COMPONENTES PRINCIPALES
Estating Analytics. DCP
2024-03-05
## Warning: package 'readxl' was built under R version 4.2.3## # A tibble: 41 × 7
## Ciudad SO2 Temp Man Pop Wind Rain
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 Phoenix 10 70.3 213 582 6 7.05
## 2 Little Rock 13 61 91 132 8.2 48.5
## 3 San Francisco 12 56.7 453 716 8.7 20.7
## 4 Denver 17 51.9 454 515 9 13.0
## 5 Hartford 56 49.1 412 158 9 43.4
## 6 Wilmington 36 54 80 80 9 40.2
## 7 Washington 29 57.3 434 757 9.3 38.9
## 8 Jacksonville 14 68.4 136 529 8.8 54.5
## 9 Miami 10 75.5 207 335 9 59.8
## 10 Atlanta 24 61.5 368 497 9.1 48.3
## # ℹ 31 more rows## [1] 41 7Análisis de componentes principales
ACP utilizando matriz de correlaciones
## Call:
## princomp(x = data_series2[, -1], cor = TRUE)
##
## Standard deviations:
## Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6
## 1.6182426 1.1824721 0.9704808 0.8883957 0.4758577 0.1597823
##
## 6 variables and 41 observations.## Importance of components:
## Comp.1 Comp.2 Comp.3 Comp.4 Comp.5
## Standard deviation 1.6182426 1.1824721 0.9704808 0.8883957 0.47585770
## Proportion of Variance 0.4364515 0.2330400 0.1569722 0.1315411 0.03774009
## Cumulative Proportion 0.4364515 0.6694915 0.8264637 0.9580048 0.99574494
## Comp.6
## Standard deviation 0.159782280
## Proportion of Variance 0.004255063
## Cumulative Proportion 1.000000000Matriz de correlacion
## SO2 Temp Man Pop Wind Rain
## SO2 1.00000000 -0.43360020 0.64476873 0.49377958 0.09469045 0.05429434
## Temp -0.43360020 1.00000000 -0.19004216 -0.06267813 -0.34973963 0.38625342
## Man 0.64476873 -0.19004216 1.00000000 0.95526935 0.23794683 -0.03241688
## Pop 0.49377958 -0.06267813 0.95526935 1.00000000 0.21264375 -0.02611873
## Wind 0.09469045 -0.34973963 0.23794683 0.21264375 1.00000000 -0.01299438
## Rain 0.05429434 0.38625342 -0.03241688 -0.02611873 -0.01299438 1.00000000Cargas de cada componente y matriz de correlación
Cargas de cada componente
## Importance of components:
## Comp.1 Comp.2 Comp.3 Comp.4 Comp.5
## Standard deviation 1.6182426 1.1824721 0.9704808 0.8883957 0.47585770
## Proportion of Variance 0.4364515 0.2330400 0.1569722 0.1315411 0.03774009
## Cumulative Proportion 0.4364515 0.6694915 0.8264637 0.9580048 0.99574494
## Comp.6
## Standard deviation 0.159782280
## Proportion of Variance 0.004255063
## Cumulative Proportion 1.000000000
##
## Loadings:
## Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6
## SO2 0.482 0.109 0.614 0.596 0.149
## Temp -0.289 0.646 -0.386 0.589
## Man 0.578 0.225 0.106 -0.179 -0.130 -0.745
## Pop 0.533 0.290 0.115 -0.354 -0.266 0.650
## Wind 0.246 -0.288 -0.811 -0.328 0.301
## Rain 0.603 -0.550 0.457 -0.345##
## Loadings:
## Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6
## SO2 0.482 0.109 0.614 0.596 0.149
## Temp -0.289 0.646 -0.386 0.589
## Man 0.578 0.225 0.106 -0.179 -0.130 -0.745
## Pop 0.533 0.290 0.115 -0.354 -0.266 0.650
## Wind 0.246 -0.288 -0.811 -0.328 0.301
## Rain 0.603 -0.550 0.457 -0.345
##
## Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6
## SS loadings 1.000 1.000 1.000 1.000 1.000 1.000
## Proportion Var 0.167 0.167 0.167 0.167 0.167 0.167
## Cumulative Var 0.167 0.333 0.500 0.667 0.833 1.000## Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6
## [1,] -1.69854799 0.3307039 3.35431015 -1.58693052 0.903326659 0.08599409
## [2,] -1.68933620 0.9179076 -0.04569071 0.43169616 -0.311486385 -0.19138215
## [3,] -0.34960289 -0.5764095 1.13202346 -1.05216604 -0.114573312 0.01242862
## [4,] -0.13580606 -1.5655185 1.26940024 -0.90901629 0.004302937 -0.15911041
## [5,] 0.21618124 -0.3787419 -0.08849580 1.70565487 0.048647297 -0.25450455
## [6,] -0.79517292 -0.3026105 -0.07463581 0.94367037 0.145312121 -0.04732920
## [7,] -0.01467187 0.3402769 0.01393394 -0.07655339 -0.056181027 0.19200619
## [8,] -1.48481923 1.9944547 -0.52016758 -0.10773050 0.080505710 0.17829770
## [9,] -1.96149572 2.7961387 -0.87487832 -0.33687873 0.521556105 -0.19267563
## [10,] -0.69495892 1.0845492 -0.37289434 0.16441644 -0.024983209 -0.06980895
## [11,] 7.61666514 1.9097665 0.99735457 -0.55425955 -0.056695352 -0.17515390
## [12,] 0.15138296 -0.2380671 -0.26955484 0.09849411 -0.382518877 0.29649500
## [13,] -0.40609554 -1.6500198 -0.99478259 -0.25313309 -0.069564671 -0.01704810
## [14,] -0.54451589 -1.2500608 -1.80668872 -1.31536171 0.613547645 -0.03371453
## [15,] -0.42805758 0.4700481 0.32013083 0.58779673 -0.399417916 0.19934558
## [16,] -1.75520000 2.1209090 -0.44407667 0.03091434 -0.147529393 -0.13993073
## [17,] 0.82557400 0.3769788 -0.14073602 0.39667201 0.095349712 0.23229938
## [18,] 1.95854518 -0.2552045 0.17007870 -0.68659489 -0.605846946 0.28819436
## [19,] 1.11660054 -1.7440801 -0.18283511 -0.21943948 -0.588926210 -0.10089997
## [20,] -0.36700082 -0.3256206 -0.45203695 -0.38763508 -0.338685407 -0.09738829
## [21,] 0.88590019 0.1287327 0.19437268 0.52371766 0.637448000 -0.23540470
## [22,] -0.40157988 -1.2967451 -0.74084435 -0.53946435 -0.070495865 0.01275419
## [23,] -1.11900548 -1.6828635 1.45073896 -1.21393005 0.608484581 0.02003326
## [24,] -0.32285541 -1.1786361 0.36259246 1.31922488 0.028045542 0.13333385
## [25,] 0.26361022 -1.5541625 -1.86950128 -0.63626402 -0.470178365 -0.12303874
## [26,] -0.64483584 0.3467480 1.16131605 0.63966777 -0.821098025 -0.23780188
## [27,] 1.93485949 -0.5911341 -0.50489251 0.58161019 0.568149762 -0.30021204
## [28,] -0.32917419 -0.3216126 0.36940317 0.43471569 -0.564882569 0.16942213
## [29,] 3.38980370 1.2662450 0.43753533 -0.04392728 -0.067238564 0.13424337
## [30,] 0.65311965 -0.5485146 0.11391232 1.19034489 0.428675269 0.27620631
## [31,] 1.20083307 -0.6146977 -0.80220219 2.27616058 1.465815945 0.11847117
## [32,] -0.89140752 1.1427817 -0.51169622 -0.27386006 -0.429875914 0.02641683
## [33,] -1.07128777 0.9465552 0.35514062 0.36628956 -0.494258603 -0.04222737
## [34,] -0.19622659 0.7622427 -0.73233339 -1.69556467 0.503663934 -0.13550362
## [35,] 0.06456567 1.8936451 -1.13486704 -1.57692452 0.167069060 0.18944335
## [36,] -0.58240476 -1.7539663 1.25291865 -0.10005961 0.315020932 -0.04905692
## [37,] -0.63383350 0.1940580 -1.13637206 0.18057175 0.553585890 0.15057172
## [38,] -1.09046339 0.5914529 0.66897002 0.71772267 -0.295594520 -0.05093688
## [39,] -0.01356076 -0.3830201 -0.14404990 0.38897266 -0.425307593 0.03673172
## [40,] -1.44207636 0.3119773 1.31448208 1.36743374 -0.417305885 -0.06061559
## [41,] 0.78635202 -1.7144861 -1.09438185 -0.78005323 -0.535862495 -0.03894467Biplot análisis de componentes principales
Relación entre todas las variables.
Método matricial, ocupando eigen.
T1cp<-princomp(data_series2[,-1],cor=TRUE) summary(T1cp) cov1<-cor(data_series2[,-1]) ei1<-eigen(cov1) ei1 val1<-round(ei1\(values[1:6]/sum(ei1\)values),4) val1 ## Peso de cada variable
## Importance of components:
## Comp.1 Comp.2 Comp.3 Comp.4 Comp.5
## Standard deviation 1.6182426 1.1824721 0.9704808 0.8883957 0.47585770
## Proportion of Variance 0.4364515 0.2330400 0.1569722 0.1315411 0.03774009
## Cumulative Proportion 0.4364515 0.6694915 0.8264637 0.9580048 0.99574494
## Comp.6
## Standard deviation 0.159782280
## Proportion of Variance 0.004255063
## Cumulative Proportion 1.000000000## eigen() decomposition
## $values
## [1] 2.61870900 1.39824026 0.94183296 0.78924686 0.22644055 0.02553038
##
## $vectors
## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 0.48202425 0.03597091 -0.10886658 0.6140010 -0.5961241 -0.148813741
## [2,] -0.28866577 0.64556679 -0.05689778 -0.3857221 -0.5890272 0.030720007
## [3,] 0.57805937 0.22549418 -0.10599379 -0.1789520 0.1301198 0.744855742
## [4,] 0.53289744 0.29042373 -0.11476561 -0.3544397 0.2664572 -0.649520024
## [5,] 0.24614583 -0.28826301 0.81114336 -0.3281215 -0.3008086 -0.014614826
## [6,] -0.07486395 0.60304269 0.55004666 0.4570626 0.3453499 0.003289364## [1] 0.4365 0.2330 0.1570 0.1315 0.0377 0.0043