC5
## Courtelary 0.35966320 1.38445294 -0.85051250 0.901220398 0.62485501
## Delemont -1.61669718 1.01507287 0.54200749 0.500510824 0.63944520
## Franches-Mnt -2.08169474 0.73804451 0.46762748 1.485847610 0.40329414
## Moutier -0.73961186 0.58951830 -0.57296512 1.060829924 0.22746839
## Neuveville 0.37744699 0.44404417 -0.62154168 0.243445489 0.07036727
## Porrentruy -1.35457456 2.26736561 0.34677833 -0.304490831 0.82759212
## Broye -1.70588478 1.11569053 0.42755045 -0.462117868 -0.81689334
## Glane -2.15919258 1.74527576 0.39402942 -0.246773891 -0.80171700
## Gruyere -1.50143716 0.61591364 0.70040053 0.465293939 -0.20115598
## Sarine -0.95127129 1.87485258 0.65766071 -0.001952872 -0.29680368
## Veveyse -1.98977728 1.52487142 0.40148471 -0.284527045 -0.62028283
## Aigle 0.79645531 -1.34438945 -0.33373145 -0.076442876 -0.43498539
## Aubonne -0.17333509 -0.87244232 -0.82401299 -0.498793337 0.18643461
## Avenches 0.23310414 0.48391431 -0.79975220 -0.951245812 -0.11611103
## Cossonay 0.41586227 -1.06046222 -0.91823904 -0.733391216 -0.53199203
## Echallens -0.59249012 -0.29764382 -0.84865076 -0.887294641 -0.40707537
## Grandson 0.46083396 0.17817635 -0.95582929 0.464409328 0.32130229
## Lausanne 2.75464368 0.63021848 0.40597944 -0.087421447 0.25149480
## La Vallee 3.39241613 -2.05305600 0.24225300 1.694613627 -0.49963197
## Lavaux 0.15271431 -0.65027049 -0.77457628 -0.947459432 -0.31485139
## Morges 0.70627127 -0.88377615 -0.62519400 -0.219839553 -0.49024369
## Moudon -0.24966208 0.15566824 -1.17786188 -0.780165186 0.52825321
## Nyone 1.27620439 -1.24208575 -0.14250524 -0.110975582 -0.14568957
## Orbe 0.93966875 -1.85066669 -0.59225596 0.134260798 -0.06569470
## Oron -0.95731037 -0.40859623 -1.30693030 -0.632333638 0.18078555
## Payerne -0.48392114 0.82395905 -1.08715051 -0.772801139 0.28086226
## Paysd'enhaut -0.93124651 -1.17366513 -0.96561988 0.127849798 0.84214339
## Rolle 0.55359958 -1.58954300 -0.34371862 -0.108163848 0.18704679
## Vevey 1.94290010 0.59705666 -0.02021011 -0.198903657 0.08201694
## Yverdon 0.12203721 0.40960015 -0.90240418 -0.676274034 0.54017227
## Conthey -2.38317443 -2.02276611 1.04128495 0.430598800 0.13299510
## Entremont -1.93436729 -0.71850262 1.04264011 -0.724809501 0.12990280
## Herens -2.55908086 -1.12168536 0.82950051 -0.191494657 -0.07550697
## Martigwy -1.50705630 -0.60173085 0.96551279 -0.447204193 -0.31782028
## Monthey -2.08032844 -0.04531614 0.65203813 0.228938170 0.14882965
## St Maurice -1.23144667 -1.13822925 1.32843662 -0.338197959 0.15945698
## Sierre -2.98214753 -1.21675728 0.79135414 0.955631678 -0.30609367
## Sion -1.06762998 -0.32474201 1.22400362 0.509840403 -0.42575724
## Boudry 1.15534712 0.37211856 -0.78337665 0.133442264 -0.59979032
## La Chauxdfnd 1.96628970 0.91988564 -0.71244741 0.773971084 -0.29115130
## Le Locle 1.29313296 0.41023891 -0.56560353 1.130072588 0.02879514
## Neuchatel 3.04976701 1.89923565 0.33960819 -0.260340420 -0.79512594
## Val de Ruz -0.01130497 0.22092431 -1.03201259 0.643215149 0.27030163
## ValdeTravers 1.34128486 0.33591622 -0.94050348 0.780451248 -0.16578592
## V. De Geneve 5.59516797 0.55731309 2.62736774 -0.318001744 0.03805959
## Rive Droite 1.83839091 -0.70723653 1.62590990 -0.817770415 0.92780802
## Rive Gauche 2.52144140 0.01423545 1.64417740 -0.585256326 0.69047649
## PC6
## Courtelary 0.28033964
## Delemont 0.09025482
## Franches-Mnt 0.08627169
## Moutier 0.30665938
## Neuveville 0.75910816
## Porrentruy -0.70174843
## Broye -0.07757248
## Glane 0.26752807
## Gruyere -0.22788401
## Sarine -0.03293721
## Veveyse -0.12334422
## Aigle 0.27378194
## Aubonne 0.29079022
## Avenches 0.37470333
## Cossonay -0.24293294
## Echallens -0.31848413
## Grandson -0.02923246
## Lausanne 0.23982711
## La Vallee -0.24037010
## Lavaux 0.27006772
## Morges 0.12051748
## Moudon -0.33910446
## Nyone -0.25809836
## Orbe -0.41163208
## Oron 0.13453598
## Payerne 0.36132900
## Paysd'enhaut 0.39630123
## Rolle 0.13279485
## Vevey -0.24947330
## Yverdon -0.09193142
## Conthey -0.01592934
## Entremont -0.21341405
## Herens -0.03701734
## Martigwy -0.38226288
## Monthey -0.31143720
## St Maurice -0.28510792
## Sierre 0.64117811
## Sion 0.26705293
## Boudry -0.01819963
## La Chauxdfnd -0.85239150
## Le Locle -0.06110993
## Neuchatel 0.45717792
## Val de Ruz 0.21233262
## ValdeTravers -0.72666398
## V. De Geneve 0.43474730
## Rive Droite 0.22632172
## Rive Gauche -0.37534182