Métodos Multivariados
Sebastián Meza
2024-02-11
Problema Una empresa inmobiliaria líder en una gran ciudad está buscando comprender en profundidad el mercado de viviendas urbanas para tomar decisiones estratégicas más informadas. La empresa posee una base de datos extensa que contiene información detallada sobre diversas propiedades residenciales disponibles en el mercado. Se requiere realizar un análisis holístico de estos datos para identificar patrones, relaciones y segmentaciones relevantes que permitan mejorar la toma de decisiones en cuanto a la compra, venta y valoración de propiedades.
0. Instalación de paquetes y librerías
1. Importación de la data
vivienda <- readRDS("C:/Users/sebas/OneDrive/Maestria/Semestre 2/Mod. Estadísticos para toma de decisiones/Módulo 1_Modelos Estadísticos/Unidad 1_Modelos Multivariados/Vivienda.RDS")2. Análisis Exploratorio
# Vista global de las variables
glimpse(vivienda)## Rows: 8,322
## Columns: 13
## $ id <dbl> 1147, 1169, 1350, 5992, 1212, 1724, 2326, 4386, 1209, 159…
## $ zona <chr> "Zona Oriente", "Zona Oriente", "Zona Oriente", "Zona Sur…
## $ piso <chr> NA, NA, NA, "02", "01", "01", "01", "01", "02", "02", "02…
## $ estrato <dbl> 3, 3, 3, 4, 5, 5, 4, 5, 5, 5, 6, 4, 5, 6, 4, 5, 5, 4, 5, …
## $ preciom <dbl> 250, 320, 350, 400, 260, 240, 220, 310, 320, 780, 750, 62…
## $ areaconst <dbl> 70, 120, 220, 280, 90, 87, 52, 137, 150, 380, 445, 355, 2…
## $ parqueaderos <dbl> 1, 1, 2, 3, 1, 1, 2, 2, 2, 2, NA, 3, 2, 2, 1, 4, 2, 2, 2,…
## $ banios <dbl> 3, 2, 2, 5, 2, 3, 2, 3, 4, 3, 7, 5, 6, 2, 4, 4, 4, 3, 2, …
## $ habitaciones <dbl> 6, 3, 4, 3, 3, 3, 3, 4, 6, 3, 6, 5, 6, 2, 5, 5, 4, 3, 3, …
## $ tipo <chr> "Casa", "Casa", "Casa", "Casa", "Apartamento", "Apartamen…
## $ barrio <chr> "20 de julio", "20 de julio", "20 de julio", "3 de julio"…
## $ longitud <dbl> -76.51168, -76.51237, -76.51537, -76.54000, -76.51350, -7…
## $ latitud <dbl> 3.43382, 3.43369, 3.43566, 3.43500, 3.45891, 3.36971, 3.4…Observamos que la data cuenta con una dimensión de 5 variables y 1.363 viviendas. Para las variables tenemos las siguientes:
- zona = ubicación geográfica de la ciudad de Cali dividido por zonas.
- estrato = clasificación utilizada para categorizar en base a factores socioeconómicos.
- preciom = precio del inmueble en millones.
- areaconst = superficie total del inmueble.
- tipo = clasificación categórica para el tipo de inmueble (apto).
Adicionalmente, notamos variables variables categóricas que tienen el formato adecuado.
# Enfoque detallado de la data
skimr::skim(vivienda)| Name | vivienda |
| Number of rows | 8322 |
| Number of columns | 13 |
| _______________________ | |
| Column type frequency: | |
| character | 4 |
| numeric | 9 |
| ________________________ | |
| Group variables | None |
Variable type: character
| skim_variable | n_missing | complete_rate | min | max | empty | n_unique | whitespace |
|---|---|---|---|---|---|---|---|
| zona | 3 | 1.00 | 8 | 12 | 0 | 5 | 0 |
| piso | 2638 | 0.68 | 2 | 2 | 0 | 12 | 0 |
| tipo | 3 | 1.00 | 4 | 11 | 0 | 2 | 0 |
| barrio | 3 | 1.00 | 4 | 29 | 0 | 436 | 0 |
Variable type: numeric
| skim_variable | n_missing | complete_rate | mean | sd | p0 | p25 | p50 | p75 | p100 | hist |
|---|---|---|---|---|---|---|---|---|---|---|
| id | 3 | 1.00 | 4160.00 | 2401.63 | 1.00 | 2080.50 | 4160.00 | 6239.50 | 8319.00 | ▇▇▇▇▇ |
| estrato | 3 | 1.00 | 4.63 | 1.03 | 3.00 | 4.00 | 5.00 | 5.00 | 6.00 | ▅▆▁▇▆ |
| preciom | 2 | 1.00 | 433.89 | 328.65 | 58.00 | 220.00 | 330.00 | 540.00 | 1999.00 | ▇▂▁▁▁ |
| areaconst | 3 | 1.00 | 174.93 | 142.96 | 30.00 | 80.00 | 123.00 | 229.00 | 1745.00 | ▇▁▁▁▁ |
| parqueaderos | 1605 | 0.81 | 1.84 | 1.12 | 1.00 | 1.00 | 2.00 | 2.00 | 10.00 | ▇▁▁▁▁ |
| banios | 3 | 1.00 | 3.11 | 1.43 | 0.00 | 2.00 | 3.00 | 4.00 | 10.00 | ▇▇▃▁▁ |
| habitaciones | 3 | 1.00 | 3.61 | 1.46 | 0.00 | 3.00 | 3.00 | 4.00 | 10.00 | ▂▇▂▁▁ |
| longitud | 3 | 1.00 | -76.53 | 0.02 | -76.59 | -76.54 | -76.53 | -76.52 | -76.46 | ▁▅▇▂▁ |
| latitud | 3 | 1.00 | 3.42 | 0.04 | 3.33 | 3.38 | 3.42 | 3.45 | 3.50 | ▃▇▅▇▅ |
Para las variables categóricas encontramos que zona contiene 5 valores únicos y dos tipos de vivienda que corresponden a casa y apartamento. Para las variables númericas tenemos, precio de la vivienda con una media de 433 millones de pesos COP y área construida con una media de 174.93 metros cuadrados.
Los datos faltantes se presentan 19,28% para parqueaderos y 31,7% para piso con respecto a la cantidad total de registros.
#Resumen
summary(vivienda)## id zona piso estrato
## Min. : 1 Length:8322 Length:8322 Min. :3.000
## 1st Qu.:2080 Class :character Class :character 1st Qu.:4.000
## Median :4160 Mode :character Mode :character Median :5.000
## Mean :4160 Mean :4.634
## 3rd Qu.:6240 3rd Qu.:5.000
## Max. :8319 Max. :6.000
## NA's :3 NA's :3
## preciom areaconst parqueaderos banios
## Min. : 58.0 Min. : 30.0 Min. : 1.000 Min. : 0.000
## 1st Qu.: 220.0 1st Qu.: 80.0 1st Qu.: 1.000 1st Qu.: 2.000
## Median : 330.0 Median : 123.0 Median : 2.000 Median : 3.000
## Mean : 433.9 Mean : 174.9 Mean : 1.835 Mean : 3.111
## 3rd Qu.: 540.0 3rd Qu.: 229.0 3rd Qu.: 2.000 3rd Qu.: 4.000
## Max. :1999.0 Max. :1745.0 Max. :10.000 Max. :10.000
## NA's :2 NA's :3 NA's :1605 NA's :3
## habitaciones tipo barrio longitud
## Min. : 0.000 Length:8322 Length:8322 Min. :-76.59
## 1st Qu.: 3.000 Class :character Class :character 1st Qu.:-76.54
## Median : 3.000 Mode :character Mode :character Median :-76.53
## Mean : 3.605 Mean :-76.53
## 3rd Qu.: 4.000 3rd Qu.:-76.52
## Max. :10.000 Max. :-76.46
## NA's :3 NA's :3
## latitud
## Min. :3.333
## 1st Qu.:3.381
## Median :3.416
## Mean :3.418
## 3rd Qu.:3.452
## Max. :3.498
## NA's :3# Observa los datos nulos en el conjunto de datos
print(colSums(is.na(vivienda)))## id zona piso estrato preciom areaconst
## 3 3 2638 3 2 3
## parqueaderos banios habitaciones tipo barrio longitud
## 1605 3 3 3 3 3
## latitud
## 3# Contabilizar las filas con valores faltantes mayores al 77% o 10/13
filas_NA <- vivienda %>%
mutate(num_faltantes = rowSums(is.na(.))) %>%
filter(num_faltantes >= 10)
filas_NA## # A tibble: 3 × 14
## id zona piso estrato preciom areaconst parqueaderos banios habitaciones
## <dbl> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 NA <NA> <NA> NA NA NA NA NA NA
## 2 NA <NA> <NA> NA NA NA NA NA NA
## 3 NA <NA> <NA> NA 330 NA NA NA NA
## # ℹ 5 more variables: tipo <chr>, barrio <chr>, longitud <dbl>, latitud <dbl>,
## # num_faltantes <dbl># Se excluyen los datos faltantes
datavivienda <- na.omit(vivienda)# Valores únicos tipo de vivienda
unique(datavivienda$tipo)## [1] "Casa" "Apartamento"2.1 Diagrama caja precios
# Identificación de valores atípicos precio
iqr_precio <- quantile(datavivienda$preciom, 0.75) - quantile(datavivienda$preciom, 0.25)
umbral_inferior_precio <- quantile(datavivienda$preciom, 0.25) - 1.5 * iqr_precio
umbral_superior_precio <- quantile(datavivienda$preciom, 0.75) + 1.5 * iqr_precio
outliers_precio <- datavivienda %>%
filter(preciom < umbral_inferior_precio | preciom > umbral_superior_precio)# Boxplot para precio de la vivienda
ggplot(datavivienda, aes(x = "", y = preciom)) +
geom_boxplot(fill = "lightblue", color = "black") +
geom_point(data = outliers_precio, aes(x = 1, y = preciom)) +
geom_hline(yintercept = c(umbral_inferior_precio, umbral_superior_precio),
linetype = "dashed", color = "red", size = 1) +
labs(title = "Valores Atípicos - Precio de la Vivienda",
x = "",
y = "Precio en millones (COP)") +
theme_minimal() +
theme(axis.text.x = element_blank(),
axis.ticks.x = element_blank())## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.
Se observan posibles datos atípicos.
2.2 Diagrama caja area construida
# Identificación de valores atípicos
iqr_area <- quantile(datavivienda$areaconst, 0.75) - quantile(datavivienda$areaconst, 0.25)
umbral_inferior_area <- quantile(datavivienda$areaconst, 0.25) - 1.5 * iqr_area
umbral_superior_area <- quantile(datavivienda$areaconst, 0.75) + 1.5 * iqr_area
outliers_area <- datavivienda %>%
filter(areaconst < umbral_inferior_area | areaconst > umbral_superior_area)# Boxplot para area construida de la vivienda
ggplot(datavivienda, aes(x = "", y = areaconst)) +
geom_boxplot(fill = "lightblue", color = "black") +
geom_point(data = outliers_area, aes(x = 1, y = areaconst)) +
geom_hline(yintercept = c(umbral_inferior_area, umbral_superior_area),
linetype = "dashed", color = "red", size = 1) +
labs(title = "Valores Atípicos - Área Construida",
x = "",
y = "m2") +
theme_minimal() +
theme(axis.text.x = element_blank(),
axis.ticks.x = element_blank())
Se observan posibles datos atípicos.
2.3 Prueba Chi-cuadrado
# Estrato - zona
t_est_zon = table(vivienda$estrato,vivienda$zona)
chisq.test(t_est_zon)##
## Pearson's Chi-squared test
##
## data: t_est_zon
## X-squared = 3830.4, df = 12, p-value < 2.2e-16El valor p muy pequeño (menor que el umbral de significancia 0.05) indica que hay evidencia significativa para rechazar la hipótesis nula de independencia entre las dos variables. Es decir, hay suficiente evidencia para concluir que las dos variables están relacionadas de alguna manera.
# Estrato - tipo
t_est_zon = table(vivienda$estrato,vivienda$tipo)
chisq.test(t_est_zon)##
## Pearson's Chi-squared test
##
## data: t_est_zon
## X-squared = 224.33, df = 3, p-value < 2.2e-16El valor p muy pequeño (menor que el umbral de significancia 0.05) indica que hay evidencia significativa para rechazar la hipótesis nula de independencia entre las dos variables. Es decir, hay suficiente evidencia para concluir que las dos variables están relacionadas de alguna manera.
# Tipo - zona
t_est_zon = table(vivienda$tipo,vivienda$zona)
chisq.test(t_est_zon)##
## Pearson's Chi-squared test
##
## data: t_est_zon
## X-squared = 690.93, df = 4, p-value < 2.2e-16El valor p muy pequeño (menor que el umbral de significancia 0.05) indica que hay evidencia significativa para rechazar la hipótesis nula de independencia entre las dos variables. Es decir, hay suficiente evidencia para concluir que las dos variables están relacionadas de alguna manera.
2.4 Matriz de correlaciones
library(corrplot)## corrplot 0.92 loadedcorrelation_matrix <- cor(datavivienda[, c("habitaciones", "banios", "areaconst","preciom", "estrato")])
corrplot(correlation_matrix, method = "color", addCoef.col = "black")
correlation_table <- as.table(correlation_matrix)
print(correlation_table)## habitaciones banios areaconst preciom estrato
## habitaciones 1.00000000 0.59749611 0.55643197 0.29492577 -0.05218848
## banios 0.59749611 1.00000000 0.68066785 0.68928462 0.40814595
## areaconst 0.55643197 0.68066785 1.00000000 0.69755191 0.26985962
## preciom 0.29492577 0.68928462 0.69755191 1.00000000 0.58698562
## estrato -0.05218848 0.40814595 0.26985962 0.58698562 1.00000000Las 3 correlaciones más fuertes en nuestra data son areaconstr-preciom con 0.7 seguido de banios-preciom con 0.69 y areaconstr-banios con 0.68.
3. Análisis
3.1 Análisis de Conglomerados
Objetivo: Agrupar las propiedades residenciales en segmentos homogéneos con características similares para entender las dinámicas de las ofertas específicas en diferentes partes de la ciudad y en diferentes estratos socioeconómicos.
Es una técnica utilizada en estadística y aprendizaje automático para identificar grupos de objetos o individuos similares en un conjunto de datos. La finalidad principal del análisis de conglomerados es encontrar estructuras intrínsecas o patrones en los datos, agrupando objetos que son más similares entre sí que con aquellos en otros grupos.
## Analisis de conglomerados
datavivienda_ac <- select(datavivienda, estrato, preciom, areaconst, habitaciones, banios)# Estandarización de las variables
datavivienda_ac <- scale(datavivienda_ac)
as.data.frame(datavivienda_ac)## estrato preciom areaconst habitaciones banios
## 1 -0.9046263 -0.175630966 0.760978853 -0.4241459 1.3178809
## 2 0.1749079 -0.605583891 -0.612904129 -0.4241459 -0.9022913
## 3 0.1749079 -0.667005737 -0.634597019 -0.4241459 -0.1622339
## 4 -0.9046263 -0.728427584 -0.887680726 -0.4241459 -0.9022913
## 5 0.1749079 -0.452029275 -0.273048865 0.3272519 -0.1622339
## 6 0.1749079 -0.421318352 -0.179046346 1.8300475 0.5778235
## 7 0.1749079 0.991384115 1.484075159 -0.4241459 -0.1622339
## 8 -0.9046263 0.515364805 1.303301082 1.0786497 1.3178809
## 9 0.1749079 0.899251345 0.450047441 1.8300475 2.0579382
## 10 1.2544421 0.192900112 -0.555056425 -1.1755437 -0.9022913
## 11 -0.9046263 0.438587497 -0.106736715 1.0786497 0.5778235
## 12 0.1749079 -0.114209120 0.182501808 1.0786497 0.5778235
## 13 0.1749079 0.100767342 -0.410437164 0.3272519 0.5778235
## 14 -0.9046263 -0.421318352 -0.482746794 -0.4241459 -0.1622339
## 15 0.1749079 -0.221697351 -0.518901610 -0.4241459 -0.9022913
## 16 -1.9841605 -0.866626738 -0.685213760 -0.4241459 -0.9022913
## 17 1.2544421 1.114227808 1.462382270 0.3272519 0.5778235
## 18 1.2544421 -0.022076350 -0.518901610 0.3272519 -0.1622339
## 19 -0.9046263 -0.513451121 -0.569518351 -0.4241459 -0.9022913
## 20 0.1749079 -0.114209120 -0.367051385 -0.4241459 -0.1622339
## 21 1.2544421 0.500009344 -0.287510792 0.3272519 -0.1622339
## 22 0.1749079 -0.881982200 -0.858756874 -1.1755437 -1.6423486
## 23 -1.9841605 -1.164522693 -0.974452283 -1.1755437 -1.6423486
## 24 1.2544421 1.267782424 0.182501808 -0.4241459 1.3178809
## 25 -0.9046263 -0.897337661 -0.822602058 -0.4241459 -0.9022913
## 26 -0.9046263 -0.897337661 -0.822602058 -1.1755437 -0.9022913
## 27 1.2544421 -0.144920043 -0.395975238 -0.4241459 -0.1622339
## 28 -1.9841605 -0.974114969 -0.829833021 -1.1755437 -0.9022913
## 29 1.2544421 1.974133657 0.298197217 -0.4241459 -0.1622339
## 30 1.2544421 2.066266426 0.450047441 -0.4241459 0.5778235
## 31 -1.9841605 -1.035536816 -0.829833021 -0.4241459 -1.6423486
## 32 1.2544421 4.277452896 0.920060040 -0.4241459 0.5778235
## 33 1.2544421 0.899251345 0.030651583 -0.4241459 0.5778235
## 34 1.2544421 4.584562128 1.628694420 -0.4241459 1.3178809
## 35 1.2544421 1.267782424 0.724824037 0.3272519 1.3178809
## 36 -0.9046263 -0.826702538 -0.764754354 -1.1755437 -0.9022913
## 37 -1.9841605 -0.928048584 -0.822602058 -1.1755437 -0.9022913
## 38 1.2544421 1.667024425 0.544049961 0.3272519 1.3178809
## 39 -1.9841605 -0.897337661 -0.822602058 -1.1755437 -0.9022913
## 40 1.2544421 1.636313502 0.956214855 -0.4241459 0.5778235
## 41 1.2544421 1.820579041 0.471740330 0.3272519 1.3178809
## 42 1.2544421 2.281242889 0.399430699 0.3272519 1.3178809
## 43 -0.9046263 -0.949546231 -0.822602058 -1.1755437 -0.9022913
## 44 -0.9046263 -0.897337661 -0.822602058 -1.1755437 -0.9022913
## 45 -1.9841605 -1.103100847 -0.815371095 -0.4241459 -0.9022913
## 46 1.2544421 0.714985806 0.081268325 0.3272519 0.5778235
## 47 1.2544421 1.513469809 0.305428180 0.3272519 1.3178809
## 48 1.2544421 1.513469809 0.305428180 -0.4241459 0.5778235
## 49 -0.9046263 -0.881982200 -0.815371095 -1.1755437 -0.9022913
## 50 1.2544421 1.206360577 0.081268325 0.3272519 0.5778235
## 51 -1.9841605 -1.063176647 -0.829833021 -0.4241459 -0.9022913
## 52 1.2544421 0.714985806 0.102961214 0.3272519 1.3178809
## 53 1.2544421 0.653563960 -0.019965158 -0.4241459 1.3178809
## 54 0.1749079 0.684274883 0.037882546 -0.4241459 0.5778235
## 55 -0.9046263 -0.897337661 -0.822602058 -1.1755437 -0.9022913
## 56 1.2544421 1.206360577 0.139116029 -0.4241459 1.3178809
## 57 1.2544421 0.684274883 -0.106736715 -0.4241459 1.3178809
## 58 1.2544421 1.037450500 0.341582995 0.3272519 1.3178809
## 59 1.2544421 2.895461353 0.732055000 -0.4241459 0.5778235
## 60 -0.9046263 -1.004825892 -0.895273237 -1.1755437 -1.6423486
## 61 1.2544421 1.974133657 0.399430699 -0.4241459 0.5778235
## 62 1.2544421 2.250531966 0.399430699 -0.4241459 1.3178809
## 63 1.2544421 1.052805961 -0.019965158 1.0786497 2.0579382
## 64 1.2544421 0.837829499 0.110192177 0.3272519 1.3178809
## 65 1.2544421 0.684274883 -0.077812863 -0.4241459 0.5778235
## 66 -0.9046263 -0.989470431 -0.902142652 -1.1755437 -0.9022913
## 67 1.2544421 1.992560211 0.262042401 -0.4241459 0.5778235
## 68 1.2544421 2.588352121 0.399430699 -0.4241459 0.5778235
## 69 -0.9046263 2.741906737 0.370506847 0.3272519 1.3178809
## 70 1.2544421 1.359915193 0.066806399 -0.4241459 0.5778235
## 71 1.2544421 1.605602579 0.146346992 1.0786497 0.5778235
## 72 1.2544421 2.741906737 0.399430699 0.3272519 1.3178809
## 73 1.2544421 1.820579041 0.298197217 -0.4241459 1.3178809
## 74 1.2544421 -0.114209120 -0.497208720 -0.4241459 -0.9022913
## 75 1.2544421 2.434797505 2.084245093 0.3272519 2.0579382
## 76 -1.9841605 0.592142113 0.471740330 0.3272519 0.5778235
## 77 -1.9841605 0.131478266 1.296070119 0.3272519 -0.9022913
## 78 -1.9841605 -0.498095660 0.182501808 4.0842409 1.3178809
## 79 -1.9841605 -1.035536816 -0.656289908 -0.4241459 -0.9022913
## 80 -1.9841605 -0.897337661 -0.865987837 -0.4241459 -0.9022913
## 81 -0.9046263 -0.559517506 -0.395975238 0.3272519 -0.9022913
## 82 -1.9841605 -0.728427584 -0.179046346 0.3272519 -0.9022913
## 83 -0.9046263 -0.989470431 -0.829833021 -0.4241459 -0.9022913
## 84 -0.9046263 -0.728427584 -0.721368575 -0.4241459 -0.9022913
## 85 -1.9841605 -0.759138507 -0.743061465 -0.4241459 -0.9022913
## 86 -1.9841605 -0.820560353 1.701004051 -1.1755437 -0.9022913
## 87 -1.9841605 -1.050892277 -0.461053905 0.3272519 -0.9022913
## 88 -1.9841605 -0.789849430 -0.207970198 0.3272519 -0.9022913
## 89 -1.9841605 -0.166417689 1.512999011 1.0786497 -0.1622339
## 90 -1.9841605 -1.225944539 -0.902142652 -1.1755437 -1.6423486
## 91 -1.9841605 -0.636294814 0.905598114 4.0842409 1.3178809
## 92 -1.9841605 -0.175630966 -0.085043826 -0.4241459 -0.1622339
## 93 -1.9841605 -0.728427584 1.990242573 2.5814453 0.5778235
## 94 -1.9841605 -0.697716661 -0.808140132 -1.1755437 -0.9022913
## 95 0.1749079 0.592142113 0.182501808 -0.4241459 0.5778235
## 96 0.1749079 0.346454728 -0.229663087 0.3272519 0.5778235
## 97 0.1749079 -0.347612136 -0.489977757 -0.4241459 -0.9022913
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## 570 1.2544421 0.100767342 -0.215201161 0.3272519 0.5778235
## 571 1.2544421 -0.022076350 -0.395975238 -0.4241459 0.5778235
## 572 1.2544421 -0.022076350 -0.395975238 -0.4241459 -0.1622339
## 573 1.2544421 0.592142113 -0.215201161 0.3272519 0.5778235
## 574 1.2544421 1.329204270 0.522357071 1.0786497 1.3178809
## 575 1.2544421 0.438587497 -0.215201161 -0.4241459 0.5778235
## 576 1.2544421 1.298493347 0.616359591 1.0786497 1.3178809
## 577 0.1749079 -0.298474659 -0.410437164 -0.4241459 -0.9022913
## 578 0.1749079 -0.022076350 -0.374282348 -0.4241459 -0.1622339
## 579 0.1749079 -0.022076350 -0.374282348 -0.4241459 -0.1622339
## 580 0.1749079 1.144938731 0.905598114 1.0786497 1.3178809
## 581 1.2544421 2.281242889 1.079141227 0.3272519 0.5778235
## 582 1.2544421 3.816789048 0.544049961 -0.4241459 -0.1622339
## 583 1.2544421 2.895461353 2.351790726 0.3272519 0.5778235
## 584 1.2544421 -0.329185582 -0.352589459 -0.4241459 -0.1622339
## 585 1.2544421 -0.022076350 -0.417668127 0.3272519 0.5778235
## 586 1.2544421 0.899251345 1.028524486 1.0786497 2.0579382
## 587 1.2544421 0.285032881 -0.150122493 -0.4241459 -0.1622339
## 588 1.2544421 0.576786652 2.641029249 0.3272519 0.5778235
## 589 1.2544421 -0.329185582 -0.511670647 -0.4241459 -0.9022913
## 590 1.2544421 4.123898280 4.231841123 1.0786497 2.0579382
## 591 1.2544421 0.853184960 0.551280924 1.8300475 2.0579382
## 592 0.1749079 0.745696729 -0.265817902 0.3272519 1.3178809
## 593 1.2544421 0.991384115 1.708235014 0.3272519 1.3178809
## 594 0.1749079 -0.329185582 -0.352589459 0.3272519 -0.1622339
## 595 1.2544421 2.281242889 1.773313681 1.0786497 1.3178809
## 596 1.2544421 3.202570584 0.797133668 -0.4241459 0.5778235
## 597 1.2544421 1.329204270 0.833288483 1.0786497 1.3178809
## 598 1.2544421 0.285032881 -0.280279829 0.3272519 0.5778235
## 599 1.2544421 2.588352121 1.628694420 1.0786497 2.0579382
## 600 1.2544421 0.714985806 1.990242573 -0.4241459 -0.1622339
## 601 1.2544421 1.151080915 0.276504327 -0.4241459 -0.9022913
## 602 1.2544421 0.675061606 -0.482746794 -0.4241459 -0.9022913
## 603 1.2544421 0.008634573 -0.215201161 -0.4241459 1.3178809
## 604 1.2544421 1.206360577 2.568719618 -0.4241459 0.5778235
## 605 1.2544421 1.974133657 1.194836636 -0.4241459 1.3178809
## 606 0.1749079 0.546075729 -0.106736715 0.3272519 0.5778235
## 607 0.1749079 2.050910965 1.252684341 1.0786497 1.3178809
## 608 0.1749079 2.895461353 1.267146267 1.0786497 1.3178809
## 609 0.1749079 1.237071500 0.905598114 1.0786497 1.3178809
## 610 0.1749079 1.206360577 0.674207296 0.3272519 -0.1622339
## 611 1.2544421 2.281242889 1.773313681 1.0786497 2.0579382
## 612 1.2544421 0.714985806 0.037882546 0.3272519 1.3178809
## 613 1.2544421 -0.022076350 -0.504439683 0.3272519 0.5778235
## 614 0.1749079 1.359915193 2.243326281 1.0786497 0.5778235
## 615 1.2544421 1.267782424 2.279481096 1.0786497 2.0579382
## 616 1.2544421 1.206360577 0.905598114 1.0786497 2.0579382
## 617 1.2544421 3.049015969 1.715465977 1.0786497 2.0579382
## 618 1.2544421 3.049015969 5.461104844 1.0786497 2.0579382
## 619 0.1749079 1.667024425 2.785648510 1.0786497 3.5380530
## 620 1.2544421 0.223611035 0.001727731 1.0786497 0.5778235
## 621 1.2544421 1.206360577 1.628694420 -0.4241459 1.3178809
## 622 1.2544421 0.837829499 0.616359591 1.8300475 2.0579382
## 623 1.2544421 0.745696729 0.493433219 1.0786497 2.0579382
## 624 1.2544421 1.513469809 0.587435739 0.3272519 2.0579382
## 625 1.2544421 2.434797505 3.971526453 1.8300475 2.0579382
## 626 1.2544421 -0.636294814 -0.583980277 -0.4241459 -0.9022913
## 627 1.2544421 0.991384115 0.905598114 0.3272519 1.3178809
## 628 1.2544421 1.037450500 0.905598114 0.3272519 2.0579382
## 629 1.2544421 1.037450500 0.905598114 0.3272519 2.0579382
## 630 1.2544421 0.023990034 -0.251355976 0.3272519 1.3178809
## 631 1.2544421 1.206360577 0.601897665 0.3272519 0.5778235
## 632 0.1749079 -0.022076350 0.110192177 -0.4241459 0.5778235
## 633 1.2544421 0.033203311 0.081268325 1.0786497 0.5778235
## 634 0.1749079 -0.022076350 -0.301972718 -0.4241459 0.5778235
## 635 1.2544421 1.206360577 0.544049961 1.0786497 1.3178809
## 636 1.2544421 0.131478266 -0.215201161 0.3272519 0.5778235
## 637 1.2544421 0.899251345 0.182501808 0.3272519 1.3178809
## 638 1.2544421 1.605602579 5.967272258 0.3272519 1.3178809
## 639 1.2544421 1.052805961 0.760978853 0.3272519 1.3178809
## 640 1.2544421 1.206360577 0.601897665 0.3272519 0.5778235
## 641 1.2544421 1.513469809 2.496409988 2.5814453 3.5380530
## 642 1.2544421 0.868540422 1.028524486 -0.4241459 -0.9022913
## 643 1.2544421 0.745696729 0.225887586 0.3272519 0.5778235
## 644 1.2544421 2.834039506 1.484075159 0.3272519 1.3178809
## 645 1.2544421 1.206360577 5.678033736 1.8300475 1.3178809
## 646 0.1749079 1.452047963 0.601897665 0.3272519 1.3178809
## 647 1.2544421 2.741906737 1.144219895 0.3272519 2.0579382
## 648 1.2544421 0.054700958 -0.265817902 -1.1755437 -0.9022913
## 649 1.2544421 1.359915193 2.351790726 1.8300475 2.7979956
## 650 1.2544421 1.513469809 1.115296043 -0.4241459 -0.1622339
## 651 1.2544421 3.049015969 2.568719618 1.0786497 2.7979956
## 652 1.2544421 0.745696729 -0.034427084 -0.4241459 0.5778235
## 653 1.2544421 1.206360577 1.071910264 0.3272519 0.5778235
## 654 1.2544421 0.684274883 4.521079645 0.3272519 1.3178809
## 655 1.2544421 0.438587497 1.990242573 1.8300475 0.5778235
## 656 1.2544421 0.883895884 1.028524486 0.3272519 0.5778235
## 657 1.2544421 1.513469809 0.905598114 1.0786497 1.3178809
## 658 1.2544421 1.206360577 1.310532045 1.0786497 -0.1622339
## 659 1.2544421 0.070056419 -0.576749314 -0.4241459 -0.9022913
## 660 1.2544421 2.803328583 1.990242573 0.3272519 0.5778235
## 661 1.2544421 0.730341268 0.377737810 -0.4241459 -0.1622339
## 662 0.1749079 1.452047963 1.122527006 1.0786497 1.3178809
## 663 1.2544421 0.377165651 0.037882546 -0.4241459 0.5778235
## 664 1.2544421 2.434797505 0.905598114 -0.4241459 0.5778235
## 665 1.2544421 -0.144920043 -0.367051385 -0.4241459 -0.1622339
## 666 1.2544421 0.285032881 0.168039881 0.3272519 0.5778235
## 667 1.2544421 1.052805961 1.267146267 0.3272519 1.3178809
## 668 1.2544421 0.899251345 0.905598114 1.0786497 1.3178809
## 669 0.1749079 0.131478266 0.225887586 1.0786497 2.0579382
## 670 1.2544421 0.714985806 0.370506847 0.3272519 0.5778235
## 671 1.2544421 0.592142113 -0.164584420 -0.4241459 0.5778235
## 672 1.2544421 -0.022076350 -0.193508272 -0.4241459 -0.1622339
## 673 1.2544421 2.265887427 2.496409988 1.0786497 2.0579382
## 674 1.2544421 1.052805961 0.666976333 -0.4241459 0.5778235
## 675 1.2544421 1.359915193 0.811595594 0.3272519 0.5778235
## 676 1.2544421 1.267782424 1.050217375 0.3272519 0.5778235
## 677 1.2544421 0.653563960 0.370506847 0.3272519 0.5778235
## 678 1.2544421 2.281242889 2.387945542 1.0786497 2.7979956
## 679 1.2544421 0.899251345 1.628694420 0.3272519 1.3178809
## 680 1.2544421 1.206360577 0.724824037 0.3272519 1.3178809
## 681 1.2544421 0.745696729 0.254811438 0.3272519 1.3178809
## 682 1.2544421 1.206360577 0.948983892 0.3272519 0.5778235
## 683 1.2544421 1.513469809 1.469613233 -0.4241459 1.3178809
## 684 1.2544421 3.141148738 1.447920344 0.3272519 1.3178809
## 685 1.2544421 0.684274883 0.789902705 -0.4241459 1.3178809
## 686 1.2544421 0.730341268 0.037882546 0.3272519 1.3178809
## 687 1.2544421 1.974133657 1.852854275 0.3272519 0.5778235
## 688 1.2544421 0.991384115 1.122527006 0.3272519 0.5778235
## 689 1.2544421 3.816789048 0.905598114 0.3272519 0.5778235
## 690 1.2544421 -0.022076350 -0.070581900 -0.4241459 0.5778235
## 691 1.2544421 0.684274883 0.500664182 0.3272519 1.3178809
## 692 1.2544421 0.346454728 0.905598114 0.3272519 -0.1622339
## 693 1.2544421 3.816789048 1.390072639 1.0786497 2.7979956
## 694 1.2544421 1.206360577 1.701004051 -0.4241459 0.5778235
## 695 1.2544421 0.991384115 0.377737810 0.3272519 0.5778235
## 696 0.1749079 0.714985806 -0.041658047 0.3272519 1.3178809
## 697 1.2544421 0.377165651 -0.323665607 0.3272519 1.3178809
## 698 1.2544421 -0.022076350 -0.106736715 -0.4241459 -0.1622339
## 699 1.2544421 2.895461353 3.212275331 1.0786497 2.7979956
## 700 1.2544421 1.206360577 1.267146267 0.3272519 1.3178809
## 701 1.2544421 0.131478266 0.298197217 -0.4241459 1.3178809
## 702 1.2544421 0.377165651 -0.323665607 0.3272519 1.3178809
## 703 1.2544421 0.500009344 1.990242573 1.8300475 1.3178809
## 704 1.2544421 1.175649654 0.905598114 0.3272519 2.0579382
## 705 1.2544421 3.970343664 1.209298563 0.3272519 1.3178809
## 706 1.2544421 1.206360577 0.392199736 0.3272519 2.0579382
## 707 1.2544421 1.206360577 0.666976333 1.0786497 2.7979956
## 708 1.2544421 0.653563960 0.370506847 -0.4241459 1.3178809
## 709 1.2544421 1.052805961 0.544049961 0.3272519 1.3178809
## 710 1.2544421 3.509679816 6.328820411 1.8300475 2.7979956
## 711 1.2544421 1.329204270 0.833288483 -0.4241459 0.5778235
## 712 1.2544421 1.206360577 0.601897665 -0.4241459 1.3178809
## 713 1.2544421 0.899251345 0.905598114 0.3272519 0.5778235
## 714 1.2544421 0.530720267 1.628694420 0.3272519 2.0579382
## 715 1.2544421 1.052805961 1.990242573 0.3272519 2.0579382
## 716 1.2544421 0.899251345 0.204194697 0.3272519 0.5778235
## 717 1.2544421 1.160294192 1.086372190 0.3272519 1.3178809
## 718 1.2544421 1.359915193 1.809468497 0.3272519 2.0579382
## 719 1.2544421 0.899251345 0.760978853 -0.4241459 1.3178809
## 720 1.2544421 0.807118576 -0.179046346 1.0786497 1.3178809
## 721 1.2544421 1.298493347 0.760978853 0.3272519 1.3178809
## 722 1.2544421 1.605602579 0.652514407 0.3272519 1.3178809
## 723 1.2544421 2.127688273 2.279481096 -0.4241459 2.0579382
## 724 1.2544421 2.127688273 1.628694420 0.3272519 2.0579382
## 725 1.2544421 -0.098853658 0.037882546 -0.4241459 0.5778235
## 726 1.2544421 3.356125200 1.324993972 0.3272519 1.3178809
## 727 1.2544421 1.974133657 1.766082718 1.0786497 1.3178809
## 728 1.2544421 0.991384115 0.500664182 1.8300475 2.0579382
## 729 1.2544421 1.421337039 0.833288483 0.3272519 1.3178809
## 730 1.2544421 3.389907216 1.621463457 -0.4241459 0.5778235
## 731 1.2544421 2.895461353 0.905598114 -0.4241459 1.3178809
## 732 1.2544421 0.899251345 0.797133668 0.3272519 1.3178809
## 733 1.2544421 0.899251345 -0.063350937 -0.4241459 1.3178809
## 734 1.2544421 3.816789048 1.390072639 0.3272519 2.0579382
## 735 1.2544421 -0.283119198 -0.482746794 -0.4241459 -0.1622339
## 736 1.2544421 -0.421318352 -0.634597019 -0.4241459 -0.1622339
## 737 1.2544421 -0.452029275 -0.693890916 -0.4241459 -0.9022913
## 738 1.2544421 3.509679816 1.773313681 0.3272519 2.0579382
## 739 1.2544421 3.356125200 1.447920344 1.0786497 2.7979956
## 740 1.2544421 1.974133657 1.339455898 -0.4241459 0.5778235
## 741 1.2544421 0.315743805 -0.265817902 -0.4241459 0.5778235
## 742 1.2544421 1.421337039 0.905598114 0.3272519 0.5778235
## 743 0.1749079 1.820579041 1.122527006 0.3272519 0.5778235
## 744 1.2544421 0.423232036 -0.207970198 0.3272519 0.5778235
## 745 1.2544421 3.663234432 0.471740330 2.5814453 3.5380530
## 746 0.1749079 1.667024425 2.351790726 0.3272519 1.3178809
## 747 1.2544421 -0.022076350 0.544049961 0.3272519 -0.1622339
## 748 1.2544421 0.592142113 0.370506847 1.0786497 1.3178809
## 749 1.2544421 0.223611035 -0.179046346 -0.4241459 0.5778235
## 750 1.2544421 0.177544650 -0.800909169 0.3272519 0.5778235
## 751 1.2544421 0.054700958 -0.106736715 -0.4241459 0.5778235
## 752 1.2544421 0.653563960 0.471740330 -0.4241459 0.5778235
## 753 0.1749079 -0.022076350 -0.301972718 -0.4241459 0.5778235
## 754 1.2544421 -0.405962890 -0.591211240 -0.4241459 -0.9022913
## 755 0.1749079 0.622853037 -0.179046346 -0.4241459 0.5778235
## 756 0.1749079 0.131478266 0.218656623 0.3272519 1.3178809
## 757 0.1749079 0.131478266 0.218656623 0.3272519 1.3178809
## 758 0.1749079 0.008634573 0.218656623 0.3272519 0.5778235
## 759 1.2544421 1.974133657 1.787775608 1.0786497 1.3178809
## 760 1.2544421 -0.470455829 -0.721368575 -1.1755437 -0.9022913
## 761 1.2544421 0.223611035 -0.251355976 0.3272519 0.5778235
## 762 1.2544421 -0.022076350 -0.106736715 0.3272519 -0.1622339
## 763 1.2544421 2.281242889 2.988115476 2.5814453 2.7979956
## 764 1.2544421 3.755367202 6.256510781 1.0786497 2.7979956
## 765 -0.9046263 -0.774493969 -0.721368575 -0.4241459 0.5778235
## 766 1.2544421 0.070056419 -0.301972718 1.0786497 -0.1622339
## 767 1.2544421 0.346454728 -0.323665607 0.3272519 0.5778235
## 768 1.2544421 3.202570584 2.351790726 -0.4241459 2.0579382
## 769 1.2544421 2.434797505 0.486202256 0.3272519 -0.1622339
## 770 1.2544421 3.356125200 1.447920344 -0.4241459 -0.1622339
## 771 1.2544421 0.346454728 -0.287510792 -0.4241459 -0.1622339
## 772 1.2544421 -0.086569289 -0.207970198 -0.4241459 -0.1622339
## 773 1.2544421 0.131478266 0.218656623 1.0786497 1.3178809
## 774 1.2544421 0.131478266 0.037882546 -0.4241459 0.5778235
## 775 1.2544421 0.223611035 -0.056119974 -0.4241459 1.3178809
## 776 1.2544421 1.974133657 1.744389829 1.0786497 2.0579382
## 777 1.2544421 0.407876574 0.262042401 -0.4241459 -0.1622339
## 778 1.2544421 0.285032881 -0.106736715 -0.4241459 -0.1622339
## 779 1.2544421 -0.144920043 -0.179046346 -0.4241459 0.5778235
## 780 1.2544421 0.684274883 0.478971293 -0.4241459 0.5778235
## 781 1.2544421 0.254321958 0.218656623 1.8300475 1.3178809
## 782 1.2544421 0.592142113 -0.034427084 0.3272519 0.5778235
## 783 1.2544421 1.267782424 0.117423140 -0.4241459 0.5778235
## 784 0.1749079 -0.452029275 -0.583980277 -0.4241459 -0.9022913
## 785 1.2544421 0.285032881 -0.280279829 0.3272519 0.5778235
## 786 1.2544421 0.192900112 -0.395975238 -0.4241459 -0.1622339
## 787 1.2544421 0.131478266 0.760978853 1.0786497 1.3178809
## 788 1.2544421 0.192900112 -0.179046346 0.3272519 0.5778235
## 789 1.2544421 0.192900112 0.001727731 0.3272519 1.3178809
## 790 1.2544421 0.285032881 -0.323665607 0.3272519 -0.1622339
## 791 1.2544421 0.192900112 -0.063350937 0.3272519 1.3178809
## 792 1.2544421 0.592142113 -0.106736715 -0.4241459 1.3178809
## 793 1.2544421 0.039345496 -0.793678206 0.3272519 0.5778235
## 794 1.2544421 0.223611035 -0.070581900 -0.4241459 0.5778235
## 795 1.2544421 0.039345496 -0.179046346 0.3272519 0.5778235
## 796 1.2544421 0.070056419 -0.106736715 1.0786497 1.3178809
## 797 1.2544421 0.238966497 0.218656623 -0.4241459 -0.1622339
## 798 1.2544421 0.223611035 -0.164584420 -0.4241459 -0.1622339
## 799 1.2544421 3.509679816 5.316485582 2.5814453 4.2781104
## 800 1.2544421 -0.114209120 -0.179046346 0.3272519 0.5778235
## 801 1.2544421 0.039345496 -0.092274789 1.0786497 -0.1622339
## 802 1.2544421 0.223611035 -0.041658047 0.3272519 0.5778235
## 803 1.2544421 2.127688273 2.641029249 1.8300475 3.5380530
## 804 1.2544421 2.588352121 3.074887033 1.0786497 2.7979956
## 805 1.2544421 1.620958040 2.062552204 0.3272519 2.7979956
## 806 1.2544421 -0.175630966 -0.265817902 0.3272519 1.3178809
## 807 1.2544421 -0.114209120 -0.265817902 0.3272519 1.3178809
## 808 1.2544421 0.622853037 -0.048889011 0.3272519 0.5778235
## 809 1.2544421 1.206360577 0.117423140 -0.4241459 0.5778235
## 810 0.1749079 4.123898280 2.207171465 2.5814453 3.5380530
## 811 1.2544421 0.116122804 -0.779216280 0.3272519 0.5778235
## 812 1.2544421 3.202570584 2.351790726 1.0786497 1.3178809
## 813 1.2544421 3.202570584 2.207171465 -0.4241459 0.5778235
## 814 1.2544421 0.622853037 0.254811438 -0.4241459 1.3178809
## 815 1.2544421 -0.160275505 -0.179046346 0.3272519 1.3178809
## 816 0.1749079 0.622853037 -0.121198641 -0.4241459 0.5778235
## 817 1.2544421 3.509679816 3.291815925 0.3272519 2.7979956
## 818 1.2544421 -0.098853658 -0.468284868 -0.4241459 -0.1622339
## 819 1.2544421 1.974133657 1.484075159 0.3272519 0.5778235
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## 842 0.1749079 2.281242889 2.351790726 1.8300475 2.7979956
## 843 1.2544421 -0.190986428 -0.482746794 -0.4241459 -0.1622339
## 844 1.2544421 1.206360577 0.088499288 0.3272519 1.3178809
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## 878 1.2544421 1.513469809 0.811595594 -0.4241459 1.3178809
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## 886 1.2544421 3.816789048 0.833288483 -0.4241459 0.5778235
## 887 1.2544421 0.592142113 0.059575435 -0.4241459 -0.1622339
## 888 1.2544421 -0.482740198 -0.605673166 -0.4241459 -0.9022913
## 889 1.2544421 0.592142113 0.074037362 -0.4241459 -0.1622339
## 890 1.2544421 1.206360577 0.124654103 -0.4241459 1.3178809
## 891 1.2544421 0.991384115 -0.179046346 -0.4241459 0.5778235
## 892 1.2544421 -0.375251967 -0.580364796 -0.4241459 -0.9022913
## 893 1.2544421 0.438587497 0.059575435 -0.4241459 -0.9022913
## 894 1.2544421 2.741906737 1.910701980 0.3272519 2.0579382
## 895 1.2544421 2.127688273 1.223760489 1.0786497 1.3178809
## 896 1.2544421 2.127688273 1.238222415 1.0786497 2.0579382
## 897 1.2544421 0.592142113 0.074037362 0.3272519 0.5778235
## 898 1.2544421 0.592142113 0.348813958 -0.4241459 1.3178809
## 899 1.2544421 2.127688273 2.091476056 1.0786497 2.0579382
## 900 1.2544421 0.592142113 0.074037362 0.3272519 0.5778235
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## 911 1.2544421 0.453942959 -0.424899090 -1.1755437 0.5778235
## 912 1.2544421 3.202570584 0.471740330 1.8300475 1.3178809
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## 926 1.2544421 -0.390607429 -0.591211240 -0.4241459 -0.9022913
## 927 1.2544421 0.929962268 0.182501808 -0.4241459 -0.9022913
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## 931 1.2544421 1.206360577 1.267146267 0.3272519 0.5778235
## 932 1.2544421 4.431007512 1.050217375 3.3328431 1.3178809
## 933 1.2544421 1.513469809 3.074887033 0.3272519 0.5778235
## 934 1.2544421 4.123898280 3.002577402 0.3272519 1.3178809
## 935 1.2544421 0.899251345 0.905598114 0.3272519 2.0579382
## 936 1.2544421 2.281242889 2.351790726 0.3272519 -0.1622339
## 937 1.2544421 1.974133657 2.641029249 2.5814453 2.7979956
## 938 1.2544421 2.895461353 0.905598114 1.0786497 2.0579382
## 939 1.2544421 3.816789048 2.713338880 0.3272519 2.0579382
## 940 1.2544421 0.899251345 -0.244125013 -1.1755437 1.3178809
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## 967 1.2544421 0.684274883 0.616359591 1.0786497 1.3178809
## 968 1.2544421 2.434797505 3.074887033 1.8300475 2.0579382
## 969 0.1749079 0.745696729 0.760978853 1.0786497 1.3178809
## 970 0.1749079 0.745696729 0.110192177 1.0786497 1.3178809
## 971 1.2544421 2.434797505 3.074887033 1.8300475 2.0579382
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## 974 1.2544421 1.820579041 2.207171465 0.3272519 1.3178809
## 975 0.1749079 2.281242889 1.484075159 1.0786497 0.5778235
## 976 1.2544421 2.281242889 4.521079645 1.8300475 2.7979956
## 977 1.2544421 2.434797505 3.508744817 2.5814453 3.5380530
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## 979 0.1749079 0.592142113 0.724824037 1.0786497 1.3178809
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## 1017 1.2544421 1.513469809 1.990242573 0.3272519 0.5778235
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## 1024 1.2544421 0.899251345 1.773313681 1.0786497 1.3178809
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## 1033 1.2544421 0.500009344 -0.229663087 -0.4241459 0.5778235
## 1034 1.2544421 3.478968893 2.568719618 0.3272519 1.3178809
## 1035 1.2544421 1.022095038 1.628694420 -0.4241459 1.3178809
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## 1749 -0.9046263 0.285032881 1.368379750 1.0786497 -0.1622339
## 1750 0.1749079 0.094625158 0.182501808 -1.1755437 0.5778235
## 1751 -0.9046263 -0.881982200 -0.569518351 -1.1755437 -0.1622339
## 1752 0.1749079 -0.605583891 -0.540594499 -0.4241459 -0.9022913
## 1753 0.1749079 0.100767342 -0.489977757 -0.4241459 -0.9022913
## 1754 0.1749079 -0.728427584 -0.504439683 0.3272519 -0.1622339
## 1755 -1.9841605 -0.390607429 0.110192177 3.3328431 0.5778235
## 1756 -0.9046263 -0.881982200 -0.793678206 -1.1755437 -0.9022913
## 1757 0.1749079 0.131478266 1.194836636 1.8300475 1.3178809
## 1758 -0.9046263 0.162189189 0.254811438 0.3272519 0.5778235
## 1759 0.1749079 0.269677420 0.254811438 1.0786497 -0.1622339
## 1760 0.1749079 2.127688273 1.773313681 0.3272519 -0.1622339
## 1761 0.1749079 -0.482740198 0.247580475 1.0786497 0.5778235
## 1762 0.1749079 0.039345496 0.833288483 1.8300475 1.3178809
## 1763 0.1749079 0.438587497 0.905598114 -0.4241459 1.3178809
## 1764 -0.9046263 -0.937261861 -0.649058945 0.3272519 -0.1622339
## 1765 0.1749079 0.899251345 1.245453378 3.3328431 1.3178809
## 1766 0.1749079 -0.237052813 1.628694420 1.8300475 0.5778235
## 1767 0.1749079 -0.267763736 0.182501808 0.3272519 -0.1622339
## 1768 0.1749079 0.192900112 1.701004051 2.5814453 2.0579382
## 1769 0.1749079 0.807118576 1.939625832 4.0842409 2.7979956
## 1770 0.1749079 -0.728427584 -0.569518351 0.3272519 -0.1622339
## 1771 0.1749079 -0.728427584 -0.569518351 0.3272519 -0.1622339
## 1772 0.1749079 0.837829499 2.026397389 3.3328431 1.3178809
## 1773 1.2544421 -0.544162045 -0.352589459 -0.4241459 -0.1622339
## 1774 -0.9046263 -0.881982200 -0.829833021 -1.1755437 -0.9022913
## 1775 0.1749079 -0.574872968 -0.482746794 0.3272519 -0.1622339
## 1776 0.1749079 -0.574872968 -0.649058945 -0.4241459 -0.9022913
## 1777 -0.9046263 0.192900112 1.267146267 0.3272519 -0.9022913
## 1778 1.2544421 0.131478266 0.464509367 1.0786497 -0.1622339
## 1779 -0.9046263 -0.068142735 0.883905225 1.0786497 0.5778235
## 1780 -0.9046263 -0.129564582 0.883905225 -2.6783393 -0.9022913
## 1781 0.1749079 0.070056419 0.854981372 1.0786497 -0.9022913
## 1782 0.1749079 1.974133657 2.351790726 1.0786497 1.3178809
## 1783 0.1749079 0.131478266 -0.215201161 -0.4241459 -0.1622339
## 1784 -0.9046263 -0.805204892 -0.851525911 -1.1755437 -1.6423486
## 1785 0.1749079 -0.452029275 -0.627366056 -1.9269415 -0.9022913
## 1786 0.1749079 -0.175630966 0.327121069 0.3272519 0.5778235
## 1787 0.1749079 -0.697716661 -0.685213760 -1.1755437 -0.1622339
## 1788 0.1749079 -0.129564582 0.879349718 1.0786497 0.5778235
## 1789 0.1749079 -0.144920043 0.023420620 0.3272519 0.5778235
## 1790 0.1749079 0.435516405 1.650387309 2.5814453 2.7979956
## 1791 0.1749079 -0.022076350 0.023420620 1.0786497 0.5778235
## 1792 0.1749079 0.331099266 0.905598114 1.0786497 0.5778235
## 1793 0.1749079 0.331099266 0.652514407 1.0786497 2.0579382
## 1794 -0.9046263 -0.022076350 -0.034427084 -0.4241459 -0.9022913
## 1795 0.1749079 -0.022076350 0.760978853 0.3272519 -0.1622339
## 1796 0.1749079 -0.114209120 0.760978853 1.0786497 0.5778235
## 1797 0.1749079 0.377165651 2.315635911 0.3272519 -0.1622339
## 1798 0.1749079 -0.605583891 -0.656289908 -1.1755437 -0.9022913
## 1799 -0.9046263 -0.636294814 -0.757523391 -1.1755437 -0.9022913
## 1800 0.1749079 -0.728427584 -0.743061465 0.3272519 -0.1622339
## 1801 -0.9046263 -0.667005737 -0.612904129 -0.4241459 -0.9022913
## 1802 -0.9046263 -0.544162045 -0.468284868 -0.4241459 -0.1622339
## 1803 -1.9841605 0.745696729 0.905598114 0.3272519 1.3178809
## 1804 -1.9841605 -0.989470431 -0.721368575 -0.4241459 -0.9022913
## 1805 1.2544421 2.281242889 4.000450305 4.0842409 2.7979956
## 1806 0.1749079 -0.482740198 -0.612904129 0.3272519 -0.1622339
## 1807 -0.9046263 -1.020181354 -0.743061465 -1.1755437 -0.9022913
## 1808 1.2544421 0.592142113 0.356044921 -0.4241459 1.3178809
## 1809 1.2544421 0.039345496 -0.316434644 -0.4241459 -0.1622339
## 1810 1.2544421 -0.206341890 -0.540594499 -1.1755437 -0.1622339
## 1811 1.2544421 -0.114209120 -0.656289908 -1.1755437 -0.1622339
## 1812 0.1749079 -0.037431812 -0.316434644 -0.4241459 -0.1622339
## 1813 1.2544421 0.039345496 0.349537054 1.0786497 -0.1622339
## 1814 0.1749079 0.899251345 1.628694420 1.0786497 1.3178809
## 1815 0.1749079 1.820579041 4.882627799 1.0786497 1.3178809
## 1816 1.2544421 0.070056419 -0.432130053 -0.4241459 -0.1622339
## 1817 0.1749079 -0.022076350 -0.179046346 -0.4241459 -0.1622339
## 1818 1.2544421 0.745696729 2.062552204 1.0786497 2.0579382
## 1819 1.2544421 1.513469809 0.666976333 0.3272519 1.3178809
## 1820 1.2544421 0.570644467 0.361395834 0.3272519 1.3178809
## 1821 1.2544421 1.912711811 3.436435186 2.5814453 -2.3824060
## 1822 1.2544421 1.206360577 4.058298009 4.0842409 3.5380530
## 1823 1.2544421 1.513469809 2.120399908 2.5814453 3.5380530
## 1824 1.2544421 -0.851271277 -0.869386389 -1.9269415 -0.9022913
## 1825 0.1749079 -0.160275505 -0.005503232 0.3272519 0.5778235
## 1826 1.2544421 0.899251345 0.052344472 -0.4241459 -0.1622339
## 1827 1.2544421 -0.022076350 -0.649058945 -1.1755437 -0.1622339
## 1828 1.2544421 0.899251345 0.196963734 -0.4241459 0.5778235
## 1829 1.2544421 1.513469809 0.616359591 -0.4241459 0.5778235
## 1830 0.1749079 1.605602579 0.847750409 -0.4241459 1.3178809
## 1831 1.2544421 0.960673192 0.240349512 -0.4241459 -0.1622339
## 1832 1.2544421 1.206360577 0.977907744 0.3272519 0.5778235
## 1833 1.2544421 1.513469809 0.616359591 -0.4241459 0.5778235
## 1834 1.2544421 -0.083498197 0.283735290 -0.4241459 0.5778235
## 1835 1.2544421 1.974133657 0.534649709 0.3272519 1.3178809
## 1836 1.2544421 2.281242889 0.717593074 -1.1755437 0.5778235
## 1837 0.1749079 2.434797505 0.977907744 0.3272519 1.3178809
## 1838 0.1749079 0.192900112 0.327121069 0.3272519 0.5778235
## 1839 -1.9841605 -0.605583891 -0.352589459 -0.4241459 -1.6423486
## 1840 -1.9841605 -0.667005737 -0.106736715 -0.4241459 -0.9022913
## 1841 -1.9841605 -0.617868260 -0.265817902 -0.4241459 -1.6423486
## 1842 -1.9841605 -0.083498197 0.348813958 2.5814453 1.3178809
## 1843 -1.9841605 -0.636294814 -0.034427084 1.0786497 -0.9022913
## 1844 -1.9841605 -0.728427584 -0.179046346 0.3272519 -0.1622339
## 1845 -1.9841605 -0.682361199 -0.200739235 1.0786497 0.5778235
## 1846 -1.9841605 -0.636294814 -0.034427084 1.0786497 -0.9022913
## 1847 -1.9841605 -0.206341890 0.927291003 2.5814453 0.5778235
## 1848 -1.9841605 -0.636294814 -0.179046346 4.0842409 -0.9022913
## 1849 -1.9841605 -1.050892277 -0.829833021 -0.4241459 -1.6423486
## 1850 -0.9046263 -0.795991615 -0.641827982 -0.4241459 -0.1622339
## 1851 -1.9841605 -1.004825892 -0.873218800 -0.4241459 -0.9022913
## 1852 -1.9841605 -1.004825892 -0.873218800 -0.4241459 -0.9022913
## 1853 1.2544421 0.530720267 -0.019965158 0.3272519 0.5778235
## 1854 1.2544421 3.816789048 1.194836636 -0.4241459 0.5778235
## 1855 1.2544421 1.605602579 0.153577955 0.3272519 1.3178809
## 1856 1.2544421 0.622853037 -0.244125013 -0.4241459 0.5778235
## 1857 1.2544421 1.206360577 0.110192177 -0.4241459 0.5778235
## 1858 1.2544421 0.192900112 0.912829077 0.3272519 0.5778235
## 1859 -1.9841605 -0.835915815 -0.309203681 0.3272519 -0.9022913
## 1860 -1.9841605 -0.620939353 0.016189657 1.0786497 0.5778235
## 1861 -1.9841605 0.438587497 2.207171465 4.8356387 2.7979956
## 1862 -1.9841605 -1.057034462 -0.815371095 -0.4241459 -0.9022913
## 1863 -0.9046263 -0.636294814 -0.649058945 -0.4241459 -0.1622339
## 1864 -0.9046263 -0.759138507 -0.706906649 -0.4241459 -0.1622339
## 1865 -0.9046263 -0.482740198 0.811595594 0.3272519 -0.1622339
## 1866 -1.9841605 -0.943404046 -0.779216280 -1.1755437 -0.9022913
## 1867 -0.9046263 -0.713072122 -0.576749314 -0.4241459 -0.1622339
## 1868 -0.9046263 0.254321958 0.948983892 0.3272519 0.5778235
## 1869 -0.9046263 -0.184844243 -0.103265853 0.3272519 0.5778235
## 1870 -0.9046263 -0.022076350 0.905598114 1.0786497 1.3178809
## 1871 -0.9046263 -0.114209120 0.797133668 0.3272519 0.5778235
## 1872 0.1749079 -0.114209120 0.182501808 1.0786497 0.5778235
## 1873 0.1749079 -0.759138507 -0.576749314 -0.4241459 -0.9022913
## 1874 0.1749079 -0.421318352 -0.634597019 -0.4241459 -0.9022913
## 1875 0.1749079 -0.083498197 1.317763008 1.0786497 -0.1622339
## 1876 0.1749079 -0.329185582 -0.649058945 -0.4241459 -0.9022913
## 1877 0.1749079 -0.421318352 -0.634597019 -0.4241459 -0.9022913
## 1878 0.1749079 -0.482740198 -0.540594499 -0.4241459 -0.9022913
## 1879 0.1749079 -0.083498197 -0.338127533 -0.4241459 -0.1622339
## 1880 0.1749079 -0.667005737 -0.649058945 -0.4241459 -0.9022913
## 1881 0.1749079 -0.206341890 -0.142891530 -0.4241459 -0.1622339
## 1882 -0.9046263 -0.037431812 1.317763008 0.3272519 -0.1622339
## 1883 0.1749079 -0.513451121 -0.482746794 -0.4241459 -0.9022913
## 1884 0.1749079 -0.728427584 -0.540594499 -0.4241459 -0.9022913
## 1885 0.1749079 -0.605583891 -0.714137612 -0.4241459 -0.9022913
## 1886 0.1749079 -0.513451121 -0.634597019 -0.4241459 -0.9022913
## 1887 0.1749079 0.085411881 0.384968773 0.3272519 -0.1622339
## 1888 -0.9046263 0.070056419 0.666976333 0.3272519 0.5778235
## 1889 0.1749079 -0.728427584 -0.540594499 -0.4241459 -0.9022913
## 1890 0.1749079 -0.083498197 0.594666702 -1.1755437 -0.1622339
## 1891 0.1749079 0.192900112 1.194836636 2.5814453 1.3178809
## 1892 0.1749079 -0.436673813 -0.410437164 -0.4241459 -0.1622339
## 1893 0.1749079 -0.175630966 -0.547825462 -0.4241459 -0.1622339
## 1894 0.1749079 -0.528806583 -0.620135092 -0.4241459 -0.9022913
## 1895 0.1749079 -0.421318352 -0.323665607 -0.4241459 -0.1622339
## 1896 0.1749079 -0.378323059 0.493433219 -2.6783393 -2.3824060
## 1897 0.1749079 -0.636294814 -0.620135092 0.3272519 -0.1622339
## 1898 0.1749079 -0.482740198 -0.540594499 -0.4241459 -0.9022913
## 1899 0.1749079 -0.482740198 -0.526132573 -0.4241459 -0.9022913
## 1900 0.1749079 -0.421318352 -0.576749314 -0.4241459 -0.9022913
## 1901 0.1749079 -0.482740198 -0.547825462 -0.4241459 -0.9022913
## 1902 -0.9046263 -0.513451121 -0.482746794 -0.4241459 -0.9022913
## 1903 0.1749079 -0.083498197 0.305428180 -0.4241459 -0.1622339
## 1904 0.1749079 -0.421318352 -0.641827982 -0.4241459 -0.9022913
## 1905 0.1749079 -0.513451121 -0.489977757 -0.4241459 -0.9022913
## 1906 0.1749079 1.636313502 0.833288483 -0.4241459 -0.1622339
## 1907 0.1749079 0.407876574 1.592539605 -0.4241459 0.5778235
## 1908 0.1749079 0.407876574 1.339455898 1.8300475 0.5778235
## 1909 0.1749079 -0.605583891 -0.540594499 0.3272519 -0.1622339
## 1910 0.1749079 0.039345496 1.165912784 1.0786497 0.5778235
## 1911 0.1749079 -0.574872968 -0.757523391 -1.1755437 -0.9022913
## 1912 0.1749079 -0.267763736 -0.106736715 -0.4241459 -0.1622339
## 1913 0.1749079 -0.421318352 -0.649058945 -0.4241459 -0.9022913
## 1914 0.1749079 -0.574872968 -0.663520871 -1.1755437 -0.9022913
## 1915 0.1749079 -0.605583891 -0.641827982 0.3272519 -0.1622339
## 1916 0.1749079 1.513469809 1.990242573 1.0786497 1.3178809
## 1917 -0.9046263 -0.667005737 -0.555056425 0.3272519 -0.1622339
## 1918 0.1749079 -0.605583891 -0.634597019 0.3272519 -0.1622339
## 1919 0.1749079 -0.237052813 1.050217375 0.3272519 -0.1622339
## 1920 0.1749079 0.991384115 2.351790726 0.3272519 -0.9022913
## 1921 0.1749079 -0.329185582 0.645283444 0.3272519 -0.1622339
## 1922 0.1749079 0.285032881 1.390072639 3.3328431 -0.1622339
## 1923 0.1749079 -0.789849430 -0.851525911 -1.1755437 -0.9022913
## 1924 0.1749079 -0.190986428 -0.215201161 0.3272519 -0.9022913
## 1925 -0.9046263 0.208255574 1.122527006 2.5814453 2.0579382
## 1926 0.1749079 0.361810189 1.990242573 1.8300475 0.5778235
## 1927 -0.9046263 0.346454728 0.688669222 0.3272519 0.5778235
## 1928 0.1749079 0.991384115 2.351790726 1.0786497 1.3178809
## 1929 -0.9046263 -0.851271277 -0.735830502 -0.4241459 -0.9022913
## 1930 0.1749079 -0.421318352 0.182501808 0.3272519 0.5778235
## 1931 0.1749079 -0.175630966 -0.446591979 -0.4241459 -0.1622339
## 1932 0.1749079 -0.421318352 -0.106736715 0.3272519 -0.1622339
## 1933 0.1749079 -0.513451121 -0.663520871 -0.4241459 -0.9022913
## 1934 0.1749079 -0.667005737 -0.771985317 -0.4241459 -0.9022913
## 1935 0.1749079 0.438587497 3.074887033 0.3272519 1.3178809
## 1936 0.1749079 -0.682361199 -0.757523391 -0.4241459 -0.9022913
## 1937 0.1749079 -0.221697351 -0.543631503 -1.1755437 -0.1622339
## 1938 0.1749079 -0.620939353 -0.637489404 -1.1755437 -0.9022913
## 1939 0.1749079 -0.221697351 -0.547825462 -0.4241459 -0.1622339
## 1940 0.1749079 0.607497575 1.628694420 1.8300475 1.3178809
## 1941 -0.9046263 0.438587497 3.074887033 0.3272519 1.3178809
## 1942 0.1749079 -0.620939353 -0.612904129 -1.1755437 -0.9022913
## 1943 0.1749079 -0.022076350 0.760978853 0.3272519 0.5778235
## 1944 0.1749079 0.346454728 2.612105397 1.8300475 2.0579382
## 1945 1.2544421 0.223611035 0.912829077 1.0786497 0.5778235
## 1946 0.1749079 -0.636294814 -0.612904129 -1.1755437 -0.9022913
## 1947 0.1749079 -0.114209120 0.182501808 0.3272519 0.5778235
## 1948 0.1749079 -0.513451121 -0.468284868 -0.4241459 -0.1622339
## 1949 0.1749079 0.131478266 0.963445818 -0.4241459 0.5778235
## 1950 0.1749079 0.285032881 1.484075159 1.0786497 0.5778235
## 1951 0.1749079 -0.421318352 0.399430699 0.3272519 0.5778235
## 1952 0.1749079 -0.298474659 -0.034427084 0.3272519 0.5778235
## 1953 0.1749079 0.991384115 2.351790726 1.8300475 1.3178809
## 1954 0.1749079 -0.329185582 -0.468284868 -0.4241459 0.5778235
## 1955 0.1749079 -0.559517506 -0.699675686 -0.4241459 -0.9022913
## 1956 0.1749079 -0.025147443 2.785648510 1.0786497 0.5778235
## 1957 0.1749079 -0.052787274 2.134861835 1.0786497 0.5778235
## 1958 0.1749079 -0.175630966 0.254811438 -0.4241459 -0.1622339
## 1959 0.1749079 -0.190986428 -0.215201161 0.3272519 0.5778235
## 1960 0.1749079 0.377165651 0.522357071 0.3272519 -0.9022913
## 1961 0.1749079 0.285032881 1.317763008 1.8300475 -0.1622339
## 1962 0.1749079 -0.436673813 -0.424899090 0.3272519 -0.1622339
## 1963 -0.9046263 -0.237052813 -0.352589459 0.3272519 -0.1622339
## 1964 0.1749079 0.622853037 1.165912784 1.0786497 0.5778235
## 1965 0.1749079 0.392521113 2.040859315 1.0786497 0.5778235
## 1966 0.1749079 0.592142113 2.062552204 1.0786497 0.5778235
## 1967 0.1749079 0.238966497 2.279481096 1.8300475 0.5778235
## 1968 0.1749079 -0.559517506 -0.649058945 -0.4241459 -0.9022913
## 1969 0.1749079 -0.359896505 -0.641827982 -0.4241459 -0.9022913
## 1970 0.1749079 -0.163346597 0.688669222 0.3272519 0.5778235
## 1971 0.1749079 -0.114209120 0.544049961 0.3272519 -0.1622339
## 1972 0.1749079 -0.421318352 -0.641827982 -0.4241459 -0.9022913
## 1973 0.1749079 -0.581015152 -0.497208720 -0.4241459 -0.1622339
## 1974 0.1749079 -0.728427584 -0.757523391 -0.4241459 -0.9022913
## 1975 0.1749079 -0.544162045 -0.540594499 -0.4241459 -0.9022913
## 1976 0.1749079 -0.421318352 -0.540594499 -0.4241459 -0.1622339
## 1977 0.1749079 -0.390607429 -0.511670647 -0.4241459 -0.9022913
## 1978 0.1749079 -0.574872968 -0.540594499 -0.4241459 -0.9022913
## 1979 0.1749079 -0.498095660 -0.714137612 -1.1755437 -0.9022913
## 1980 0.1749079 -0.743783045 -0.526132573 -0.4241459 -0.9022913
## 1981 0.1749079 -0.160275505 -0.620135092 -0.4241459 -0.1622339
## 1982 0.1749079 0.162189189 -0.135660567 -0.4241459 0.5778235
## 1983 0.1749079 -0.144920043 -0.446591979 -0.4241459 -0.1622339
## 1984 0.1749079 -0.605583891 -0.540594499 0.3272519 -0.1622339
## 1985 0.1749079 -0.482740198 -0.497208720 0.3272519 -0.1622339
## 1986 0.1749079 -0.206341890 -0.656289908 -0.4241459 -0.9022913
## 1987 0.1749079 -0.344541044 -0.634597019 -0.4241459 -0.9022913
## 1988 0.1749079 1.513469809 3.364125555 1.0786497 2.0579382
## 1989 0.1749079 -0.697716661 -0.771985317 -0.4241459 -0.9022913
## 1990 0.1749079 -0.667005737 -0.612904129 -1.1755437 -0.9022913
## 1991 0.1749079 -0.200199705 -0.612904129 -1.1755437 -0.9022913
## 1992 0.1749079 0.070056419 -0.258586939 -0.4241459 0.5778235
## 1993 0.1749079 -0.547233137 -0.663520871 -0.4241459 -0.9022913
## 1994 0.1749079 -0.359896505 -0.656289908 -0.4241459 -0.9022913
## 1995 0.1749079 0.223611035 -0.316434644 -1.9269415 -0.9022913
## 1996 0.1749079 -0.283119198 -0.612904129 -1.9269415 -0.9022913
## 1997 0.1749079 0.156047004 -0.367051385 -0.4241459 1.3178809
## 1998 -0.9046263 -0.636294814 -0.721368575 -0.4241459 -0.9022913
## 1999 -0.9046263 -0.943404046 -0.685213760 -0.4241459 -1.6423486
## 2000 0.1749079 -0.498095660 -0.721368575 -1.1755437 -0.9022913
## 2001 0.1749079 -0.498095660 -0.721368575 -1.1755437 -0.9022913
## 2002 0.1749079 -0.528806583 -0.670751834 -0.4241459 -0.9022913
## 2003 0.1749079 -0.728427584 -0.641827982 -0.4241459 -0.9022913
## 2004 0.1749079 -0.421318352 -0.649058945 -0.4241459 -0.9022913
## 2005 0.1749079 -0.482740198 -0.482746794 0.3272519 0.5778235
## 2006 0.1749079 -0.605583891 -0.612904129 -0.4241459 -0.9022913
## 2007 0.1749079 -0.682361199 -0.576749314 -0.4241459 -0.1622339
## 2008 -0.9046263 -0.528806583 -0.714137612 -1.1755437 -0.9022913
## 2009 0.1749079 -0.605583891 -0.612904129 -0.4241459 -0.9022913
## 2010 -0.9046263 -0.237052813 -0.374282348 -0.4241459 -0.1622339
## 2011 -0.9046263 -0.667005737 -0.576749314 -0.4241459 -0.1622339
## 2012 0.1749079 -0.237052813 -0.135660567 0.3272519 0.5778235
## 2013 0.1749079 -0.820560353 -0.721368575 -1.1755437 -1.6423486
## 2014 0.1749079 -0.636294814 -0.540594499 -0.4241459 -0.9022913
## 2015 0.1749079 -0.697716661 -0.656289908 -0.4241459 -0.9022913
## 2016 0.1749079 -0.667005737 -0.757523391 -0.4241459 -0.9022913
## 2017 0.1749079 -0.114209120 -0.540594499 -1.1755437 -0.1622339
## 2018 0.1749079 -0.482740198 -0.540594499 -0.4241459 -0.9022913
## 2019 0.1749079 -0.144920043 -0.453822942 -0.4241459 -0.1622339
## 2020 0.1749079 -0.513451121 -0.808140132 -1.1755437 -0.9022913
## 2021 0.1749079 0.070056419 -0.388744274 0.3272519 1.3178809
## 2022 0.1749079 -0.528806583 -0.743061465 -1.1755437 -0.9022913
## 2023 0.1749079 0.192900112 -0.395975238 0.3272519 1.3178809
## 2024 0.1749079 -0.605583891 -0.612904129 0.3272519 -0.1622339
## 2025 0.1749079 -0.498095660 -0.887680726 -1.1755437 -0.9022913
## 2026 0.1749079 -0.881982200 -0.489977757 -0.4241459 -0.9022913
## 2027 0.1749079 -0.743783045 -0.714137612 -0.4241459 -0.9022913
## 2028 0.1749079 -0.574872968 -0.569518351 -0.4241459 -0.1622339
## 2029 0.1749079 -0.636294814 -0.670751834 -1.1755437 -0.9022913
## 2030 0.1749079 -0.421318352 -0.482746794 -0.4241459 -0.9022913
## 2031 0.1749079 -0.789849430 -0.699675686 -0.4241459 -0.9022913
## 2032 0.1749079 -0.267763736 -0.106736715 0.3272519 0.5778235
## 2033 0.1749079 -0.682361199 -0.533363536 -0.4241459 -0.9022913
## 2034 0.1749079 -0.052787274 -0.424899090 -0.4241459 -0.1622339
## 2035 0.1749079 -0.261621551 -0.367051385 -0.4241459 -0.1622339
## 2036 0.1749079 -0.605583891 -0.743061465 -1.1755437 -0.9022913
## 2037 -0.9046263 -0.866626738 -0.829833021 -0.4241459 -0.9022913
## 2038 0.1749079 -0.421318352 -0.265817902 -0.4241459 -0.9022913
## 2039 0.1749079 -0.175630966 -0.504439683 -0.4241459 -0.9022913
## 2040 0.1749079 -0.359896505 -0.656289908 -0.4241459 -0.9022913
## 2041 0.1749079 -0.743783045 -0.721368575 -0.4241459 -0.9022913
## 2042 0.1749079 -0.639365907 -0.287510792 -0.4241459 -0.9022913
## 2043 0.1749079 -0.513451121 -0.715149947 -1.1755437 -0.9022913
## 2044 -0.9046263 -0.513451121 -0.714137612 -1.1755437 -0.9022913
## 2045 1.2544421 -0.528806583 -0.627366056 -0.4241459 -0.1622339
## 2046 0.1749079 -0.421318352 -0.620135092 -0.4241459 -0.1622339
## 2047 0.1749079 -0.452029275 -0.663520871 -1.1755437 -0.9022913
## 2048 0.1749079 -0.528806583 -0.670751834 -0.4241459 -0.9022913
## 2049 0.1749079 -0.298474659 -0.489977757 -0.4241459 -0.1622339
## 2050 0.1749079 -0.267763736 -0.649058945 -0.4241459 -0.9022913
## 2051 0.1749079 -0.390607429 -0.439361016 0.3272519 -0.1622339
## 2052 0.1749079 -0.052787274 -0.309203681 -1.1755437 -0.9022913
## 2053 0.1749079 -0.482740198 -0.627366056 -0.4241459 -0.1622339
## 2054 0.1749079 -0.436673813 -0.641827982 -0.4241459 -0.9022913
## 2055 0.1749079 -0.559517506 -0.627366056 -0.4241459 -0.1622339
## 2056 0.1749079 -0.765280692 -0.743061465 -0.4241459 -0.9022913
## 2057 0.1749079 -0.498095660 -0.656289908 -1.1755437 -0.9022913
## 2058 0.1749079 -0.267763736 -0.439361016 0.3272519 0.5778235
## 2059 0.1749079 -0.129564582 -0.446591979 -0.4241459 -0.1622339
## 2060 0.1749079 -0.513451121 -0.649058945 -0.4241459 -0.9022913
## 2061 0.1749079 0.039345496 -0.316434644 0.3272519 0.5778235
## 2062 0.1749079 0.039345496 -0.316434644 0.3272519 0.5778235
## 2063 0.1749079 0.039345496 -0.142891530 0.3272519 0.5778235
## 2064 0.1749079 -0.467384737 -0.612904129 -0.4241459 -0.9022913
## 2065 0.1749079 -0.129564582 -0.540594499 -0.4241459 0.5778235
## 2066 -0.9046263 -0.114209120 -0.540594499 -1.1755437 -0.1622339
## 2067 0.1749079 -0.528806583 -0.620135092 -0.4241459 -0.1622339
## 2068 0.1749079 -0.467384737 -0.612904129 -0.4241459 -0.9022913
## 2069 0.1749079 -0.599441706 -0.714137612 -0.4241459 -0.9022913
## 2070 0.1749079 -0.544162045 -0.670751834 -0.4241459 -0.9022913
## 2071 0.1749079 -0.359896505 -0.634597019 -0.4241459 -0.9022913
## 2072 0.1749079 -0.298474659 -0.656289908 -0.4241459 -0.9022913
## 2073 0.1749079 -0.129564582 -0.446591979 -0.4241459 -0.1622339
## 2074 0.1749079 -0.181773151 -0.424899090 -0.4241459 -0.9022913
## 2075 0.1749079 -0.160275505 -0.446591979 -0.4241459 -0.1622339
## 2076 0.1749079 -0.559517506 -0.612904129 -0.4241459 -0.9022913
## 2077 -0.9046263 -0.421318352 -0.612904129 -0.4241459 -0.9022913
## 2078 0.1749079 -0.114209120 -0.511670647 -0.4241459 -0.9022913
## 2079 0.1749079 -0.058929458 -0.511670647 -0.4241459 0.5778235
## 2080 0.1749079 -0.620939353 -0.728599538 -0.4241459 -0.9022913
## 2081 0.1749079 -0.528806583 -0.656289908 -0.4241459 -0.9022913
## 2082 0.1749079 -0.114209120 -0.432130053 -0.4241459 0.5778235
## 2083 0.1749079 -0.175630966 -0.432130053 -0.4241459 -0.9022913
## 2084 0.1749079 -0.160275505 -0.609939435 -1.1755437 -0.9022913
## 2085 0.1749079 -0.482740198 -0.714137612 -1.1755437 -0.9022913
## 2086 0.1749079 -0.206341890 -0.446591979 -0.4241459 -0.1622339
## 2087 0.1749079 -0.104995843 -0.446591979 -0.4241459 -0.1622339
## 2088 0.1749079 -0.114209120 -0.446591979 -0.4241459 -0.1622339
## 2089 0.1749079 -0.114209120 -0.446591979 -0.4241459 -0.1622339
## 2090 0.1749079 -0.037431812 -0.446591979 -0.4241459 -0.9022913
## 2091 0.1749079 -0.528806583 -0.656289908 -0.4241459 -0.9022913
## 2092 0.1749079 -0.237052813 -0.359820422 -0.4241459 -0.1622339
## 2093 0.1749079 -0.482740198 -0.338127533 0.3272519 -0.1622339
## 2094 0.1749079 -0.605583891 -0.743061465 -1.1755437 -0.9022913
## 2095 0.1749079 -0.068142735 -0.446591979 -0.4241459 -0.1622339
## 2096 0.1749079 -0.498095660 -0.714137612 -1.1755437 -0.9022913
## 2097 1.2544421 -0.329185582 -0.215201161 -0.4241459 -0.1622339
## 2098 0.1749079 -0.237052813 -0.468284868 -0.4241459 -0.1622339
## 2099 0.1749079 -0.482740198 -0.612904129 -0.4241459 -0.9022913
## 2100 0.1749079 -0.574872968 -0.721368575 -0.4241459 -0.9022913
## 2101 0.1749079 -0.421318352 -0.649058945 -2.6783393 -0.9022913
## 2102 0.1749079 0.208255574 -0.142891530 -0.4241459 -0.1622339
## 2103 0.1749079 -0.221697351 -0.359820422 -0.4241459 -0.9022913
## 2104 0.1749079 0.177544650 -0.142891530 -0.4241459 -0.1622339
## 2105 0.1749079 -0.221697351 -0.359820422 -0.4241459 -0.1622339
## 2106 0.1749079 -0.329185582 -0.511670647 -0.4241459 -0.1622339
## 2107 -1.9841605 -0.246266090 -0.649058945 -0.4241459 -0.9022913
## 2108 0.1749079 -0.323043398 -0.649058945 -0.4241459 -0.9022913
## 2109 0.1749079 -0.175630966 -0.446591979 -0.4241459 -0.1622339
## 2110 0.1749079 -0.055858366 -0.511670647 -0.4241459 -0.1622339
## 2111 0.1749079 -0.206341890 -0.468284868 -0.4241459 -0.1622339
## 2112 0.1749079 -0.221697351 -0.656289908 -0.4241459 -0.9022913
## 2113 0.1749079 0.192900112 -0.135660567 1.0786497 0.5778235
## 2114 0.1749079 -0.436673813 -0.656289908 -0.4241459 -0.9022913
## 2115 -0.9046263 -0.298474659 -0.663520871 -0.4241459 -0.9022913
## 2116 0.1749079 -0.114209120 -0.511670647 -2.6783393 -0.9022913
## 2117 0.1749079 -0.098853658 -0.510441383 -0.4241459 -0.1622339
## 2118 1.2544421 -0.129564582 -0.504439683 -0.4241459 -0.1622339
## 2119 0.1749079 -0.359896505 -0.649058945 -0.4241459 -0.9022913
## 2120 0.1749079 -0.206341890 -0.468284868 -0.4241459 -0.1622339
## 2121 0.1749079 -0.359896505 -0.540594499 -0.4241459 -0.9022913
## 2122 0.1749079 -0.482740198 -0.663520871 -0.4241459 -0.1622339
## 2123 0.1749079 0.070056419 -0.388744274 0.3272519 0.5778235
## 2124 0.1749079 -0.405962890 -0.540594499 -0.4241459 -0.1622339
## 2125 0.1749079 -0.482740198 -0.612904129 -0.4241459 -0.9022913
## 2126 0.1749079 -0.227839536 -0.540594499 -1.1755437 -0.1622339
## 2127 0.1749079 -0.083498197 -0.489977757 -0.4241459 0.5778235
## 2128 0.1749079 -0.114209120 -0.489977757 -0.4241459 -0.1622339
## 2129 0.1749079 -0.129564582 -0.489977757 -1.1755437 -0.9022913
## 2130 0.1749079 -0.206341890 -0.714137612 -0.4241459 -0.9022913
## 2131 0.1749079 -0.359896505 -0.540594499 -0.4241459 -0.9022913
## 2132 0.1749079 0.146833727 -0.381513311 -0.4241459 0.5778235
## 2133 0.1749079 -0.467384737 -0.641827982 -0.4241459 -0.9022913
## 2134 0.1749079 0.146833727 -0.381513311 -0.4241459 0.5778235
## 2135 0.1749079 -0.184844243 -0.359820422 -0.4241459 -0.1622339
## 2136 0.1749079 -0.452029275 -0.634597019 -0.4241459 -0.9022913
## 2137 0.1749079 -0.467384737 -0.634597019 -0.4241459 -0.9022913
## 2138 0.1749079 -0.421318352 -0.649058945 -0.4241459 -0.9022913
## 2139 0.1749079 -0.452029275 -0.634597019 -0.4241459 -0.9022913
## 2140 0.1749079 0.146833727 -0.388744274 -0.4241459 -0.1622339
## 2141 -1.9841605 -0.590228429 0.630821517 2.5814453 2.0579382
## 2142 -1.9841605 -0.390607429 -0.301972718 4.0842409 2.0579382
## 2143 -1.9841605 -0.697716661 0.008958694 1.0786497 -0.1622339
## 2144 -1.9841605 -0.267763736 1.628694420 4.0842409 2.0579382
## 2145 -1.9841605 -0.175630966 2.713338880 -1.1755437 -0.1622339
## 2146 -1.9841605 -0.421318352 0.168039881 0.3272519 -0.9022913
## 2147 -1.9841605 -0.912693123 -0.504439683 -1.1755437 -0.1622339
## 2148 0.1749079 -0.590228429 -0.793678206 -0.4241459 -0.9022913
## 2149 0.1749079 -0.667005737 -0.800909169 -1.1755437 -0.9022913
## 2150 0.1749079 -0.574872968 -0.721368575 -0.4241459 -0.9022913
## 2151 -0.9046263 -0.267763736 -0.395975238 -0.4241459 -0.1622339
## 2152 0.1749079 -0.298474659 -0.468284868 0.3272519 -0.1622339
## 2153 0.1749079 -0.237052813 -0.576749314 -0.4241459 -0.1622339
## 2154 1.2544421 -0.329185582 -0.547825462 -0.4241459 -0.1622339
## 2155 0.1749079 -0.052787274 -0.374282348 -0.4241459 -0.1622339
## 2156 0.1749079 -0.682361199 -0.822602058 -0.4241459 -0.9022913
## 2157 0.1749079 -0.390607429 -0.468284868 -0.4241459 -0.9022913
## 2158 0.1749079 -0.697716661 -0.735830502 -0.4241459 -0.9022913
## 2159 0.1749079 -0.667005737 -0.757523391 -0.4241459 -0.9022913
## 2160 0.1749079 0.315743805 0.905598114 1.0786497 1.3178809
## 2161 0.1749079 -0.544162045 -0.482746794 -0.4241459 -0.1622339
## 2162 0.1749079 4.123898280 1.990242573 1.8300475 2.7979956
## 2163 0.1749079 -0.175630966 -0.251355976 0.3272519 0.5778235
## 2164 0.1749079 -0.022076350 -0.468284868 0.3272519 0.5778235
## 2165 0.1749079 -0.528806583 -0.685213760 -0.4241459 -0.9022913
## 2166 -0.9046263 -0.845129092 -0.829833021 -0.4241459 -0.9022913
## 2167 0.1749079 -0.206341890 0.775440779 1.0786497 0.5778235
## 2168 0.1749079 -0.160275505 0.023420620 0.3272519 0.5778235
## 2169 0.1749079 -0.713072122 -0.808140132 -0.4241459 -0.9022913
## 2170 0.1749079 -0.467384737 -0.641827982 -0.4241459 -0.9022913
## 2171 0.1749079 -0.544162045 -0.692444723 -0.4241459 -0.9022913
## 2172 0.1749079 -0.513451121 -0.685213760 -0.4241459 -0.9022913
## 2173 0.1749079 0.070056419 0.182501808 0.3272519 0.5778235
## 2174 0.1749079 -0.667005737 -0.771985317 -0.4241459 -0.9022913
## 2175 0.1749079 -0.544162045 -0.685213760 -0.4241459 -0.9022913
## 2176 0.1749079 -0.267763736 0.037882546 -0.4241459 -0.1622339
## 2177 0.1749079 -0.267763736 0.037882546 -0.4241459 -0.1622339
## 2178 0.1749079 0.008634573 0.037882546 0.3272519 0.5778235
## 2179 0.1749079 -0.175630966 -0.070581900 0.3272519 -0.1622339
## 2180 0.1749079 -0.498095660 -0.612904129 -0.4241459 -0.9022913
## 2181 0.1749079 0.131478266 -0.446591979 0.3272519 -0.1622339
## 2182 0.1749079 -0.206341890 0.146346992 -0.4241459 0.5778235
## 2183 0.1749079 -0.052787274 -0.374282348 0.3272519 -0.1622339
## 2184 0.1749079 -0.206341890 -0.034427084 -0.4241459 -0.1622339
## 2185 0.1749079 -0.144920043 -0.150122493 0.3272519 0.5778235
## 2186 0.1749079 0.278890697 0.110192177 -0.4241459 -0.1622339
## 2187 0.1749079 -0.144920043 0.905598114 0.3272519 0.5778235
## 2188 -0.9046263 -0.206341890 -0.189892790 -0.4241459 -0.1622339
## 2189 0.1749079 -0.144920043 0.905598114 -2.6783393 0.5778235
## 2190 0.1749079 -0.022076350 0.544049961 1.0786497 1.3178809
## 2191 -0.9046263 -0.620939353 -0.649058945 -0.4241459 -0.9022913
## 2192 0.1749079 -0.544162045 -0.677982797 -0.4241459 -0.9022913
## 2193 0.1749079 -0.206341890 0.037882546 0.3272519 0.5778235
## 2194 0.1749079 -0.006720889 0.182501808 0.3272519 0.5778235
## 2195 0.1749079 0.033203311 0.399430699 0.3272519 0.5778235
## 2196 0.1749079 0.085411881 0.037882546 0.3272519 0.5778235
## 2197 0.1749079 -0.175630966 -0.251355976 -0.4241459 -0.1622339
## 2198 0.1749079 0.131478266 0.399430699 -0.4241459 0.5778235
## 2199 0.1749079 -0.083498197 0.037882546 1.0786497 1.3178809
## 2200 0.1749079 0.070056419 -0.034427084 0.3272519 0.5778235
## 2201 0.1749079 0.592142113 0.905598114 1.0786497 1.3178809
## 2202 0.1749079 -0.498095660 -0.685213760 -0.4241459 -0.9022913
## 2203 0.1749079 0.131478266 0.254811438 -0.4241459 0.5778235
## 2204 0.1749079 -0.498095660 -0.641827982 -0.4241459 -0.9022913
## 2205 -0.9046263 -0.206341890 0.037882546 -0.4241459 -0.1622339
## 2206 -0.9046263 -0.826702538 -0.829833021 -0.4241459 -0.9022913
## 2207 0.1749079 -0.359896505 -0.555056425 -0.4241459 -0.1622339
## 2208 -0.9046263 -0.835915815 -0.793678206 -0.4241459 -0.9022913
## 2209 -0.9046263 -0.851271277 -0.825132895 -0.4241459 -0.9022913
## 2210 0.1749079 -0.359896505 -0.555056425 -0.4241459 -0.1622339
## 2211 0.1749079 -0.728427584 -0.808140132 -1.1755437 -0.9022913
## 2212 0.1749079 -0.313830121 -0.649058945 0.3272519 -0.9022913
## 2213 0.1749079 -0.682361199 -0.699675686 -0.4241459 -0.9022913
## 2214 0.1749079 -0.252408274 -0.576749314 -0.4241459 -0.1622339
## 2215 0.1749079 -0.651650276 -0.800909169 -0.4241459 -0.9022913
## 2216 0.1749079 -0.298474659 -0.540594499 -0.4241459 -0.1622339
## 2217 0.1749079 -0.206341890 -0.359820422 -0.4241459 -0.1622339
## 2218 0.1749079 -0.405962890 -0.583980277 -0.4241459 -0.1622339
## 2219 0.1749079 -0.436673813 -0.685213760 -0.4241459 -0.9022913
## 2220 0.1749079 -0.452029275 -0.641827982 -0.4241459 -0.9022913
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## 2226 0.1749079 -0.405962890 -0.468284868 -0.4241459 -0.1622339
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## 2228 0.1749079 -0.421318352 -0.641827982 -0.4241459 -0.9022913
## 2229 0.1749079 -0.436673813 -0.641827982 -0.4241459 -0.9022913
## 2230 0.1749079 -0.467384737 -0.641827982 -0.4241459 -0.9022913
## 2231 0.1749079 -0.359896505 -0.504439683 0.3272519 -0.1622339
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## 2237 0.1749079 -0.436673813 -0.612904129 -0.4241459 -0.9022913
## 2238 0.1749079 1.605602579 2.351790726 1.0786497 1.3178809
## 2239 0.1749079 -0.436673813 -0.641827982 -0.4241459 -0.9022913
## 2240 0.1749079 -0.329185582 -0.511670647 0.3272519 -0.1622339
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## 2242 0.1749079 -0.329185582 -0.511670647 0.3272519 -0.1622339
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## 2252 -0.9046263 -0.835915815 -0.793678206 -0.4241459 -0.9022913
## 2253 -0.9046263 -0.835915815 -0.793678206 -0.4241459 -0.9022913
## 2254 0.1749079 -0.298474659 -0.504439683 -0.4241459 -0.1622339
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## 2258 0.1749079 -0.304616844 -0.504439683 -0.4241459 -0.1622339
## 2259 0.1749079 -0.636294814 -0.721368575 -1.1755437 -0.9022913
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## 2263 -0.9046263 -0.513451121 -0.547825462 0.3272519 -0.1622339
## 2264 -0.9046263 -0.820560353 -0.793678206 0.3272519 -0.9022913
## 2265 0.1749079 -0.452029275 -0.482746794 -0.4241459 -0.9022913
## 2266 0.1749079 -0.605583891 -0.829833021 -1.1755437 -0.9022913
## 2267 -0.9046263 -0.359896505 -0.533363536 -0.4241459 -0.9022913
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## 2271 0.1749079 -0.534948768 -0.656289908 -0.4241459 -0.9022913
## 2272 0.1749079 -0.513451121 -0.670751834 -0.4241459 -0.9022913
## 2273 0.1749079 -0.329185582 -0.468284868 -0.4241459 -0.1622339
## 2274 0.1749079 -0.298474659 -0.526132573 -0.4241459 -0.1622339
## 2275 0.1749079 -0.590228429 -0.844294947 -1.1755437 -0.9022913
## 2276 0.1749079 -0.636294814 -0.779216280 -0.4241459 -0.9022913
## 2277 0.1749079 -0.215555166 -0.215201161 -0.4241459 0.5778235
## 2278 0.1749079 -0.636294814 -0.779216280 -0.4241459 -0.9022913
## 2279 0.1749079 -0.022076350 -0.468284868 1.0786497 0.5778235
## 2280 -1.9841605 -0.605583891 0.139116029 1.0786497 -0.9022913
## 2281 -1.9841605 -0.559517506 0.110192177 1.8300475 -0.1622339
## 2282 -1.9841605 -0.544162045 0.298197217 1.8300475 0.5778235
## 2283 -1.9841605 -0.605583891 0.305428180 0.3272519 -0.1622339
## 2284 -1.9841605 0.131478266 0.254811438 1.0786497 -0.9022913
## 2285 -1.9841605 -0.820560353 -0.179046346 -0.4241459 -0.9022913
## 2286 -0.9046263 -0.083498197 0.363275884 0.3272519 -0.1622339
## 2287 -0.9046263 -0.390607429 0.471740330 -0.4241459 -0.9022913
## 2288 -0.9046263 -0.329185582 0.760978853 0.3272519 -0.1622339
## 2289 -0.9046263 -0.390607429 0.724824037 1.0786497 -0.1622339
## 2290 -0.9046263 -0.697716661 0.544049961 1.0786497 -0.1622339
## 2291 -0.9046263 -0.390607429 0.616359591 0.3272519 -0.1622339
## 2292 -0.9046263 0.254321958 0.760978853 1.8300475 -0.1622339
## 2293 -0.9046263 -0.390607429 0.601897665 -0.4241459 -0.1622339
## 2294 -0.9046263 -0.283119198 0.168039881 1.0786497 -0.1622339
## 2295 -0.9046263 -0.267763736 0.298197217 -2.6783393 -0.9022913
## 2296 -0.9046263 -0.627081537 -0.251355976 0.3272519 -0.1622339
## 2297 -0.9046263 -0.298474659 0.298197217 0.3272519 -0.9022913
## 2298 -0.9046263 0.039345496 -0.338127533 4.8356387 3.5380530
## 2299 0.1749079 0.146833727 1.339455898 1.0786497 1.3178809
## 2300 -1.9841605 -0.682361199 -0.612904129 2.5814453 -0.1622339
## 2301 0.1749079 0.131478266 1.975780647 4.0842409 1.3178809
## 2302 -1.9841605 -0.759138507 0.471740330 3.3328431 -0.1622339
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## 2304 -1.9841605 -0.851271277 -0.251355976 1.0786497 -0.1622339
## 2305 -1.9841605 -0.559517506 -0.649058945 4.0842409 -0.1622339
## 2306 -1.9841605 -0.928048584 -0.612904129 -0.4241459 -0.9022913
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## 2308 -0.9046263 -0.881982200 -0.757523391 -0.4241459 -0.9022913
## 2309 -0.9046263 -0.651650276 -0.540594499 -1.1755437 -0.1622339
## 2310 -1.9841605 -0.405962890 -0.222432124 1.0786497 -0.1622339
## 2311 -1.9841605 -1.035536816 -0.757523391 -0.4241459 -1.6423486
## 2312 -1.9841605 -0.851271277 -0.822602058 -0.4241459 -0.1622339
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## 2316 -1.9841605 -0.952617323 -0.750292428 -0.4241459 -0.9022913
## 2317 -1.9841605 -0.667005737 -0.106736715 -0.4241459 -0.9022913
## 2318 -1.9841605 -0.390607429 1.165912784 2.5814453 -0.1622339
## 2319 -1.9841605 -0.298474659 0.276504327 1.0786497 1.3178809
## 2320 -1.9841605 -0.206341890 1.050217375 2.5814453 0.5778235
## 2321 -1.9841605 -0.329185582 -0.179046346 1.0786497 -0.9022913
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## 2324 -1.9841605 -0.313830121 -0.106736715 0.3272519 0.5778235
## 2325 -1.9841605 -1.133811770 -0.829833021 -0.4241459 -1.6423486
## 2326 -1.9841605 -0.298474659 1.773313681 4.0842409 2.0579382
## 2327 -1.9841605 -0.083498197 1.267146267 4.0842409 4.2781104
## 2328 -1.9841605 -1.057034462 -0.808140132 -0.4241459 -0.9022913
## 2329 -1.9841605 -1.057034462 -0.808140132 -0.4241459 -0.9022913
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## 2332 -1.9841605 -0.528806583 -0.034427084 4.0842409 1.3178809
## 2333 -1.9841605 -0.989470431 -0.757523391 -0.4241459 -1.6423486
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## 2335 -1.9841605 -0.958759508 -0.793678206 -0.4241459 -0.9022913
## 2336 0.1749079 0.438587497 0.392199736 0.3272519 1.3178809
## 2337 0.1749079 -0.928048584 -0.829833021 -0.4241459 -0.9022913
## 2338 -1.9841605 -0.559517506 1.035755449 2.5814453 0.5778235
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## 2346 -1.9841605 -0.989470431 -0.829833021 -0.4241459 -0.9022913
## 2347 -0.9046263 -0.605583891 0.760978853 1.8300475 0.5778235
## 2348 -1.9841605 0.192900112 1.194836636 4.0842409 2.0579382
## 2349 -1.9841605 -0.928048584 -0.757523391 -0.4241459 -0.9022913
## 2350 -1.9841605 -1.010968077 -0.829833021 -0.4241459 -0.9022913
## 2351 -1.9841605 -1.081603200 -0.844294947 -0.4241459 -0.9022913
## 2352 -0.9046263 0.070056419 0.327121069 0.3272519 0.5778235
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## 2355 -0.9046263 1.052805961 1.447920344 1.0786497 -0.1622339
## 2356 -0.9046263 -0.421318352 -0.692444723 -0.4241459 -0.1622339
## 2357 -0.9046263 -0.482740198 -0.612904129 -0.4241459 -0.1622339
## 2358 -0.9046263 -0.713072122 -0.468284868 -0.4241459 -0.1622339
## 2359 -0.9046263 -0.743783045 -0.649058945 0.3272519 -0.9022913
## 2360 0.1749079 -0.667005737 -0.468284868 -0.4241459 -0.1622339
## 2361 -0.9046263 -0.636294814 -0.468284868 0.3272519 -0.1622339
## 2362 -0.9046263 0.223611035 0.182501808 4.8356387 2.7979956
## 2363 0.1749079 0.070056419 1.628694420 4.8356387 1.3178809
## 2364 0.1749079 -0.636294814 -0.540594499 -0.4241459 -0.9022913
## 2365 -0.9046263 0.131478266 1.845623312 2.5814453 2.0579382
## 2366 -0.9046263 -0.805204892 -0.627366056 -0.4241459 -0.9022913
## 2367 -0.9046263 -0.636294814 -0.612904129 -0.4241459 -0.9022913
## 2368 -0.9046263 -0.636294814 -0.692444723 -0.4241459 -0.9022913
## 2369 -0.9046263 -0.667005737 -0.497208720 -0.4241459 -0.1622339
## 2370 -0.9046263 -0.835915815 -0.656289908 -0.4241459 -0.9022913
## 2371 -0.9046263 -0.237052813 0.392199736 -0.4241459 -0.1622339
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## 2373 0.1749079 -0.359896505 -0.316434644 0.3272519 -0.1622339
## 2374 -0.9046263 -0.237052813 -0.432130053 0.3272519 -0.9022913
## 2375 0.1749079 1.667024425 2.351790726 1.0786497 1.3178809
## 2376 0.1749079 -0.544162045 -0.612904129 -1.1755437 -0.1622339
## 2377 1.2544421 2.849394968 0.739285963 -0.4241459 0.5778235
## 2378 0.1749079 -0.298474659 -0.359820422 -1.1755437 -0.9022913
## 2379 1.2544421 -0.452029275 -0.649058945 -0.4241459 -0.9022913
## 2380 1.2544421 -0.390607429 -0.649058945 -1.1755437 -0.9022913
## 2381 1.2544421 -0.206341890 -0.489977757 -0.4241459 -0.9022913
## 2382 0.1749079 -0.052787274 -0.359820422 -0.4241459 0.5778235
## 2383 1.2544421 -0.052787274 -0.453822942 0.3272519 0.5778235
## 2384 1.2544421 0.776407653 -0.280279829 -0.4241459 1.3178809
## 2385 1.2544421 0.407876574 -0.244125013 0.3272519 0.5778235
## 2386 0.1749079 -0.452029275 -0.649058945 -1.1755437 -0.9022913
## 2387 1.2544421 -0.267763736 -0.518901610 -0.4241459 -0.9022913
## 2388 1.2544421 0.223611035 -0.374282348 -0.4241459 0.5778235
## 2389 1.2544421 0.822474037 1.773313681 0.3272519 1.3178809
## 2390 1.2544421 0.238966497 -0.374282348 -0.4241459 0.5778235
## 2391 0.1749079 -0.651650276 -0.786447243 -1.9269415 -1.6423486
## 2392 1.2544421 0.131478266 -0.395975238 -1.1755437 -0.1622339
## 2393 0.1749079 -0.022076350 -0.034427084 0.3272519 0.5778235
## 2394 0.1749079 -0.452029275 -0.685213760 -1.9269415 -2.3824060
## 2395 1.2544421 1.028237223 -0.222432124 -0.4241459 -0.1622339
## 2396 0.1749079 -0.022076350 -0.417668127 -0.4241459 -0.9022913
## 2397 0.1749079 -0.114209120 -0.576749314 -0.4241459 -0.9022913
## 2398 1.2544421 3.509679816 1.990242573 -0.4241459 0.5778235
## 2399 1.2544421 3.018305045 0.739285963 0.3272519 1.3178809
## 2400 0.1749079 -0.083498197 -0.359820422 -0.4241459 -0.1622339
## 2401 1.2544421 -0.206341890 0.023420620 0.3272519 0.5778235
## 2402 0.1749079 -0.175630966 -0.417668127 -0.4241459 -0.1622339
## 2403 0.1749079 0.745696729 0.399430699 0.3272519 1.3178809
## 2404 1.2544421 0.162189189 -0.352589459 -0.4241459 -0.1622339
## 2405 0.1749079 0.192900112 -0.352589459 -0.4241459 -0.1622339
## 2406 1.2544421 -0.375251967 -0.656289908 -1.1755437 -0.9022913
## 2407 1.2544421 -0.375251967 -0.649058945 -0.4241459 -0.9022913
## 2408 1.2544421 -0.221697351 -0.518901610 -0.4241459 -0.9022913
## 2409 1.2544421 1.319990993 0.066806399 0.3272519 1.3178809
## 2410 1.2544421 -0.022076350 -0.359820422 0.3272519 0.5778235
## 2411 0.1749079 -0.083498197 -0.432130053 -0.4241459 -0.1622339
## 2412 1.2544421 2.588352121 0.341582995 0.3272519 1.3178809
## 2413 1.2544421 2.075479703 1.990242573 0.3272519 1.3178809
## 2414 -0.9046263 -0.759138507 -0.222432124 0.3272519 -0.1622339
## 2415 1.2544421 1.329204270 0.168039881 -0.4241459 0.5778235
## 2416 1.2544421 0.899251345 -0.222432124 -0.4241459 0.5778235
## 2417 0.1749079 -0.329185582 -0.649058945 -0.4241459 -0.1622339
## 2418 1.2544421 -0.329185582 -0.649058945 -0.4241459 -0.9022913
## 2419 0.1749079 0.070056419 0.037882546 -0.4241459 0.5778235
## 2420 1.2544421 -0.083498197 -0.432130053 -0.4241459 -0.9022913
## 2421 1.2544421 0.684274883 0.399430699 -0.4241459 0.5778235
## 2422 -0.9046263 -0.083498197 -0.251355976 -0.4241459 -0.1622339
## 2423 1.2544421 1.513469809 2.062552204 1.8300475 1.3178809
## 2424 0.1749079 -0.206341890 -0.417668127 -0.4241459 0.5778235
## 2425 0.1749079 -0.359896505 -0.757523391 -1.9269415 -1.6423486
## 2426 1.2544421 -0.221697351 -0.526132573 -0.4241459 -0.9022913
## 2427 1.2544421 0.837829499 -0.106736715 -0.4241459 1.3178809
## 2428 1.2544421 -0.237052813 -0.518901610 -0.4241459 -0.9022913
## 2429 1.2544421 0.192900112 -0.374282348 -0.4241459 1.3178809
## 2430 1.2544421 -0.359896505 -0.649058945 -1.1755437 -0.9022913
## 2431 1.2544421 0.377165651 -0.229663087 0.3272519 1.3178809
## 2432 1.2544421 0.315743805 -0.316434644 0.3272519 0.5778235
## 2433 0.1749079 0.392521113 -0.229663087 -0.4241459 -0.1622339
## 2434 1.2544421 -0.175630966 -0.540594499 -0.4241459 -0.9022913
## 2435 1.2544421 -0.052787274 -0.562287388 -1.1755437 -0.9022913
## 2436 1.2544421 0.592142113 3.074887033 1.0786497 2.7979956
## 2437 1.2544421 0.592142113 0.703131148 -0.4241459 -0.1622339
## 2438 1.2544421 -0.175630966 -0.540594499 -0.4241459 -0.9022913
## 2439 1.2544421 0.991384115 -0.540594499 -0.4241459 2.0579382
## 2440 1.2544421 -0.175630966 -0.417668127 -0.4241459 -0.1622339
## 2441 0.1749079 3.509679816 2.568719618 -0.4241459 0.5778235
## 2442 1.2544421 0.208255574 -0.374282348 0.3272519 0.5778235
## 2443 1.2544421 -0.022076350 -0.504439683 -0.4241459 -0.9022913
## 2444 1.2544421 -0.390607429 -0.649058945 -1.1755437 -0.9022913
## 2445 1.2544421 0.377165651 0.724824037 0.3272519 0.5778235
## 2446 1.2544421 -0.114209120 -0.453822942 -0.4241459 -0.1622339
## 2447 1.2544421 -0.114209120 -0.453822942 -0.4241459 -0.9022913
## 2448 1.2544421 0.278890697 -0.323665607 -0.4241459 0.5778235
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## 2450 1.2544421 0.285032881 0.703131148 -0.4241459 -0.1622339
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## 2455 1.2544421 0.438587497 0.254811438 0.3272519 0.5778235
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## 2459 0.1749079 -0.329185582 -0.576749314 -0.4241459 -0.9022913
## 2460 1.2544421 0.945317730 0.001727731 -0.4241459 1.3178809
## 2461 1.2544421 1.903498534 0.710362111 -0.4241459 -0.1622339
## 2462 1.2544421 1.943422734 0.797133668 -0.4241459 0.5778235
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## 2464 0.1749079 0.592142113 0.131885066 1.0786497 0.5778235
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## 2467 0.1749079 -0.098853658 -0.359820422 -0.4241459 -0.1622339
## 2468 1.2544421 0.500009344 -0.171815383 -0.4241459 1.3178809
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## 2471 1.2544421 -0.298474659 -0.656289908 -1.1755437 -0.9022913
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## 2474 1.2544421 1.974133657 1.447920344 -0.4241459 1.3178809
## 2475 1.2544421 2.219821042 1.527460937 0.3272519 1.3178809
## 2476 0.1749079 0.008634573 -0.359820422 0.3272519 -0.1622339
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## 2481 1.2544421 0.899251345 -0.179046346 -0.4241459 0.5778235
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## 2483 1.2544421 1.129583269 0.153577955 0.3272519 0.5778235
## 2484 1.2544421 2.434797505 0.124654103 0.3272519 1.3178809
## 2485 1.2544421 -0.098853658 -0.461053905 0.3272519 0.5778235
## 2486 1.2544421 0.684274883 -0.034427084 0.3272519 -0.1622339
## 2487 1.2544421 4.123898280 2.062552204 0.3272519 2.0579382
## 2488 1.2544421 1.206360577 0.153577955 0.3272519 1.3178809
## 2489 1.2544421 1.206360577 0.153577955 -0.4241459 0.5778235
## 2490 1.2544421 1.359915193 0.182501808 -0.4241459 0.5778235
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## 2495 -1.9841605 -1.066247739 -0.880449763 -0.4241459 -1.6423486
## 2496 -1.9841605 -0.891195477 -0.706906649 -0.4241459 -0.1622339
## 2497 0.1749079 1.667024425 1.881778127 1.0786497 2.0579382
## 2498 -1.9841605 -0.267763736 0.587435739 0.3272519 1.3178809
## 2499 -1.9841605 -0.359896505 -0.865987837 0.3272519 0.5778235
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## 2503 -1.9841605 -0.697716661 -0.070581900 0.3272519 -0.1622339
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## 2507 -1.9841605 -0.989470431 -0.757523391 -0.4241459 -0.9022913
## 2508 -1.9841605 -1.010968077 -0.793678206 -0.4241459 -0.9022913
## 2509 -1.9841605 -1.023252446 -0.800909169 -0.4241459 -0.9022913
## 2510 0.1749079 -0.439744906 -0.779216280 -1.1755437 -0.9022913
## 2511 0.1749079 0.039345496 0.544049961 1.0786497 -0.9022913
## 2512 0.1749079 0.131478266 0.182501808 -0.4241459 -0.1622339
## 2513 0.1749079 -0.329185582 -0.468284868 0.3272519 0.5778235
## 2514 0.1749079 0.423232036 0.609128628 1.0786497 1.3178809
## 2515 0.1749079 -0.390607429 -0.323665607 -0.4241459 -0.1622339
## 2516 0.1749079 0.131478266 0.182501808 -0.4241459 -0.1622339
## 2517 0.1749079 -0.482740198 0.037882546 -0.4241459 -0.9022913
## 2518 0.1749079 -0.940332954 -0.832580787 -0.4241459 -0.9022913
## 2519 0.1749079 -0.590228429 -0.583980277 -0.4241459 -0.9022913
## 2520 0.1749079 -0.267763736 0.544049961 0.3272519 0.5778235
## 2521 0.1749079 -0.534948768 -0.815371095 -1.9269415 -0.9022913
## 2522 0.1749079 -0.436673813 -0.504439683 -0.4241459 -0.9022913
## 2523 0.1749079 -0.771422876 -0.679212061 0.3272519 0.5778235
## 2524 0.1749079 -0.329185582 -0.424248303 -0.4241459 0.5778235
## 2525 0.1749079 -0.605583891 -0.663520871 -0.4241459 -0.9022913
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## 2528 0.1749079 -0.356825413 -0.750292428 -1.1755437 -0.9022913
## 2529 0.1749079 -0.636294814 -0.649058945 -0.4241459 -0.9022913
## 2530 0.1749079 -0.605583891 -0.656289908 -0.4241459 -0.9022913
## 2531 0.1749079 -0.574872968 -0.359820422 0.3272519 -0.1622339
## 2532 0.1749079 -0.544162045 -0.540594499 -0.4241459 -0.1622339
## 2533 0.1749079 -0.651650276 -0.482746794 -0.4241459 -0.9022913
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## 2535 0.1749079 -0.488882383 -0.511670647 -0.4241459 -0.1622339
## 2536 1.2544421 -0.396749613 -0.424899090 0.3272519 -0.1622339
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## 2538 0.1749079 -0.344541044 -0.323665607 0.3272519 -0.1622339
## 2539 0.1749079 -0.359896505 0.442816478 -0.4241459 0.5778235
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## 2542 -1.9841605 -0.958759508 -0.829833021 -0.4241459 -0.9022913
## 2543 -1.9841605 -0.912693123 -0.829833021 -1.1755437 -0.9022913
## 2544 -1.9841605 -1.020181354 -0.880449763 -1.1755437 -1.6423486
## 2545 -1.9841605 -0.329185582 0.601897665 1.0786497 0.5778235
## 2546 -1.9841605 -1.050892277 -0.844294947 -0.4241459 -1.6423486
## 2547 -1.9841605 -1.050892277 -0.844294947 -0.4241459 -1.6423486
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## 2550 -1.9841605 -0.989470431 -0.685213760 -0.4241459 -1.6423486
## 2551 -1.9841605 -1.066247739 -0.902142652 -1.1755437 -0.9022913
## 2552 -1.9841605 -0.329185582 0.601897665 -0.4241459 1.3178809
## 2553 -1.9841605 -0.912693123 -0.829833021 -1.1755437 -0.9022913
## 2554 -1.9841605 -0.498095660 0.074037362 -0.4241459 1.3178809
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## 2557 -1.9841605 -0.974114969 -0.800909169 -0.4241459 -0.9022913
## 2558 -1.9841605 -0.513451121 0.074037362 -0.4241459 1.3178809
## 2559 -1.9841605 -0.986399339 -0.829833021 -0.4241459 -1.6423486
## 2560 -1.9841605 -0.574872968 0.182501808 2.5814453 1.3178809
## 2561 -1.9841605 -0.114209120 1.339455898 3.3328431 0.5778235
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## 2566 -1.9841605 -1.020181354 -0.829833021 -0.4241459 -0.9022913
## 2567 -1.9841605 -0.267763736 0.905598114 1.0786497 2.0579382
## 2568 -1.9841605 -0.574872968 0.218656623 2.5814453 0.5778235
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## 2573 -1.9841605 -1.127669585 -0.858756874 -0.4241459 -0.9022913
## 2574 -1.9841605 -1.057034462 -0.902142652 -0.4241459 -0.9022913
## 2575 -0.9046263 -0.851271277 -0.656289908 -0.4241459 -0.9022913
## 2576 0.1749079 3.202570584 1.628694420 0.3272519 -0.1622339
## 2577 0.1749079 0.714985806 0.471740330 -0.4241459 0.5778235
## 2578 -0.9046263 -1.035536816 -0.829833021 -1.1755437 -0.9022913
## 2579 1.2544421 1.298493347 1.484075159 -0.4241459 2.0579382
## 2580 0.1749079 -0.083498197 -0.432130053 -0.4241459 -0.1622339
## 2581 1.2544421 0.684274883 -0.301972718 0.3272519 0.5778235
## 2582 1.2544421 0.070056419 -0.432130053 -0.4241459 0.5778235
## 2583 1.2544421 0.407876574 0.493433219 -0.4241459 0.5778235
## 2584 1.2544421 0.377165651 0.493433219 -0.4241459 -0.1622339
## 2585 -0.9046263 -1.029394631 -0.793678206 -0.4241459 -0.9022913
## 2586 -1.9841605 -0.958759508 -0.721368575 -0.4241459 -0.9022913
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## 2590 -1.9841605 -1.050892277 -0.844294947 -0.4241459 -0.9022913
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## 2592 -1.9841605 -0.989470431 -0.829833021 -0.4241459 -0.9022913
## 2593 -1.9841605 -1.020181354 -0.880449763 -0.4241459 -0.9022913
## 2594 -1.9841605 -1.112314124 -0.829833021 -0.4241459 -0.9022913
## 2595 -0.9046263 -1.035536816 -0.880449763 -0.4241459 -0.9022913
## 2596 -0.9046263 -0.820560353 -0.740892176 -0.4241459 -0.9022913
## 2597 -0.9046263 2.281242889 4.521079645 2.5814453 2.0579382
## 2598 -0.9046263 -0.267763736 1.050217375 1.8300475 -0.1622339
## 2599 -0.9046263 -0.190986428 0.760978853 0.3272519 0.5778235
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## 2604 -0.9046263 -0.175630966 -0.287510792 -0.4241459 -0.1622339
## 2605 -0.9046263 -0.267763736 0.681438259 2.5814453 1.3178809
## 2606 -0.9046263 0.714985806 2.257788207 1.8300475 2.0579382
## 2607 -0.9046263 -0.789849430 -0.229663087 -0.4241459 -0.1622339
## 2608 -0.9046263 -0.190986428 0.616359591 0.3272519 1.3178809
## 2609 -1.9841605 -0.175630966 -0.576749314 4.0842409 0.5778235
## 2610 -0.9046263 -0.197128613 0.544049961 -0.4241459 0.5778235
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## 2612 -1.9841605 -0.636294814 0.110192177 0.3272519 -0.1622339
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## 2615 0.1749079 -0.083498197 -0.323665607 -0.4241459 -0.9022913
## 2616 0.1749079 -0.221697351 -0.410437164 0.3272519 -0.1622339
## 2617 0.1749079 -0.421318352 -0.555056425 -0.4241459 -0.9022913
## 2618 -0.9046263 -0.221697351 -0.407400159 -0.4241459 -0.1622339
## 2619 0.1749079 -0.636294814 -0.641827982 0.3272519 -0.1622339
## 2620 0.1749079 -0.190986428 -0.323665607 -0.4241459 -0.1622339
## 2621 0.1749079 -0.221697351 -0.323665607 -0.4241459 -0.1622339
## 2622 0.1749079 -0.513451121 -0.620135092 -0.4241459 -0.1622339
## 2623 1.2544421 -0.117280212 0.045113509 -0.4241459 -0.1622339
## 2624 0.1749079 -0.667005737 -0.641827982 -0.4241459 -0.9022913
## 2625 0.1749079 0.070056419 -0.034427084 0.3272519 0.5778235
## 2626 0.1749079 -0.581015152 -0.569518351 -0.4241459 -0.1622339
## 2627 0.1749079 -0.022076350 -0.034427084 0.3272519 0.5778235
## 2628 0.1749079 -0.667005737 -0.634597019 -0.4241459 -0.1622339
## 2629 0.1749079 -0.667005737 -0.649058945 0.3272519 -0.1622339
## 2630 0.1749079 -0.568730783 -0.569518351 0.3272519 -0.1622339
## 2631 0.1749079 -0.221697351 -0.294741755 0.3272519 -0.1622339
## 2632 0.1749079 -0.022076350 0.146346992 0.3272519 -0.9022913
## 2633 0.1749079 -0.144920043 -0.034427084 0.3272519 -0.1622339
## 2634 0.1749079 2.434797505 0.551280924 0.3272519 1.3178809
## 2635 -1.9841605 -0.636294814 0.399430699 0.3272519 -0.1622339
## 2636 -1.9841605 -0.636294814 -0.106736715 1.0786497 -0.9022913
## 2637 0.1749079 -0.421318352 0.182501808 1.0786497 -0.1622339
## 2638 -1.9841605 -0.452029275 -0.106736715 0.3272519 -0.9022913
## 2639 -1.9841605 -0.482740198 0.363275884 0.3272519 -0.1622339
## 2640 -1.9841605 -0.559517506 -0.323665607 0.3272519 -0.1622339
## 2641 -1.9841605 -0.482740198 -0.150122493 2.5814453 1.3178809
## 2642 -1.9841605 -0.667005737 -0.612904129 3.3328431 -0.1622339
## 2643 -1.9841605 -0.452029275 0.182501808 1.0786497 -0.9022913
## 2644 -1.9841605 -0.452029275 -0.685213760 1.0786497 -0.9022913
## 2645 -1.9841605 -0.482740198 0.182501808 1.8300475 -0.9022913
## 2646 -1.9841605 -1.112314124 -0.902142652 -1.1755437 -1.6423486
## 2647 -1.9841605 -1.081603200 -0.771985317 -0.4241459 -0.9022913
## 2648 -1.9841605 -0.544162045 1.628694420 4.8356387 0.5778235
## 2649 -1.9841605 -1.050892277 -0.829833021 -0.4241459 -0.9022913
## 2650 1.2544421 -0.390607429 -0.670751834 -0.4241459 -0.9022913
## 2651 0.1749079 -0.574872968 -0.714137612 -0.4241459 -0.9022913
## 2652 0.1749079 -0.544162045 -0.721368575 -1.1755437 -0.9022913
## 2653 0.1749079 2.588352121 3.581054447 0.3272519 0.5778235
## 2654 1.2544421 0.377165651 -0.265817902 0.3272519 0.5778235
## 2655 1.2544421 -0.574872968 -0.728599538 -1.1755437 -0.9022913
## 2656 1.2544421 0.054700958 -0.200739235 -0.4241459 -0.1622339
## 2657 1.2544421 2.895461353 1.628694420 -0.4241459 1.3178809
## 2658 1.2544421 2.895461353 0.500664182 -0.4241459 2.0579382
## 2659 1.2544421 2.895461353 0.905598114 -0.4241459 0.5778235
## 2660 1.2544421 0.070056419 0.905598114 0.3272519 0.5778235
## 2661 1.2544421 2.526930274 0.941752929 -0.4241459 0.5778235
## 2662 1.2544421 3.970343664 1.881778127 -0.4241459 1.3178809
## 2663 0.1749079 0.285032881 -0.063350937 -0.4241459 0.5778235
## 2664 0.1749079 0.315743805 -0.056119974 -0.4241459 -0.1622339
## 2665 1.2544421 2.741906737 0.471740330 -0.4241459 0.5778235
## 2666 1.2544421 0.500009344 0.037882546 -0.4241459 0.5778235
## 2667 1.2544421 0.469298421 -0.400530744 -0.4241459 -0.1622339
## 2668 1.2544421 1.974133657 0.088499288 -0.4241459 0.5778235
## 2669 1.2544421 0.070056419 -0.359820422 -1.1755437 0.5778235
## 2670 1.2544421 1.974133657 0.399430699 0.3272519 1.3178809
## 2671 1.2544421 0.208255574 -0.497208720 0.3272519 1.3178809
## 2672 1.2544421 0.438587497 0.196963734 -0.4241459 -0.1622339
## 2673 1.2544421 1.667024425 0.356044921 -0.4241459 0.5778235
## 2674 1.2544421 0.315743805 -0.056119974 0.3272519 1.3178809
## 2675 1.2544421 0.254321958 -0.309203681 -0.4241459 -0.9022913
## 2676 1.2544421 0.503080436 -0.358301920 -0.4241459 0.5778235
## 2677 0.1749079 -0.559517506 -0.728599538 -1.1755437 -0.9022913
## 2678 1.2544421 2.281242889 0.833288483 -0.4241459 0.5778235
## 2679 1.2544421 1.667024425 0.833288483 -0.4241459 0.5778235
## 2680 0.1749079 -0.544162045 -0.728599538 -1.1755437 -0.9022913
## 2681 1.2544421 1.667024425 0.826057520 -0.4241459 1.3178809
## 2682 1.2544421 -0.237052813 -0.446591979 -0.4241459 -0.1622339
## 2683 1.2544421 -0.237052813 -0.446591979 -0.4241459 -0.1622339
## 2684 0.1749079 -0.587157337 -0.793678206 -1.1755437 -1.6423486
## 2685 0.1749079 -0.390607429 -0.598442203 -0.4241459 -0.9022913
## 2686 1.2544421 2.895461353 0.442816478 0.3272519 1.3178809
## 2687 1.2544421 2.895461353 0.442816478 -0.4241459 0.5778235
## 2688 1.2544421 -0.083498197 -0.395975238 -0.4241459 -0.1622339
## 2689 1.2544421 0.423232036 -0.359820422 -0.4241459 1.3178809
## 2690 1.2544421 1.667024425 0.074037362 0.3272519 1.3178809
## 2691 1.2544421 0.407876574 -0.359820422 -0.4241459 0.5778235
## 2692 1.2544421 2.895461353 0.442816478 -0.4241459 0.5778235
## 2693 1.2544421 2.895461353 0.442816478 0.3272519 1.3178809
## 2694 1.2544421 -0.083498197 -0.395975238 -0.4241459 -0.1622339
## 2695 1.2544421 1.667024425 0.645283444 -0.4241459 -0.1622339
## 2696 -1.9841605 0.192900112 -0.287510792 -0.4241459 0.5778235
## 2697 1.2544421 2.127688273 0.074037362 -0.4241459 0.5778235
## 2698 1.2544421 1.974133657 0.746516926 -0.4241459 1.3178809
## 2699 1.2544421 1.667024425 0.833288483 -0.4241459 0.5778235
## 2700 1.2544421 0.530720267 -0.048889011 -0.4241459 -0.1622339
## 2701 1.2544421 0.530720267 -0.070581900 -0.4241459 -0.1622339
## 2702 1.2544421 0.530720267 -0.077812863 -0.4241459 -0.1622339
## 2703 1.2544421 -0.283119198 -0.612904129 -0.4241459 -0.9022913
## 2704 1.2544421 3.202570584 0.471740330 -0.4241459 1.3178809
## 2705 1.2544421 0.592142113 -0.193508272 -0.4241459 -0.1622339
## 2706 1.2544421 0.315743805 -0.269433384 -0.4241459 -0.1622339
## 2707 0.1749079 -0.390607429 -0.757523391 -0.4241459 -0.1622339
## 2708 0.1749079 0.530720267 -0.063350937 -0.4241459 -0.9022913
## 2709 0.1749079 1.820579041 0.688669222 -0.4241459 -0.1622339
## 2710 1.2544421 0.315743805 -0.200739235 -0.4241459 0.5778235
## 2711 1.2544421 0.223611035 -0.273048865 0.3272519 0.5778235
## 2712 1.2544421 0.315743805 -0.063350937 -0.4241459 0.5778235
## 2713 1.2544421 -0.390607429 -0.641827982 -0.4241459 -0.1622339
## 2714 1.2544421 -0.276977013 -0.072172712 0.3272519 -0.1622339
## 2715 1.2544421 0.503080436 -0.403206201 -1.1755437 -0.1622339
## 2716 1.2544421 0.503080436 -0.400530744 -0.4241459 -0.1622339
## 2717 1.2544421 2.281242889 0.471740330 -0.4241459 1.3178809
## 2718 1.2544421 2.649773967 0.471740330 -0.4241459 1.3178809
## 2719 1.2544421 0.500009344 -0.063350937 -0.4241459 -0.1622339
## 2720 1.2544421 0.223611035 -0.265817902 0.3272519 -0.1622339
## 2721 0.1749079 0.561431190 -0.056119974 -0.4241459 -2.3824060
## 2722 1.2544421 2.219821042 0.182501808 0.3272519 1.3178809
## 2723 1.2544421 0.223611035 -0.273048865 -0.4241459 -0.1622339
## 2724 1.2544421 0.223611035 -0.265817902 0.3272519 -0.1622339
## 2725 0.1749079 0.223611035 -0.321207079 -0.4241459 -0.1622339
## 2726 0.1749079 0.561431190 -0.063350937 -0.4241459 -0.9022913
## 2727 1.2544421 0.208255574 -0.273048865 -0.4241459 -0.1622339
## 2728 1.2544421 2.895461353 0.254811438 -0.4241459 0.5778235
## 2729 1.2544421 -0.022076350 -0.497208720 -1.1755437 -0.9022913
## 2730 1.2544421 0.592142113 0.688669222 0.3272519 -0.1622339
## 2731 1.2544421 1.206360577 0.298197217 -0.4241459 0.5778235
## 2732 1.2544421 0.530720267 -0.063350937 0.3272519 0.5778235
## 2733 1.2544421 1.974133657 0.196963734 -0.4241459 0.5778235
## 2734 1.2544421 2.895461353 1.050217375 -0.4241459 1.3178809
## 2735 1.2544421 -0.498095660 -0.815371095 -1.1755437 -0.9022913
## 2736 0.1749079 0.008634573 -0.323665607 0.3272519 0.5778235
## 2737 1.2544421 1.206360577 1.006831597 -0.4241459 0.5778235
## 2738 1.2544421 2.588352121 0.312659143 -0.4241459 0.5778235
## 2739 1.2544421 2.281242889 1.014062560 -0.4241459 0.5778235
## 2740 0.1749079 -0.436673813 -0.728599538 -1.1755437 -0.9022913
## 2741 1.2544421 1.206360577 0.298197217 -0.4241459 1.3178809
## 2742 1.2544421 2.281242889 1.014062560 0.3272519 1.3178809
## 2743 1.2544421 2.281242889 0.732055000 0.3272519 0.5778235
## 2744 1.2544421 4.277452896 2.424100357 0.3272519 2.0579382
## 2745 1.2544421 1.974133657 0.797133668 0.3272519 1.3178809
## 2746 0.1749079 3.202570584 0.471740330 0.3272519 1.3178809
## 2747 1.2544421 2.803328583 0.334352032 -0.4241459 1.3178809
## 2748 1.2544421 2.895461353 0.399430699 -0.4241459 0.5778235
## 2749 1.2544421 -0.519593306 -0.728599538 -1.1755437 -0.9022913
## 2750 0.1749079 -0.329185582 -0.656289908 -0.4241459 -0.9022913
## 2751 1.2544421 -0.452029275 -0.721368575 -1.1755437 -0.9022913
## 2752 1.2544421 -0.313830121 -0.656289908 -1.1755437 -0.9022913
## 2753 1.2544421 2.434797505 0.804364631 0.3272519 1.3178809
## 2754 0.1749079 -0.390607429 -0.649058945 -0.4241459 -0.9022913
## 2755 1.2544421 2.588352121 1.339455898 0.3272519 1.3178809
## 2756 1.2544421 0.285032881 -0.273048865 -0.4241459 -0.9022913
## 2757 0.1749079 0.008634573 -0.576749314 -0.4241459 -0.9022913
## 2758 -1.9841605 -1.060105554 -0.200739235 0.3272519 -0.9022913
## 2759 -1.9841605 -0.620939353 0.196963734 2.5814453 -0.9022913
## 2760 -1.9841605 -0.482740198 0.457278404 1.8300475 -0.9022913
## 2761 -1.9841605 -0.482740198 0.544049961 1.8300475 1.3178809
## 2762 0.1749079 0.346454728 1.050217375 0.3272519 1.3178809
## 2763 -0.9046263 -0.528806583 -0.583980277 -1.1755437 -0.9022913
## 2764 -0.9046263 -0.077356012 0.168039881 1.0786497 0.5778235
## 2765 0.1749079 -0.298474659 1.628694420 0.3272519 -0.1622339
## 2766 0.1749079 -0.390607429 -0.179046346 -0.4241459 -0.1622339
## 2767 0.1749079 -0.267763736 0.544049961 1.0786497 1.3178809
## 2768 -0.9046263 -0.022076350 0.037882546 -0.4241459 1.3178809
## 2769 -1.9841605 -0.667005737 -0.540594499 -0.4241459 -0.9022913
## 2770 0.1749079 -0.283119198 0.399430699 0.3272519 -0.1622339
## 2771 0.1749079 -0.421318352 0.327121069 1.0786497 -0.1622339
## 2772 0.1749079 -0.114209120 -0.099505752 0.3272519 1.3178809
## 2773 -0.9046263 -0.574872968 -0.555056425 -0.4241459 -0.9022913
## 2774 0.1749079 0.991384115 0.594666702 1.8300475 -0.1622339
## 2775 -0.9046263 -0.544162045 -0.540594499 -0.4241459 -0.9022913
## 2776 0.1749079 -0.114209120 0.168039881 1.0786497 -0.1622339
## 2777 0.1749079 -0.421318352 0.327121069 -0.4241459 -0.1622339
## 2778 0.1749079 -0.421318352 0.327121069 0.3272519 -0.1622339
## 2779 0.1749079 0.131478266 -0.085043826 1.0786497 1.3178809
## 2780 0.1749079 -0.144920043 -0.179046346 -0.4241459 -0.1622339
## 2781 -0.9046263 -0.495024568 -0.485639180 0.3272519 -0.1622339
## 2782 -0.9046263 -0.544162045 -0.518901610 0.3272519 -0.1622339
## 2783 0.1749079 0.131478266 0.757363371 0.3272519 1.3178809
## 2784 0.1749079 0.070056419 -0.359820422 0.3272519 -0.1622339
## 2785 0.1749079 -0.697716661 -0.555056425 -0.4241459 -0.9022913
## 2786 -0.9046263 -0.636294814 -0.786447243 0.3272519 -0.1622339
## 2787 -0.9046263 -0.620939353 -0.540594499 -0.4241459 -0.9022913
## 2788 0.1749079 -0.605583891 -0.504439683 -0.4241459 -0.1622339
## 2789 0.1749079 -0.175630966 0.616359591 1.8300475 1.3178809
## 2790 0.1749079 -0.237052813 -0.179046346 0.3272519 0.5778235
## 2791 -0.9046263 -0.835915815 -0.555056425 0.3272519 -0.1622339
## 2792 0.1749079 0.684274883 1.845623312 1.0786497 0.5778235
## 2793 0.1749079 -0.559517506 -0.468284868 -0.4241459 -0.9022913
## 2794 0.1749079 -0.716143214 -0.475515831 -0.4241459 -0.1622339
## 2795 0.1749079 -0.679290107 -0.473780400 -0.4241459 -0.1622339
## 2796 0.1749079 0.131478266 -0.265817902 0.3272519 0.5778235
## 2797 0.1749079 -0.237052813 -0.323665607 -0.4241459 -0.1622339
## 2798 0.1749079 -0.498095660 -0.482746794 -0.4241459 -0.9022913
## 2799 -0.9046263 -0.946475138 -0.902142652 -1.1755437 -1.6423486
## 2800 0.1749079 -0.676219014 -0.475515831 -0.4241459 -0.1622339
## 2801 0.1749079 -0.237052813 -0.323665607 0.3272519 -0.1622339
## 2802 0.1749079 -0.467384737 -0.417668127 -0.4241459 -0.9022913
## 2803 0.1749079 -0.716143214 -0.473780400 0.3272519 0.5778235
## 2804 0.1749079 -0.679290107 -0.526132573 0.3272519 -0.1622339
## 2805 0.1749079 -0.679290107 -0.526132573 0.3272519 0.5778235
## 2806 0.1749079 -0.679290107 -0.533363536 -0.4241459 -0.1622339
## 2807 0.1749079 -0.771422876 -0.475515831 0.3272519 0.5778235
## 2808 0.1749079 -0.679290107 -0.533363536 -0.4241459 -0.9022913
## 2809 -0.9046263 -0.298474659 -0.106736715 -0.4241459 0.5778235
## 2810 0.1749079 -0.206341890 -0.359820422 0.3272519 1.3178809
## 2811 0.1749079 -0.206341890 -0.359820422 0.3272519 1.3178809
## 2812 -1.9841605 -1.103100847 -0.837063984 -0.4241459 -0.9022913
## 2813 0.1749079 -0.267763736 -0.663520871 -1.1755437 -0.9022913
## 2814 -0.9046263 -0.937261861 -0.786447243 -0.4241459 -0.1622339
## 2815 -0.9046263 -0.949546231 -0.706906649 -0.4241459 -0.9022913
## 2816 -0.9046263 -0.937261861 -0.670751834 -0.4241459 -0.9022913
## 2817 -0.9046263 -0.912693123 -0.685213760 -0.4241459 -0.9022913
## 2818 -0.9046263 -0.544162045 -0.323665607 0.3272519 0.5778235
## 2819 -0.9046263 -0.857413461 -0.692444723 -0.4241459 -0.9022913
## 2820 -0.9046263 -0.866626738 -0.699675686 -0.4241459 -0.9022913
## 2821 -0.9046263 -0.857413461 -0.728599538 -0.4241459 -0.9022913
## 2822 -0.9046263 -0.958759508 -0.699675686 -0.4241459 -0.9022913
## 2823 -0.9046263 -0.928048584 -0.685213760 -0.4241459 -0.9022913
## 2824 -0.9046263 -0.928048584 -0.706906649 -0.4241459 -0.9022913
## 2825 -0.9046263 -0.912693123 -0.714137612 -0.4241459 -0.9022913
## 2826 -0.9046263 -0.943404046 -0.706906649 -0.4241459 -0.9022913
## 2827 -0.9046263 -0.928048584 -0.670751834 -0.4241459 -0.9022913
## 2828 -0.9046263 -0.912693123 -0.685213760 -0.4241459 -1.6423486
## 2829 -0.9046263 -0.943404046 -0.685213760 -0.4241459 -0.1622339
## 2830 -0.9046263 -1.004825892 -0.728599538 -0.4241459 -0.9022913
## 2831 0.1749079 0.100767342 0.139116029 0.3272519 1.3178809
## 2832 0.1749079 -0.022076350 0.666976333 -0.4241459 -0.1622339
## 2833 -1.9841605 -0.820560353 -0.627366056 -0.4241459 -0.9022913
## 2834 0.1749079 -0.052787274 1.773313681 1.8300475 1.3178809
## 2835 -1.9841605 -0.022076350 1.267146267 1.0786497 1.3178809
## 2836 0.1749079 -0.022076350 1.773313681 1.8300475 0.5778235
## 2837 0.1749079 0.592142113 0.833288483 -0.4241459 0.5778235
## 2838 0.1749079 0.530720267 0.760978853 1.0786497 0.5778235
## 2839 0.1749079 0.285032881 1.484075159 1.0786497 -0.9022913
## 2840 -0.9046263 -0.851271277 -0.743061465 -0.4241459 -0.9022913
## 2841 -0.9046263 -0.789849430 -0.706906649 0.3272519 -0.1622339
## 2842 -0.9046263 -0.789849430 -0.497208720 -0.4241459 -0.9022913
## 2843 0.1749079 -0.795991615 -0.497208720 -0.4241459 -0.1622339
## 2844 0.1749079 -0.789849430 -0.656289908 -0.4241459 -0.1622339
## 2845 0.1749079 -0.329185582 0.008958694 -0.4241459 -0.9022913
## 2846 0.1749079 0.438587497 0.833288483 0.3272519 0.5778235
## 2847 0.1749079 0.131478266 1.628694420 1.0786497 2.7979956
## 2848 0.1749079 0.438587497 0.833288483 0.3272519 -0.1622339
## 2849 0.1749079 0.438587497 0.905598114 0.3272519 0.5778235
## 2850 0.1749079 -0.605583891 -0.338127533 0.3272519 0.5778235
## 2851 0.1749079 -0.792920522 -0.533363536 0.3272519 -0.1622339
## 2852 -1.9841605 -0.559517506 0.254811438 0.3272519 -0.9022913
## 2853 0.1749079 0.070056419 0.471740330 4.8356387 3.5380530
## 2854 -0.9046263 -1.035536816 -0.743061465 -0.4241459 -1.6423486
## 2855 1.2544421 1.359915193 1.122527006 0.3272519 0.5778235
## 2856 1.2544421 3.663234432 9.582753790 -0.4241459 1.3178809
## 2857 1.2544421 4.431007512 1.990242573 0.3272519 0.5778235
## 2858 1.2544421 3.509679816 2.026397389 1.0786497 2.0579382
## 2859 1.2544421 0.929962268 0.327121069 -0.4241459 1.3178809
## 2860 1.2544421 3.816789048 2.084245093 0.3272519 1.3178809
## 2861 1.2544421 0.177544650 -0.077812863 -0.4241459 -0.1622339
## 2862 1.2544421 3.816789048 1.484075159 0.3272519 0.5778235
## 2863 1.2544421 0.644350683 -0.106736715 -0.4241459 -0.1622339
## 2864 1.2544421 0.177544650 -0.395975238 -0.4241459 -0.1622339
## 2865 1.2544421 2.281242889 1.628694420 0.3272519 0.5778235
## 2866 1.2544421 0.285032881 -0.410437164 -0.4241459 -0.1622339
## 2867 1.2544421 2.127688273 0.905598114 0.3272519 1.3178809
## 2868 1.2544421 0.331099266 -0.410437164 -0.4241459 -0.1622339
## 2869 1.2544421 0.177544650 -0.070581900 -0.4241459 0.5778235
## 2870 1.2544421 -0.421318352 -0.757523391 -1.9269415 -1.6423486
## 2871 1.2544421 -0.083498197 -0.518901610 -0.4241459 -0.1622339
## 2872 1.2544421 2.434797505 1.122527006 0.3272519 0.5778235
## 2873 1.2544421 0.469298421 0.196963734 -0.4241459 0.5778235
## 2874 0.1749079 3.509679816 1.773313681 0.3272519 0.5778235
## 2875 1.2544421 0.911535715 0.037882546 -0.4241459 -0.1622339
## 2876 1.2544421 3.509679816 1.165912784 0.3272519 1.3178809
## 2877 1.2544421 3.509679816 1.165912784 0.3272519 1.3178809
## 2878 1.2544421 0.407876574 0.182501808 0.3272519 0.5778235
## 2879 1.2544421 -0.101924751 -0.482746794 -0.4241459 -0.1622339
## 2880 1.2544421 0.807118576 -0.236894050 0.3272519 0.5778235
## 2881 1.2544421 0.899251345 0.688669222 1.0786497 1.3178809
## 2882 1.2544421 4.123898280 2.351790726 1.0786497 2.0579382
## 2883 0.1749079 0.070056419 -0.215201161 -0.4241459 -0.1622339
## 2884 1.2544421 0.530720267 -0.301972718 -0.4241459 0.5778235
## 2885 1.2544421 2.281242889 2.713338880 1.0786497 0.5778235
## 2886 1.2544421 2.889319168 3.212275331 1.0786497 2.7979956
## 2887 1.2544421 3.816789048 1.773313681 0.3272519 2.0579382
## 2888 1.2544421 2.434797505 2.821803326 1.8300475 2.7979956
## 2889 1.2544421 3.202570584 9.582753790 -0.4241459 1.3178809
## 2890 1.2544421 0.070056419 -0.301972718 -0.4241459 -0.1622339
## 2891 1.2544421 2.895461353 3.212275331 1.0786497 2.7979956
## 2892 1.2544421 1.452047963 0.124654103 -0.4241459 0.5778235
## 2893 1.2544421 -0.022076350 -0.395975238 -0.4241459 1.3178809
## 2894 1.2544421 3.141148738 2.069783167 0.3272519 0.5778235
## 2895 1.2544421 0.407876574 -0.287510792 -0.4241459 -0.1622339
## 2896 1.2544421 1.329204270 0.977907744 0.3272519 1.3178809
## 2897 1.2544421 3.663234432 1.990242573 -0.4241459 2.0579382
## 2898 0.1749079 4.123898280 1.990242573 0.3272519 1.3178809
## 2899 1.2544421 0.929962268 -0.106736715 0.3272519 1.3178809
## 2900 0.1749079 2.588352121 1.990242573 1.8300475 1.3178809
## 2901 1.2544421 0.438587497 0.160808918 -0.4241459 0.5778235
## 2902 1.2544421 0.438587497 -0.345358496 -0.4241459 1.3178809
## 2903 1.2544421 1.359915193 0.833288483 1.0786497 2.0579382
## 2904 1.2544421 2.895461353 3.212275331 1.0786497 2.7979956
## 2905 1.2544421 0.285032881 -0.186277309 0.3272519 0.5778235
## 2906 1.2544421 1.298493347 0.450047441 0.3272519 1.3178809
## 2907 1.2544421 2.588352121 3.074887033 1.0786497 2.7979956
## 2908 1.2544421 0.285032881 -0.229663087 -0.4241459 -0.1622339
## 2909 1.2544421 -0.206341890 -0.511670647 -0.4241459 -0.1622339
## 2910 1.2544421 3.509679816 3.942602600 1.8300475 2.0579382
## 2911 1.2544421 3.202570584 3.045963181 1.0786497 2.0579382
## 2912 1.2544421 0.991384115 0.760978853 0.3272519 1.3178809
## 2913 1.2544421 1.974133657 0.724824037 0.3272519 1.3178809
## 2914 1.2544421 1.605602579 1.628694420 -0.4241459 -0.1622339
## 2915 1.2544421 0.681203791 0.544049961 1.0786497 2.0579382
## 2916 1.2544421 3.356125200 1.773313681 0.3272519 2.0579382
## 2917 1.2544421 0.991384115 0.826057520 1.0786497 1.3178809
## 2918 1.2544421 1.129583269 1.267146267 -0.4241459 0.5778235
## 2919 1.2544421 0.315743805 -0.323665607 -0.4241459 -0.1622339
## 2920 1.2544421 1.544180732 2.857958141 1.0786497 2.0579382
## 2921 1.2544421 0.837829499 1.158681821 1.0786497 2.7979956
## 2922 1.2544421 0.223611035 -0.034427084 0.3272519 0.5778235
## 2923 1.2544421 1.974133657 1.050217375 0.3272519 2.0579382
## 2924 1.2544421 0.377165651 -0.265817902 -2.6783393 0.5778235
## 2925 1.2544421 0.684274883 0.544049961 1.0786497 2.0579382
## 2926 1.2544421 1.206360577 0.168039881 0.3272519 0.5778235
## 2927 1.2544421 0.407876574 -0.273048865 -0.4241459 0.5778235
## 2928 1.2544421 0.131478266 -0.395975238 -0.4241459 -0.1622339
## 2929 1.2544421 0.346454728 -0.294741755 0.3272519 0.5778235
## 2930 1.2544421 0.622853037 -0.106736715 -0.4241459 0.5778235
## 2931 1.2544421 0.899251345 0.182501808 0.3272519 1.3178809
## 2932 1.2544421 0.899251345 0.117423140 0.3272519 1.3178809
## 2933 1.2544421 1.114227808 0.276504327 -0.4241459 -0.1622339
## 2934 1.2544421 1.513469809 1.990242573 0.3272519 0.5778235
## 2935 1.2544421 0.039345496 -0.410437164 -0.4241459 -0.1622339
## 2936 0.1749079 0.438587497 -0.330896570 -0.4241459 -0.1622339
## 2937 1.2544421 2.281242889 5.967272258 0.3272519 1.3178809
## 2938 1.2544421 3.049015969 2.077014130 0.3272519 1.3178809
## 2939 1.2544421 3.049015969 0.760978853 0.3272519 1.3178809
## 2940 1.2544421 2.281242889 1.339455898 0.3272519 2.0579382
## 2941 1.2544421 -0.175630966 -0.518901610 -0.4241459 -0.9022913
## 2942 1.2544421 2.588352121 2.207171465 0.3272519 2.0579382
## 2943 1.2544421 0.131478266 -0.301972718 0.3272519 0.5778235
## 2944 1.2544421 0.899251345 -0.077812863 0.3272519 1.3178809
## 2945 1.2544421 1.544180732 1.267146267 0.3272519 1.3178809
## 2946 1.2544421 1.359915193 4.839242020 0.3272519 0.5778235
## 2947 1.2544421 3.049015969 0.833288483 0.3272519 1.3178809
## 2948 1.2544421 0.346454728 -0.048889011 -0.4241459 -0.1622339
## 2949 1.2544421 1.544180732 0.493433219 -0.4241459 0.5778235
## 2950 1.2544421 2.588352121 1.990242573 1.0786497 2.0579382
## 2951 1.2544421 1.298493347 1.093603153 1.0786497 2.0579382
## 2952 1.2544421 -0.175630966 -0.511670647 -0.4241459 -0.1622339
## 2953 1.2544421 0.745696729 -0.142891530 0.3272519 0.5778235
## 2954 1.2544421 0.745696729 -0.179046346 0.3272519 0.5778235
## 2955 1.2544421 2.588352121 4.774163353 0.3272519 2.0579382
## 2956 1.2544421 2.281242889 0.797133668 0.3272519 1.3178809
## 2957 1.2544421 3.816789048 1.990242573 0.3272519 2.0579382
## 2958 1.2544421 1.974133657 1.983011610 0.3272519 2.0579382
## 2959 1.2544421 1.359915193 1.447920344 1.8300475 0.5778235
## 2960 1.2544421 1.359915193 1.245453378 0.3272519 0.5778235
## 2961 1.2544421 0.070056419 -0.576749314 -0.4241459 -0.9022913
## 2962 1.2544421 1.298493347 5.967272258 0.3272519 1.3178809
## 2963 1.2544421 1.636313502 0.905598114 -0.4241459 0.5778235
## 2964 1.2544421 2.189110119 1.310532045 -0.4241459 1.3178809
## 2965 1.2544421 -0.144920043 -0.410437164 -0.4241459 -0.1622339
## 2966 1.2544421 1.421337039 0.905598114 0.3272519 2.0579382
## 2967 1.2544421 1.083516884 0.616359591 -0.4241459 0.5778235
## 2968 1.2544421 2.281242889 2.894112956 0.3272519 2.0579382
## 2969 1.2544421 0.377165651 -0.316434644 -0.4241459 0.5778235
## 2970 1.2544421 1.513469809 0.457278404 -0.4241459 0.5778235
## 2971 0.1749079 0.530720267 0.001727731 0.3272519 1.3178809
## 2972 1.2544421 0.561431190 -0.207970198 0.3272519 0.5778235
## 2973 1.2544421 0.899251345 0.905598114 1.0786497 1.3178809
## 2974 1.2544421 2.434797505 2.351790726 0.3272519 2.0579382
## 2975 1.2544421 2.281242889 2.351790726 0.3272519 2.0579382
## 2976 1.2544421 2.526930274 1.990242573 1.0786497 1.3178809
## 2977 1.2544421 2.281242889 2.127630872 1.0786497 2.0579382
## 2978 1.2544421 1.022095038 0.688669222 0.3272519 1.3178809
## 2979 1.2544421 0.223611035 -0.374282348 0.3272519 0.5778235
## 2980 1.2544421 3.816789048 1.390072639 0.3272519 2.0579382
## 2981 1.2544421 4.123898280 6.618058934 0.3272519 1.3178809
## 2982 1.2544421 1.359915193 1.194836636 0.3272519 1.3178809
## 2983 1.2544421 2.434797505 0.905598114 1.0786497 2.7979956
## 2984 1.2544421 2.588352121 2.713338880 0.3272519 2.0579382
## 2985 1.2544421 1.267782424 4.759701427 0.3272519 1.3178809
## 2986 1.2544421 1.344559732 1.122527006 0.3272519 2.0579382
## 2987 1.2544421 1.206360577 1.050217375 0.3272519 2.0579382
## 2988 1.2544421 2.526930274 0.876674262 -0.4241459 1.3178809
## 2989 1.2544421 2.158399196 0.478971293 -0.4241459 0.5778235
## 2990 1.2544421 1.513469809 1.780544644 0.3272519 1.3178809
## 2991 1.2544421 2.281242889 2.821803326 1.0786497 1.3178809
## 2992 1.2544421 0.254321958 -0.251355976 -0.4241459 -0.1622339
## 2993 1.2544421 0.407876574 -0.287510792 -0.4241459 -0.1622339
## 2994 1.2544421 0.438587497 0.182501808 0.3272519 1.3178809
## 2995 1.2544421 0.807118576 -0.070581900 -0.4241459 0.5778235
## 2996 1.2544421 1.974133657 0.565742850 1.8300475 2.0579382
## 2997 1.2544421 0.377165651 -0.309203681 0.3272519 1.3178809
## 2998 1.2544421 3.816789048 1.397303602 1.0786497 2.0579382
## 2999 1.2544421 0.128407173 -0.229663087 0.3272519 1.3178809
## 3000 1.2544421 4.277452896 1.628694420 0.3272519 2.0579382
## 3001 1.2544421 2.526930274 1.267146267 0.3272519 1.3178809
## 3002 1.2544421 2.741906737 3.074887033 1.8300475 2.7979956
## 3003 1.2544421 2.895461353 3.212275331 1.0786497 2.7979956
## 3004 0.1749079 0.622853037 -0.027196121 1.8300475 2.0579382
## 3005 1.2544421 2.127688273 3.797983339 1.8300475 2.0579382
## 3006 1.2544421 1.452047963 1.067716306 0.3272519 1.3178809
## 3007 1.2544421 1.513469809 0.833288483 0.3272519 1.3178809
## 3008 1.2544421 3.509679816 1.122527006 -0.4241459 1.3178809
## 3009 1.2544421 0.171402466 -0.106736715 0.3272519 0.5778235
## 3010 1.2544421 0.285032881 -0.280279829 0.3272519 0.5778235
## 3011 1.2544421 0.745696729 0.760978853 0.3272519 0.5778235
## 3012 0.1749079 -0.129564582 -0.504439683 -0.4241459 -0.9022913
## 3013 1.2544421 1.513469809 0.276504327 0.3272519 1.3178809
## 3014 1.2544421 0.008634573 -0.323665607 1.0786497 1.3178809
## 3015 1.2544421 0.622853037 -0.027196121 -0.4241459 0.5778235
## 3016 1.2544421 0.192900112 -0.034427084 0.3272519 0.5778235
## 3017 1.2544421 -0.605583891 -0.865987837 -1.9269415 -1.6423486
## 3018 1.2544421 0.438587497 -0.280279829 -0.4241459 0.5778235
## 3019 0.1749079 -0.605583891 -0.865987837 -1.9269415 -1.6423486
## 3020 1.2544421 -0.022076350 -0.497208720 -0.4241459 -0.1622339
## 3021 1.2544421 -0.022076350 -0.323665607 -0.4241459 -0.1622339
## 3022 1.2544421 -0.206341890 -0.504439683 -0.4241459 -0.1622339
## 3023 1.2544421 -0.022076350 -0.417668127 -0.4241459 -0.1622339
## 3024 1.2544421 -0.083498197 -0.417668127 0.3272519 0.5778235
## 3025 1.2544421 1.175649654 0.580204776 0.3272519 2.0579382
## 3026 1.2544421 1.206360577 1.578077679 0.3272519 1.3178809
## 3027 1.2544421 1.329204270 1.093603153 0.3272519 1.3178809
## 3028 1.2544421 -0.083498197 -0.417668127 -0.4241459 -0.1622339
## 3029 1.2544421 1.298493347 1.122527006 0.3272519 1.3178809
## 3030 1.2544421 1.605602579 0.522357071 0.3272519 1.3178809
## 3031 1.2544421 0.469298421 -0.265817902 -0.4241459 0.5778235
## 3032 1.2544421 1.175649654 0.363275884 0.3272519 1.3178809
## 3033 1.2544421 3.816789048 1.773313681 1.8300475 2.7979956
## 3034 1.2544421 2.434797505 1.484075159 0.3272519 0.5778235
## 3035 1.2544421 0.469298421 0.160808918 -0.4241459 -0.9022913
## 3036 1.2544421 2.588352121 1.484075159 1.0786497 2.0579382
## 3037 1.2544421 0.315743805 -0.316434644 0.3272519 0.5778235
## 3038 1.2544421 1.267782424 0.276504327 0.3272519 1.3178809
## 3039 1.2544421 0.438587497 0.399430699 0.3272519 1.3178809
## 3040 1.2544421 0.592142113 0.110192177 -0.4241459 -0.1622339
## 3041 1.2544421 0.285032881 0.001727731 -0.4241459 0.5778235
## 3042 1.2544421 0.622853037 -0.113967678 -0.4241459 0.5778235
## 3043 1.2544421 3.509679816 0.833288483 0.3272519 1.3178809
## 3044 1.2544421 3.970343664 0.833288483 -0.4241459 0.5778235
## 3045 1.2544421 0.745696729 0.544049961 1.0786497 1.3178809
## 3046 1.2544421 -0.528806583 -0.851525911 -1.9269415 -0.9022913
## 3047 1.2544421 1.820579041 1.050217375 -0.4241459 2.0579382
## 3048 1.2544421 -0.375251967 -0.468284868 0.3272519 -0.1622339
## 3049 1.2544421 1.820579041 -0.034427084 -0.4241459 2.0579382
## 3050 1.2544421 0.622853037 0.023420620 -0.4241459 1.3178809
## 3051 1.2544421 0.745696729 -0.027196121 1.0786497 0.5778235
## 3052 1.2544421 0.960673192 1.361148787 -0.4241459 -0.1622339
## 3053 1.2544421 0.530720267 0.001727731 0.3272519 1.3178809
## 3054 1.2544421 1.359915193 -0.070581900 -0.4241459 1.3178809
## 3055 1.2544421 0.162189189 -0.193508272 -0.4241459 -0.1622339
## 3056 1.2544421 0.423232036 -0.251355976 -0.4241459 0.5778235
## 3057 1.2544421 0.745696729 -0.186277309 0.3272519 1.3178809
## 3058 1.2544421 0.745696729 -0.135660567 0.3272519 1.3178809
## 3059 1.2544421 0.745696729 -0.106736715 0.3272519 1.3178809
## 3060 1.2544421 0.039345496 -0.280279829 -0.4241459 -0.1622339
## 3061 1.2544421 0.039345496 -0.265817902 -0.4241459 0.5778235
## 3062 1.2544421 0.008634573 -0.395975238 -0.4241459 0.5778235
## 3063 1.2544421 0.447800774 -0.301972718 -0.4241459 1.3178809
## 3064 0.1749079 0.561431190 0.182501808 0.3272519 0.5778235
## 3065 1.2544421 0.484653882 -0.092274789 0.3272519 1.3178809
## 3066 1.2544421 0.423232036 -0.301972718 -0.4241459 1.3178809
## 3067 1.2544421 -0.022076350 -0.367051385 -0.4241459 0.5778235
## 3068 1.2544421 1.421337039 0.399430699 0.3272519 0.5778235
## 3069 1.2544421 0.714985806 -0.251355976 -0.4241459 0.5778235
## 3070 1.2544421 0.100767342 -0.439361016 0.3272519 1.3178809
## 3071 1.2544421 0.070056419 -0.323665607 0.3272519 0.5778235
## 3072 1.2544421 0.377165651 -0.280279829 -0.4241459 -0.1622339
## 3073 1.2544421 0.745696729 -0.106736715 0.3272519 1.3178809
## 3074 1.2544421 1.191005116 0.088499288 0.3272519 1.3178809
## 3075 1.2544421 0.346454728 -0.287510792 -0.4241459 0.5778235
## 3076 0.1749079 0.438587497 -0.215201161 -0.4241459 1.3178809
## 3077 1.2544421 0.285032881 -0.446591979 0.3272519 -0.1622339
## 3078 1.2544421 -0.022076350 -0.518901610 0.3272519 -0.1622339
## 3079 1.2544421 0.285032881 -0.446591979 0.3272519 -0.1622339
## 3080 1.2544421 0.407876574 -0.287510792 0.3272519 1.3178809
## 3081 1.2544421 -0.651650276 -0.899973363 -1.9269415 -1.6423486
## 3082 1.2544421 1.052805961 -0.106736715 -0.4241459 1.3178809
## 3083 1.2544421 1.052805961 -0.106736715 -0.4241459 1.3178809
## 3084 1.2544421 -0.252408274 -0.482746794 -0.4241459 -0.1622339
## 3085 1.2544421 0.714985806 -0.106736715 0.3272519 1.3178809
## 3086 1.2544421 0.530720267 -0.179046346 -0.4241459 1.3178809
## 3087 1.2544421 0.438587497 -0.193508272 0.3272519 1.3178809
## 3088 1.2544421 0.438587497 -0.193508272 -0.4241459 1.3178809
## 3089 1.2544421 0.192900112 -0.251355976 -0.4241459 -0.1622339
## 3090 0.1749079 0.131478266 -0.374282348 -0.4241459 -0.1622339
## 3091 1.2544421 0.377165651 -0.345358496 -0.4241459 0.5778235
## 3092 1.2544421 -0.390607429 -0.627366056 -1.1755437 -0.9022913
## 3093 1.2544421 0.177544650 -0.309203681 -1.1755437 -0.1622339
## 3094 1.2544421 0.116122804 -0.251355976 0.3272519 0.5778235
## 3095 1.2544421 0.131478266 -0.258586939 0.3272519 -0.1622339
## 3096 1.2544421 0.192900112 -0.280279829 -1.1755437 0.5778235
## 3097 1.2544421 -0.022076350 -0.395975238 -0.4241459 -0.1622339
## 3098 1.2544421 0.407876574 -0.287510792 0.3272519 1.3178809
## 3099 1.2544421 0.377165651 -0.273048865 0.3272519 0.5778235
## 3100 1.2544421 1.083516884 -0.077812863 -0.4241459 1.3178809
## 3101 1.2544421 0.407876574 -0.287510792 -0.4241459 0.5778235
## 3102 1.2544421 0.438587497 -0.367051385 0.3272519 0.5778235
## 3103 1.2544421 -0.022076350 -0.410437164 -0.4241459 -0.9022913
## 3104 1.2544421 0.100767342 -0.468284868 -0.4241459 -0.9022913
## 3105 1.2544421 1.163365285 0.088499288 -0.4241459 1.3178809
## 3106 1.2544421 0.407876574 -0.338127533 -0.4241459 0.5778235
## 3107 1.2544421 0.407876574 -0.345358496 -0.4241459 1.3178809
## 3108 1.2544421 0.315743805 -0.345358496 -0.4241459 1.3178809
## 3109 1.2544421 0.714985806 -0.179046346 0.3272519 1.3178809
## 3110 1.2544421 2.281242889 0.262042401 -0.4241459 -0.1622339
## 3111 1.2544421 0.745696729 -0.106736715 0.3272519 1.3178809
## 3112 1.2544421 0.776407653 -0.121198641 -0.4241459 1.3178809
## 3113 1.2544421 0.745696729 -0.121198641 -0.4241459 0.5778235
## 3114 1.2544421 1.237071500 0.088499288 -0.4241459 1.3178809
## 3115 1.2544421 0.420160944 -0.301972718 0.3272519 1.3178809
## 3116 1.2544421 0.745696729 -0.106736715 0.3272519 1.3178809
## 3117 1.2544421 0.592142113 -0.265817902 0.3272519 1.3178809
## 3118 1.2544421 0.592142113 -0.273048865 -0.4241459 -0.1622339
## 3119 1.2544421 1.974133657 0.327121069 0.3272519 0.5778235
## 3120 1.2544421 1.144938731 0.088499288 0.3272519 1.3178809
## 3121 1.2544421 0.438587497 -0.309203681 -0.4241459 0.5778235
## 3122 1.2544421 1.022095038 0.088499288 -0.4241459 0.5778235
## 3123 1.2544421 0.377165651 -0.316434644 -0.4241459 1.3178809
## 3124 1.2544421 2.741906737 0.269273364 -0.4241459 1.3178809
## 3125 1.2544421 0.423232036 -0.338127533 0.3272519 1.3178809
## 3126 1.2544421 0.662777237 -0.301972718 -0.4241459 0.5778235
## 3127 1.2544421 0.438587497 -0.338127533 0.3272519 1.3178809
## 3128 1.2544421 0.745696729 -0.323665607 0.3272519 1.3178809
## 3129 1.2544421 0.377165651 -0.287510792 -0.4241459 0.5778235
## 3130 1.2544421 0.592142113 -0.244125013 -0.4241459 0.5778235
## 3131 1.2544421 -0.175630966 -0.316434644 -0.4241459 -0.9022913
## 3132 1.2544421 3.755367202 2.373483616 0.3272519 1.3178809
## 3133 1.2544421 1.974133657 5.822652997 0.3272519 2.7979956
## 3134 1.2544421 2.772617660 0.977907744 0.3272519 2.0579382
## 3135 1.2544421 1.974133657 1.484075159 0.3272519 2.0579382
## 3136 1.2544421 1.298493347 0.544049961 0.3272519 2.0579382
## 3137 1.2544421 2.588352121 2.207171465 1.0786497 1.3178809
## 3138 1.2544421 2.281242889 4.087221862 0.3272519 0.5778235
## 3139 1.2544421 0.730341268 0.225887586 -0.4241459 0.5778235
## 3140 1.2544421 3.202570584 5.822652997 -0.4241459 1.3178809
## 3141 1.2544421 4.123898280 1.845623312 1.0786497 2.0579382
## 3142 1.2544421 1.452047963 1.875342570 -0.4241459 1.3178809
## 3143 1.2544421 1.359915193 1.108065080 1.0786497 2.0579382
## 3144 1.2544421 1.544180732 0.760978853 -0.4241459 1.3178809
## 3145 1.2544421 1.574891655 2.207171465 1.0786497 2.0579382
## 3146 1.2544421 1.974133657 1.484075159 0.3272519 2.0579382
## 3147 1.2544421 1.636313502 1.780544644 0.3272519 1.3178809
## 3148 1.2544421 0.116122804 -0.273048865 -0.4241459 -0.1622339
## 3149 1.2544421 2.680484890 0.883905225 0.3272519 1.3178809
## 3150 1.2544421 1.114227808 0.580204776 -0.4241459 0.5778235
## 3151 1.2544421 1.267782424 0.876674262 -0.4241459 0.5778235
## 3152 1.2544421 1.206360577 1.339455898 -0.4241459 1.3178809
## 3153 1.2544421 0.899251345 1.194836636 1.0786497 2.0579382
## 3154 1.2544421 2.281242889 1.628694420 1.0786497 0.5778235
## 3155 1.2544421 1.452047963 1.845623312 0.3272519 1.3178809
## 3156 1.2544421 1.144938731 5.244175952 0.3272519 0.5778235
## 3157 1.2544421 1.713090810 0.920060040 0.3272519 2.0579382
## 3158 1.2544421 1.667024425 1.628694420 0.3272519 2.0579382
## 3159 1.2544421 1.605602579 0.544049961 0.3272519 2.7979956
## 3160 1.2544421 1.605602579 1.252684341 -0.4241459 1.3178809
## 3161 1.2544421 1.544180732 0.905598114 0.3272519 2.0579382
## 3162 1.2544421 2.281242889 0.703131148 -0.4241459 1.3178809
## 3163 1.2544421 0.407876574 -0.258586939 -0.4241459 0.5778235
## 3164 1.2544421 0.254321958 -0.294741755 -0.4241459 0.5778235
## 3165 1.2544421 0.254321958 -0.280279829 -0.4241459 0.5778235
## 3166 1.2544421 -0.006720889 -0.410437164 -0.4241459 -0.1622339
## 3167 1.2544421 1.206360577 0.074037362 -0.4241459 1.3178809
## 3168 1.2544421 0.807118576 -0.034427084 0.3272519 1.3178809
## 3169 1.2544421 0.546075729 -0.301972718 0.3272519 0.5778235
## 3170 -1.9841605 -0.544162045 -0.273048865 0.3272519 -0.1622339
## 3171 -1.9841605 -0.513451121 -0.034427084 0.3272519 -0.9022913
## 3172 -1.9841605 -0.651650276 -0.656289908 4.0842409 -0.1622339
## 3173 -1.9841605 -1.066247739 -0.829833021 -0.4241459 -0.9022913
## 3174 -1.9841605 -1.066247739 -0.837063984 -0.4241459 -0.9022913
## 3175 -1.9841605 -0.912693123 -0.902142652 -1.9269415 -1.6423486
## 3176 0.1749079 -0.427460536 -0.453822942 -0.4241459 -0.1622339
## 3177 1.2544421 0.742625637 -0.077812863 -0.4241459 1.3178809
## 3178 0.1749079 0.899251345 0.363275884 1.0786497 0.5778235
## 3179 -1.9841605 -0.789849430 -0.395975238 -0.4241459 -1.6423486
## 3180 -1.9841605 -1.100029754 -0.815371095 -0.4241459 -1.6423486
## 3181 -1.9841605 -1.127669585 -0.837063984 -0.4241459 -0.9022913
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## 3184 -0.9046263 -0.574872968 -0.656289908 -0.4241459 -0.9022913
## 3185 -0.9046263 -0.197128613 0.399430699 1.8300475 0.5778235
## 3186 0.1749079 0.285032881 0.688669222 1.8300475 1.3178809
## 3187 0.1749079 -0.267763736 -0.518901610 0.3272519 0.5778235
## 3188 -0.9046263 -0.237052813 0.059575435 -0.4241459 -0.1622339
## 3189 0.1749079 -0.237052813 -0.533363536 0.3272519 0.5778235
## 3190 0.1749079 -0.359896505 -0.540594499 0.3272519 0.5778235
## 3191 -0.9046263 0.285032881 1.990242573 1.8300475 0.5778235
## 3192 0.1749079 0.592142113 1.050217375 1.8300475 0.5778235
## 3193 -0.9046263 0.500009344 0.211425660 1.8300475 1.3178809
## 3194 0.1749079 0.346454728 0.471740330 1.8300475 2.0579382
## 3195 0.1749079 -0.267763736 -0.527000288 -0.4241459 0.5778235
## 3196 -0.9046263 0.899251345 2.351790726 4.0842409 5.0181677
## 3197 0.1749079 0.592142113 0.760978853 -1.1755437 1.3178809
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## 3200 -0.9046263 0.684274883 1.339455898 0.3272519 0.5778235
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## 3202 0.1749079 -0.777565061 -0.728599538 -0.4241459 -0.9022913
## 3203 0.1749079 0.008634573 1.035755449 1.0786497 1.3178809
## 3204 0.1749079 -0.667005737 -0.540594499 -0.4241459 -0.9022913
## 3205 -0.9046263 -0.820560353 -0.656289908 -0.4241459 -0.1622339
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## 3207 -0.9046263 -0.759138507 -0.743061465 -0.4241459 -0.9022913
## 3208 -0.9046263 -0.811347076 -0.663520871 0.3272519 -0.1622339
## 3209 0.1749079 -0.083498197 0.977907744 1.0786497 0.5778235
## 3210 0.1749079 -0.237052813 0.037882546 0.3272519 -0.1622339
## 3211 0.1749079 0.070056419 0.037882546 4.8356387 2.0579382
## 3212 0.1749079 0.070056419 0.037882546 4.8356387 2.0579382
## 3213 -0.9046263 -0.759138507 -0.743061465 -0.4241459 -0.9022913
## 3214 0.1749079 0.714985806 1.874547164 4.0842409 3.5380530
## 3215 -0.9046263 -0.866626738 -0.721368575 -0.4241459 -0.9022913
## 3216 0.1749079 -0.283119198 0.037882546 0.3272519 0.5778235
## 3217 0.1749079 -0.206341890 0.471740330 0.3272519 0.5778235
## 3218 0.1749079 -0.544162045 -0.504439683 -0.4241459 -0.1622339
## 3219 -0.9046263 -0.713072122 -0.547825462 -0.4241459 -0.1622339
## 3220 -1.9841605 -0.851271277 -0.699675686 -0.4241459 -0.9022913
## 3221 -0.9046263 -0.700787753 -0.728599538 -0.4241459 -0.9022913
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## 3223 -0.9046263 -0.759138507 -0.743061465 -1.1755437 -0.9022913
## 3224 0.1749079 -0.482740198 -0.200739235 0.3272519 0.5778235
## 3225 -0.9046263 -0.713072122 -0.750292428 -1.1755437 -0.9022913
## 3226 0.1749079 -0.528806583 -0.222432124 -0.4241459 -0.1622339
## 3227 -0.9046263 0.776407653 1.556384790 1.8300475 2.0579382
## 3228 0.1749079 -0.498095660 -0.200739235 0.3272519 0.5778235
## 3229 -0.9046263 -0.022076350 1.267146267 3.3328431 2.7979956
## 3230 -0.9046263 -0.918835308 -0.706906649 -0.4241459 -0.9022913
## 3231 -0.9046263 -0.667005737 -0.721368575 -0.4241459 -0.9022913
## 3232 -0.9046263 -0.912693123 -0.612904129 -0.4241459 -0.9022913
## 3233 -1.9841605 -0.989470431 -0.779216280 -1.1755437 -0.9022913
## 3234 -0.9046263 -0.900408754 -0.706906649 -0.4241459 -0.9022913
## 3235 -0.9046263 -0.900408754 -0.706906649 -0.4241459 -0.9022913
## 3236 -0.9046263 -0.921906400 -0.706906649 -0.4241459 -0.9022913
## 3237 -0.9046263 -0.888124384 -0.706906649 -0.4241459 -0.9022913
## 3238 -0.9046263 -0.728427584 -0.829833021 -0.4241459 -0.9022913
## 3239 -0.9046263 -0.881982200 -0.808140132 -0.4241459 -0.9022913
## 3240 -0.9046263 -0.928048584 -0.822602058 -1.1755437 -0.9022913
## 3241 0.1749079 -0.697716661 -0.395975238 0.3272519 -0.1622339
## 3242 -0.9046263 -0.912693123 -0.837063984 -1.1755437 -0.9022913
## 3243 -0.9046263 -0.866626738 -0.851525911 -0.4241459 -0.9022913
## 3244 0.1749079 -0.175630966 -0.352589459 -0.4241459 -0.1622339
## 3245 0.1749079 -0.682361199 -0.757523391 -1.1755437 -0.9022913
## 3246 -0.9046263 -0.713072122 -0.779216280 -0.4241459 -0.9022913
## 3247 -0.9046263 -0.713072122 -0.815371095 -1.1755437 -0.9022913
## 3248 -0.9046263 -0.743783045 -0.771985317 -0.4241459 -0.9022913
## 3249 0.1749079 -0.396749613 -0.641827982 -0.4241459 -0.9022913
## 3250 -0.9046263 -0.703858845 -0.735830502 -0.4241459 -0.9022913
## 3251 -0.9046263 -0.697716661 -0.757523391 -0.4241459 -0.9022913
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## 3253 -0.9046263 -0.697716661 -0.735830502 -0.4241459 -0.9022913
## 3254 -0.9046263 -0.756067415 -0.706906649 -1.1755437 -0.9022913
## 3255 0.1749079 -0.759138507 -0.757523391 -1.1755437 -0.9022913
## 3256 -0.9046263 -0.743783045 -0.779216280 -1.1755437 -0.9022913
## 3257 -0.9046263 -0.765280692 -0.757523391 -1.1755437 -0.9022913
## 3258 -0.9046263 -0.636294814 -0.728599538 -1.1755437 -0.9022913
## 3259 -0.9046263 -0.713072122 -0.815371095 -1.1755437 -0.9022913
## 3260 -0.9046263 -0.759138507 -0.757523391 -1.1755437 -0.9022913
## 3261 -0.9046263 -0.759138507 -0.735830502 -0.4241459 -0.9022913
## 3262 0.1749079 -0.329185582 -0.273048865 0.3272519 -0.1622339
## 3263 0.1749079 -0.789849430 -0.829833021 -1.1755437 -0.9022913
## 3264 0.1749079 -0.359896505 -0.374282348 -0.4241459 -0.1622339
## 3265 -0.9046263 -0.743783045 -0.750292428 -1.1755437 -0.9022913
## 3266 -0.9046263 -0.743783045 -0.815371095 -1.1755437 -0.9022913
## 3267 0.1749079 -0.605583891 -0.735830502 -1.1755437 -0.9022913
## 3268 0.1749079 -0.636294814 -0.728599538 -1.1755437 -0.9022913
## 3269 -1.9841605 -0.759138507 0.471740330 2.5814453 -0.9022913
## 3270 -1.9841605 -0.989470431 -0.504439683 0.3272519 -1.6423486
## 3271 -0.9046263 -0.498095660 -0.395975238 1.0786497 0.5778235
## 3272 -0.9046263 -0.390607429 1.267146267 -0.4241459 -0.9022913
## 3273 -0.9046263 0.054700958 0.580204776 1.0786497 0.5778235
## 3274 -0.9046263 0.856256053 0.182501808 2.5814453 1.3178809
## 3275 -0.9046263 -0.190986428 1.628694420 2.5814453 1.3178809
## 3276 0.1749079 -0.636294814 -0.735830502 0.3272519 -0.1622339
## 3277 -0.9046263 0.684274883 1.664849235 2.5814453 1.3178809
## 3278 -0.9046263 -0.759138507 -0.685213760 -0.4241459 -0.1622339
## 3279 -0.9046263 -0.329185582 0.327121069 1.0786497 0.5778235
## 3280 -0.9046263 -1.032465723 -0.887680726 -1.1755437 -0.9022913
## 3281 -0.9046263 -1.041679000 -0.887680726 -1.1755437 -0.9022913
## 3282 -0.9046263 -0.789849430 -0.547825462 -0.4241459 -0.9022913
## 3283 -0.9046263 0.285032881 0.131885066 3.3328431 1.3178809
## 3284 -0.9046263 -0.743783045 -0.612904129 -0.4241459 -0.9022913
## 3285 -0.9046263 -0.805204892 -0.612904129 -0.4241459 -0.9022913
## 3286 -0.9046263 -0.943404046 -0.670751834 -0.4241459 -0.9022913
## 3287 -0.9046263 -0.943404046 -0.670751834 -0.4241459 -0.9022913
## 3288 -0.9046263 -0.682361199 -0.714137612 -1.1755437 -0.9022913
## 3289 -0.9046263 -0.667005737 -0.721368575 -0.4241459 -0.9022913
## 3290 -0.9046263 -0.866626738 -0.844294947 -0.4241459 -0.9022913
## 3291 -0.9046263 -0.912693123 -0.735830502 -0.4241459 -0.9022913
## 3292 -0.9046263 -1.017110262 -0.822602058 -1.1755437 -1.6423486
## 3293 -1.9841605 -1.066247739 -0.851525911 -0.4241459 -0.9022913
## 3294 -1.9841605 -1.109243031 -0.829833021 -0.4241459 -1.6423486
## 3295 0.1749079 -0.114209120 0.182501808 1.8300475 0.5778235
## 3296 0.1749079 -0.436673813 -0.605673166 -0.4241459 -0.9022913
## 3297 0.1749079 -0.513451121 -0.504439683 0.3272519 -0.1622339
## 3298 -0.9046263 -0.452029275 -0.504439683 -0.4241459 -0.9022913
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## 3300 0.1749079 -0.513451121 -0.504439683 0.3272519 -0.1622339
## 3301 0.1749079 -0.022076350 0.327121069 -0.4241459 -0.1622339
## 3302 0.1749079 -0.436673813 -0.605673166 -0.4241459 -0.9022913
## 3303 0.1749079 -0.482740198 -0.468284868 -0.4241459 -0.9022913
## 3304 0.1749079 -0.329185582 -0.533363536 0.3272519 -0.1622339
## 3305 0.1749079 -0.329185582 -0.497208720 -0.4241459 -0.9022913
## 3306 0.1749079 -0.037431812 -0.403206201 -0.4241459 -0.1622339
## 3307 0.1749079 0.331099266 0.327121069 1.0786497 1.3178809
## 3308 0.1749079 -0.851271277 -0.771985317 -0.4241459 -0.9022913
## 3309 0.1749079 -0.359896505 0.001727731 0.3272519 0.5778235
## 3310 0.1749079 0.008634573 0.095730251 0.3272519 -0.1622339
## 3311 0.1749079 0.070056419 0.544049961 0.3272519 0.5778235
## 3312 0.1749079 0.070056419 0.544049961 0.3272519 0.5778235
## 3313 0.1749079 -0.037431812 0.760978853 -0.4241459 -0.1622339
## 3314 0.1749079 3.202570584 3.797983339 1.8300475 2.7979956
## 3315 0.1749079 -0.605583891 -0.634597019 0.3272519 -0.1622339
## 3316 0.1749079 -0.574872968 -0.583980277 -0.4241459 -0.9022913
## 3317 0.1749079 -0.436673813 -0.475515831 0.3272519 0.5778235
## 3318 0.1749079 -0.498095660 -0.634597019 -0.4241459 -0.9022913
## 3319 0.1749079 -0.390607429 -0.504439683 -0.4241459 -0.9022913
## 3320 0.1749079 -0.298474659 -0.482746794 -0.4241459 0.5778235
## 3321 0.1749079 0.254321958 0.471740330 1.0786497 1.3178809
## 3322 0.1749079 -0.528806583 -0.634597019 -0.4241459 -0.9022913
## 3323 0.1749079 -0.098853658 -0.193508272 -0.4241459 -0.1622339
## 3324 0.1749079 -0.513451121 -0.634597019 -0.4241459 -0.9022913
## 3325 0.1749079 -0.574872968 -0.576749314 -0.4241459 -0.1622339
## 3326 0.1749079 -0.620939353 -0.576749314 -0.4241459 -0.1622339
## 3327 0.1749079 -0.405962890 -0.591211240 -0.4241459 -0.9022913
## 3328 0.1749079 -0.636294814 -0.555056425 -0.4241459 -0.1622339
## 3329 0.1749079 -0.359896505 -0.576749314 -0.4241459 -0.1622339
## 3330 0.1749079 -0.620939353 -0.583980277 0.3272519 -0.1622339
## 3331 0.1749079 0.054700958 -0.504439683 -0.4241459 -0.9022913
## 3332 0.1749079 -0.022076350 -0.395975238 0.3272519 -0.1622339
## 3333 -0.9046263 -0.912693123 -0.829833021 -0.4241459 -0.9022913
## 3334 0.1749079 -0.728427584 -0.706906649 0.3272519 -0.1622339
## 3335 0.1749079 -0.052787274 -0.555056425 -0.4241459 -0.1622339
## 3336 0.1749079 -0.805204892 -0.692444723 -0.4241459 -0.9022913
## 3337 0.1749079 -0.190986428 -0.106736715 0.3272519 -0.1622339
## 3338 0.1749079 -0.743783045 -0.627366056 -0.4241459 -0.9022913
## 3339 -0.9046263 -0.513451121 -0.757523391 -0.4241459 -0.9022913
## 3340 0.1749079 -0.620939353 -0.576749314 -0.4241459 -0.9022913
## 3341 -0.9046263 -0.488882383 -0.620135092 -0.4241459 -0.9022913
## 3342 0.1749079 -0.298474659 -0.540594499 -0.4241459 -0.1622339
## 3343 0.1749079 -0.455100367 -0.388744274 0.3272519 0.5778235
## 3344 0.1749079 -0.264692644 -0.228361514 0.3272519 0.5778235
## 3345 0.1749079 -0.298474659 -0.540594499 -0.4241459 -0.1622339
## 3346 -0.9046263 -0.310759028 -0.468284868 0.3272519 0.5778235
## 3347 0.1749079 -0.298474659 -0.468284868 -0.4241459 -0.1622339
## 3348 0.1749079 -0.329185582 -0.468284868 -0.4241459 -0.1622339
## 3349 0.1749079 -0.329185582 -0.468284868 -0.4241459 -0.1622339
## 3350 0.1749079 -0.022076350 -0.193508272 0.3272519 -0.1622339
## 3351 0.1749079 -0.022076350 -0.193508272 0.3272519 -0.1622339
## 3352 1.2544421 0.622853037 0.359009616 0.3272519 1.3178809
## 3353 0.1749079 -0.022076350 -0.193508272 -0.4241459 -0.1622339
## 3354 -1.9841605 -1.020181354 -0.612904129 -1.1755437 -1.6423486
## 3355 -1.9841605 -0.928048584 -0.793678206 0.3272519 -0.9022913
## 3356 -1.9841605 -0.912693123 -0.685213760 1.8300475 -0.1622339
## 3357 -1.9841605 -0.605583891 -0.612904129 -1.9269415 -0.9022913
## 3358 -1.9841605 -0.980257154 -0.873218800 -1.1755437 -0.9022913
## 3359 -1.9841605 -0.482740198 -0.200739235 2.5814453 -0.1622339
## 3360 -1.9841605 -0.697716661 -0.395975238 0.3272519 -0.9022913
## 3361 -1.9841605 -0.989470431 -0.880449763 -1.1755437 -0.9022913
## 3362 -1.9841605 -0.237052813 0.905598114 3.3328431 1.3178809
## 3363 -1.9841605 -1.004825892 -0.873218800 -1.1755437 -0.9022913
## 3364 -1.9841605 -0.928048584 -0.815371095 -0.4241459 -0.9022913
## 3365 -1.9841605 -0.928048584 -0.815371095 -0.4241459 -0.9022913
## 3366 -1.9841605 -0.958759508 -0.837063984 -1.1755437 -0.9022913
## 3367 -1.9841605 0.315743805 2.149323761 4.8356387 2.0579382
## 3368 -1.9841605 -0.743783045 -0.686081476 -0.4241459 -0.1622339
## 3369 -0.9046263 -0.329185582 1.267146267 1.0786497 0.5778235
## 3370 -1.9841605 -1.050892277 -0.793678206 -0.4241459 -1.6423486
## 3371 -1.9841605 -0.980257154 -0.873218800 -1.1755437 -0.9022913
## 3372 -1.9841605 -1.057034462 -0.829833021 -0.4241459 -1.6423486
## 3373 -1.9841605 -1.050892277 -0.858756874 -0.4241459 -0.9022913
## 3374 -1.9841605 0.592142113 0.204194697 0.3272519 -0.9022913
## 3375 -1.9841605 0.435516405 0.688669222 -2.6783393 -1.6423486
## 3376 0.1749079 0.899251345 1.773313681 -1.9269415 -0.1622339
## 3377 0.1749079 4.735045652 4.521079645 1.0786497 2.7979956
## 3378 -0.9046263 -0.022076350 0.384968773 1.8300475 -0.1622339
## 3379 -1.9841605 0.991384115 0.840519446 0.3272519 -0.1622339
## 3380 -0.9046263 0.054700958 -0.439361016 4.8356387 1.3178809
## 3381 -0.9046263 0.054700958 -0.439361016 4.8356387 1.3178809
## 3382 -1.9841605 -0.544162045 0.724824037 1.8300475 -0.1622339
## 3383 -1.9841605 -0.485811291 0.905598114 4.0842409 -0.1622339
## 3384 -1.9841605 -0.083498197 2.785648510 4.8356387 -0.1622339
## 3385 -1.9841605 -0.485811291 0.052344472 4.0842409 1.3178809
## 3386 0.1749079 -0.237052813 -0.179046346 0.3272519 -0.1622339
## 3387 -0.9046263 -0.974114969 -0.945528430 -1.1755437 -1.6423486
## 3388 -1.9841605 -0.636294814 -0.779216280 -1.9269415 -1.6423486
## 3389 0.1749079 0.407876574 -0.244125013 0.3272519 0.5778235
## 3390 0.1749079 -0.068142735 0.471740330 0.3272519 0.5778235
## 3391 0.1749079 0.039345496 1.202067599 3.3328431 2.7979956
## 3392 -1.9841605 -0.636294814 -0.562287388 -1.9269415 -1.6423486
## 3393 -0.9046263 0.592142113 4.224610160 3.3328431 3.5380530
## 3394 -0.9046263 0.008634573 1.122527006 4.0842409 1.3178809
## 3395 -0.9046263 -0.298474659 0.110192177 1.0786497 0.5778235
## 3396 -0.9046263 0.223611035 0.616359591 1.0786497 1.3178809
## 3397 -0.9046263 -0.574872968 -0.179046346 -0.4241459 -0.1622339
## 3398 0.1749079 0.592142113 0.254811438 1.0786497 -0.1622339
## 3399 0.1749079 -0.068142735 1.556384790 3.3328431 1.3178809
## 3400 -0.9046263 0.223611035 2.207171465 2.5814453 1.3178809
## 3401 -0.9046263 -0.175630966 -0.106736715 1.0786497 -0.9022913
## 3402 0.1749079 0.745696729 1.628694420 1.0786497 0.5778235
## 3403 -0.9046263 -0.022076350 -0.113967678 1.8300475 0.5778235
## 3404 0.1749079 0.070056419 -0.323665607 -0.4241459 -0.1622339
## 3405 0.1749079 -0.482740198 -0.446591979 -0.4241459 -0.9022913
## 3406 -0.9046263 -0.421318352 -0.374282348 0.3272519 -0.1622339
## 3407 -0.9046263 0.410947667 0.298197217 -0.4241459 -0.1622339
## 3408 0.1749079 -0.114209120 -0.518901610 -0.4241459 -0.9022913
## 3409 0.1749079 -0.329185582 -0.048889011 0.3272519 -0.1622339
## 3410 0.1749079 -0.329185582 0.601897665 1.0786497 0.5778235
## 3411 -0.9046263 -0.498095660 -0.395975238 -0.4241459 -0.1622339
## 3412 0.1749079 -0.667005737 -0.252512930 -0.4241459 0.5778235
## 3413 0.1749079 0.223611035 -0.359820422 -0.4241459 -0.1622339
## 3414 0.1749079 -0.267763736 -0.367051385 -0.4241459 -0.1622339
## 3415 0.1749079 -0.636294814 -0.779216280 -1.9269415 -1.6423486
## 3416 0.1749079 -0.022076350 0.507895145 1.0786497 -0.1622339
## 3417 0.1749079 0.392521113 0.746516926 0.3272519 -0.1622339
## 3418 0.1749079 -0.022076350 1.476844196 3.3328431 1.3178809
## 3419 0.1749079 0.377165651 -0.070581900 0.3272519 -0.9022913
## 3420 0.1749079 0.500009344 -0.106736715 -0.4241459 -0.9022913
## 3421 -0.9046263 -0.605583891 -0.576749314 -0.4241459 -0.9022913
## 3422 -0.9046263 0.192900112 1.086372190 3.3328431 4.2781104
## 3423 -0.9046263 1.513469809 3.797983339 1.8300475 0.5778235
## 3424 -0.9046263 -0.022076350 0.471740330 1.0786497 1.3178809
## 3425 0.1749079 1.605602579 1.042986412 -0.4241459 0.5778235
## 3426 0.1749079 -0.114209120 -0.526132573 -0.4241459 -0.9022913
## 3427 -0.9046263 -0.313830121 -0.110424506 0.3272519 1.3178809
## 3428 0.1749079 0.285032881 1.267146267 0.3272519 0.5778235
## 3429 1.2544421 0.285032881 1.267146267 0.3272519 0.5778235
## 3430 0.1749079 0.285032881 1.136988932 1.0786497 -0.1622339
## 3431 0.1749079 0.285032881 0.688669222 0.3272519 0.5778235
## 3432 1.2544421 0.438587497 -0.034427084 0.3272519 0.5778235
## 3433 0.1749079 0.285032881 1.136988932 1.0786497 0.5778235
## 3434 0.1749079 -0.052787274 -0.019965158 -0.4241459 0.5778235
## 3435 0.1749079 0.223611035 -0.034427084 -0.4241459 0.5778235
## 3436 0.1749079 -0.022076350 -0.142891530 1.0786497 0.5778235
## 3437 0.1749079 0.438587497 0.905598114 0.3272519 1.3178809
## 3438 0.1749079 -0.052787274 0.254811438 1.0786497 1.3178809
## 3439 0.1749079 -0.052787274 0.254811438 1.0786497 1.3178809
## 3440 0.1749079 0.131478266 -0.048889011 0.3272519 1.3178809
## 3441 0.1749079 0.285032881 0.182501808 -0.4241459 0.5778235
## 3442 0.1749079 -0.022076350 0.298197217 0.3272519 1.3178809
## 3443 -1.9841605 -0.421318352 0.920060040 0.3272519 -0.9022913
## 3444 -1.9841605 -0.405962890 0.797133668 1.0786497 -0.9022913
## 3445 -1.9841605 -0.820560353 -0.157353456 1.0786497 -0.9022913
## 3446 -1.9841605 2.741906737 2.568719618 0.3272519 2.0579382
## 3447 -1.9841605 -0.851271277 -0.179046346 0.3272519 -0.9022913
## 3448 -0.9046263 -0.452029275 -0.395975238 -0.4241459 -0.9022913
## 3449 -0.9046263 0.070056419 0.995985152 2.5814453 0.5778235
## 3450 -0.9046263 0.039345496 1.628694420 0.3272519 -0.1622339
## 3451 -1.9841605 -0.958759508 -0.721368575 -0.4241459 -0.9022913
## 3452 -0.9046263 0.070056419 1.158681821 0.3272519 -0.1622339
## 3453 0.1749079 0.285032881 1.990242573 1.0786497 1.3178809
## 3454 0.1749079 -0.052787274 0.732055000 1.8300475 0.5778235
## 3455 0.1749079 -0.359896505 1.303301082 3.3328431 1.3178809
## 3456 -0.9046263 0.899251345 0.544049961 3.3328431 2.0579382
## 3457 -0.9046263 0.223611035 1.194836636 -0.4241459 -0.1622339
## 3458 0.1749079 0.837829499 2.351790726 1.8300475 0.5778235
## 3459 0.1749079 -0.636294814 -0.504439683 0.3272519 -0.1622339
## 3460 -0.9046263 -0.175630966 1.028524486 1.8300475 1.3178809
## 3461 -0.9046263 -0.482740198 -0.085043826 -0.4241459 -0.1622339
## 3462 0.1749079 -0.482740198 -0.034427084 -0.4241459 -0.1622339
## 3463 -0.9046263 1.083516884 0.616359591 1.0786497 0.5778235
## 3464 -0.9046263 0.530720267 0.862212335 1.0786497 1.3178809
## 3465 -0.9046263 0.530720267 1.556384790 2.5814453 1.3178809
## 3466 0.1749079 3.294703354 4.347536532 4.8356387 2.0579382
## 3467 0.1749079 -0.375251967 -0.070581900 1.0786497 0.5778235
## 3468 -1.9841605 -1.004825892 -0.771985317 -0.4241459 -0.9022913
## 3469 -0.9046263 -0.835915815 -0.511670647 -0.4241459 -0.1622339
## 3470 -0.9046263 -0.820560353 -0.510802931 -0.4241459 -0.1622339
## 3471 0.1749079 -0.783707245 -0.417668127 0.3272519 -0.1622339
## 3472 0.1749079 -0.759138507 -0.417668127 0.3272519 -0.1622339
## 3473 0.1749079 -0.713072122 -0.417668127 0.3272519 -0.1622339
## 3474 0.1749079 -0.605583891 -0.244125013 -0.4241459 -0.9022913
## 3475 0.1749079 -0.482740198 -0.627366056 -0.4241459 -0.9022913
## 3476 0.1749079 -0.636294814 -0.583980277 0.3272519 -0.1622339
## 3477 0.1749079 -0.498095660 -0.468284868 -1.1755437 -0.1622339
## 3478 0.1749079 -0.329185582 0.544049961 -0.4241459 1.3178809
## 3479 0.1749079 -0.590228429 -0.468284868 -1.1755437 -0.1622339
## 3480 -0.9046263 -0.759138507 -0.793678206 -0.4241459 -0.9022913
## 3481 0.1749079 -0.267763736 0.544049961 0.3272519 1.3178809
## 3482 -0.9046263 -0.620939353 -0.338127533 -0.4241459 -0.1622339
## 3483 -0.9046263 -0.799062707 -0.685213760 -0.4241459 -0.9022913
## 3484 0.1749079 -0.789849430 -0.735830502 -0.4241459 -0.9022913
## 3485 -0.9046263 -0.713072122 -0.612904129 -0.4241459 -0.1622339
## 3486 -0.9046263 -0.820560353 -0.598442203 -0.4241459 -0.1622339
## 3487 -0.9046263 -0.605583891 -0.395975238 0.3272519 -0.1622339
## 3488 0.1749079 -0.820560353 -0.685213760 0.3272519 -0.1622339
## 3489 0.1749079 -0.682361199 -0.395975238 0.3272519 0.5778235
## 3490 -0.9046263 -0.620939353 -0.338127533 -0.4241459 -0.1622339
## 3491 -0.9046263 -0.697716661 -0.612904129 -0.4241459 -0.1622339
## 3492 -0.9046263 -0.835915815 -0.822602058 -1.1755437 -0.9022913
## 3493 0.1749079 -0.608654983 -0.656289908 -0.4241459 -0.9022913
## 3494 0.1749079 -0.611726076 -0.612904129 -0.4241459 -0.9022913
## 3495 -0.9046263 -0.820560353 -0.822602058 -1.1755437 -0.9022913
## 3496 0.1749079 -0.544162045 -0.388744274 -0.4241459 -0.9022913
## 3497 -0.9046263 -0.636294814 -0.106736715 -1.1755437 -0.9022913
## 3498 -0.9046263 -0.789849430 -0.771985317 -0.4241459 -0.9022913
## 3499 -0.9046263 -0.682361199 -0.699675686 0.3272519 -0.1622339
## 3500 -0.9046263 -0.682361199 -0.699675686 -0.4241459 -0.9022913
## 3501 0.1749079 -0.682361199 -0.699675686 0.3272519 0.5778235
## 3502 -0.9046263 -0.851271277 -0.627366056 -0.4241459 -0.1622339
## 3503 0.1749079 -0.977186062 -0.395975238 -0.4241459 -0.9022913
## 3504 0.1749079 -0.974114969 -0.395975238 -1.1755437 -0.9022913
## 3505 0.1749079 -0.329185582 -0.070581900 -0.4241459 -0.1622339
## 3506 0.1749079 -0.452029275 -0.583980277 -0.4241459 -0.9022913
## 3507 0.1749079 -0.820560353 -0.735830502 -0.4241459 -0.9022913
## 3508 0.1749079 -0.190986428 -0.273048865 -0.4241459 -0.1622339
## 3509 0.1749079 -0.574872968 -0.533363536 -0.4241459 -0.1622339
## 3510 0.1749079 -0.329185582 -0.099505752 1.0786497 0.5778235
## 3511 -1.9841605 -0.329185582 -0.157353456 1.8300475 0.5778235
## 3512 -0.9046263 -0.052787274 -0.352589459 -1.1755437 -0.1622339
## 3513 -1.9841605 -0.728427584 0.037882546 0.3272519 -0.9022913
## 3514 -1.9841605 -0.237052813 0.471740330 2.5814453 -0.1622339
## 3515 -1.9841605 -0.728427584 1.267146267 4.8356387 1.3178809
## 3516 -1.9841605 -0.943404046 -0.612904129 -0.4241459 -1.6423486
## 3517 -1.9841605 -0.464313644 0.572973813 2.5814453 -0.1622339
## 3518 -1.9841605 -0.943404046 1.267146267 3.3328431 2.0579382
## 3519 -0.9046263 0.131478266 0.182501808 0.3272519 0.5778235
## 3520 -0.9046263 -0.304616844 -0.439361016 -0.4241459 -0.9022913
## 3521 -0.9046263 -0.513451121 -0.670751834 -1.1755437 -0.9022913
## 3522 -0.9046263 -0.513451121 -0.670751834 -1.1755437 -0.9022913
## 3523 -0.9046263 -0.329185582 0.666976333 0.3272519 0.5778235
## 3524 0.1749079 -0.513451121 -0.670751834 -1.1755437 -0.9022913
## 3525 1.2544421 -0.329185582 -0.757523391 -1.1755437 -0.9022913
## 3526 -0.9046263 -0.513451121 -0.670751834 -1.1755437 -0.9022913
## 3527 0.1749079 -0.482740198 -0.612904129 -1.1755437 -0.9022913
## 3528 -0.9046263 -0.378323059 -0.497208720 -0.4241459 -0.9022913
## 3529 0.1749079 -0.298474659 1.484075159 0.3272519 -0.1622339
## 3530 0.1749079 0.116122804 1.426227454 2.5814453 -0.1622339
## 3531 -0.9046263 0.592142113 0.110192177 1.0786497 1.3178809
## 3532 0.1749079 -0.237052813 0.688669222 0.3272519 0.5778235
## 3533 -0.9046263 0.116122804 1.701004051 4.0842409 1.3178809
## 3534 -0.9046263 -0.765280692 -0.627366056 -0.4241459 -0.9022913
## 3535 0.1749079 0.592142113 0.760978853 1.0786497 0.5778235
## 3536 0.1749079 -0.083498197 -0.417668127 -0.4241459 -0.1622339
## 3537 0.1749079 -0.083498197 -0.417668127 -0.4241459 -0.1622339
## 3538 0.1749079 -0.482740198 -0.612904129 -0.4241459 -0.9022913
## 3539 0.1749079 -0.114209120 -0.417668127 -0.4241459 -0.1622339
## 3540 0.1749079 -0.114209120 -0.439361016 -1.1755437 -0.9022913
## 3541 0.1749079 -0.482740198 -0.605673166 -0.4241459 -0.9022913
## 3542 -0.9046263 -0.421318352 0.905598114 0.3272519 0.5778235
## 3543 1.2544421 -0.221697351 -0.591211240 -1.1755437 -0.1622339
## 3544 0.1749079 -0.114209120 -0.591211240 -1.1755437 -0.1622339
## 3545 0.1749079 -0.332256675 -0.417668127 -0.4241459 -0.9022913
## 3546 0.1749079 -0.022076350 -0.432130053 -0.4241459 -0.1622339
## 3547 1.2544421 0.023990034 -0.482746794 -1.1755437 -0.1622339
## 3548 0.1749079 1.114227808 0.753747890 0.3272519 -0.1622339
## 3549 0.1749079 -0.237052813 -0.453822942 -0.4241459 -0.1622339
## 3550 0.1749079 -0.789849430 -0.627366056 0.3272519 -0.1622339
## 3551 1.2544421 -0.022076350 -0.417668127 -0.4241459 -0.9022913
## 3552 -0.9046263 -0.114209120 0.544049961 1.8300475 0.5778235
## 3553 0.1749079 -0.298474659 0.771825297 1.8300475 -0.1622339
## 3554 0.1749079 -0.319972305 -0.410437164 -0.4241459 -0.1622339
## 3555 0.1749079 -0.237052813 -0.482746794 -0.4241459 -0.9022913
## 3556 -0.9046263 -0.329185582 -0.757523391 -1.1755437 -0.9022913
## 3557 0.1749079 0.023990034 -0.482746794 -0.4241459 -0.9022913
## 3558 0.1749079 0.131478266 -0.273048865 -0.4241459 0.5778235
## 3559 0.1749079 -0.298474659 -0.627366056 -1.1755437 -0.9022913
## 3560 0.1749079 -0.212484074 -0.410437164 -0.4241459 -0.1622339
## 3561 0.1749079 0.991384115 -0.251355976 -0.4241459 -0.1622339
## 3562 -0.9046263 -0.212484074 -0.410437164 -0.4241459 -0.1622339
## 3563 1.2544421 0.684274883 -0.142891530 0.3272519 1.3178809
## 3564 0.1749079 1.359915193 0.240349512 -0.4241459 1.3178809
## 3565 1.2544421 0.837829499 -0.092274789 -0.4241459 -0.1622339
## 3566 0.1749079 0.377165651 -0.063350937 -0.4241459 0.5778235
## 3567 -1.9841605 -0.676219014 -0.056119974 0.3272519 -0.1622339
## 3568 -1.9841605 -0.022076350 1.990242573 2.5814453 1.3178809
## 3569 0.1749079 0.592142113 0.471740330 0.3272519 0.5778235
## 3570 1.2544421 0.039345496 -0.461053905 -1.1755437 -0.9022913
## 3571 0.1749079 0.438587497 0.934521966 1.0786497 1.3178809
## 3572 0.1749079 0.100767342 1.267146267 -0.4241459 0.5778235
## 3573 1.2544421 2.588352121 2.727800806 4.0842409 4.2781104
## 3574 0.1749079 1.022095038 2.496409988 1.0786497 0.5778235
## 3575 1.2544421 0.748767822 -0.106736715 -0.4241459 -0.1622339
## 3576 1.2544421 0.622853037 0.182501808 -0.4241459 -0.1622339
## 3577 1.2544421 1.823650133 0.334352032 -0.4241459 0.5778235
## 3578 0.1749079 0.592142113 2.019166426 1.8300475 0.5778235
## 3579 1.2544421 0.991384115 0.724824037 -0.4241459 1.3178809
## 3580 1.2544421 1.906569626 0.370506847 -0.4241459 0.5778235
## 3581 0.1749079 -0.083498197 0.544049961 -0.4241459 -0.9022913
## 3582 0.1749079 -0.083498197 2.011935463 1.8300475 1.3178809
## 3583 1.2544421 1.983346934 0.377737810 -0.4241459 1.3178809
## 3584 1.2544421 1.482758886 0.377737810 -0.4241459 -0.1622339
## 3585 1.2544421 0.714985806 0.363275884 -0.4241459 1.3178809
## 3586 1.2544421 1.476616701 0.370506847 -0.4241459 1.3178809
## 3587 1.2544421 1.513469809 0.225887586 -0.4241459 0.5778235
## 3588 0.1749079 -0.390607429 -0.757523391 -1.9269415 -0.9022913
## 3589 0.1749079 0.285032881 0.392199736 -0.4241459 -0.1622339
## 3590 1.2544421 3.448257970 0.992369671 -0.4241459 0.5778235
## 3591 1.2544421 1.359915193 -0.077812863 0.3272519 0.5778235
## 3592 0.1749079 -0.633223722 -0.251355976 -0.4241459 -0.1622339
## 3593 1.2544421 0.285032881 -0.215201161 -1.1755437 -0.9022913
## 3594 0.1749079 1.513469809 1.990242573 0.3272519 1.3178809
## 3595 0.1749079 -0.267763736 -0.164584420 -0.4241459 1.3178809
## 3596 1.2544421 0.991384115 0.905598114 1.0786497 -0.1622339
## 3597 1.2544421 -0.129564582 -0.395975238 -0.4241459 -0.1622339
## 3598 1.2544421 0.070056419 0.319890106 0.3272519 -0.1622339
## 3599 0.1749079 2.496219351 5.605724105 4.8356387 1.3178809
## 3600 0.1749079 0.346454728 1.418996491 0.3272519 2.0579382
## 3601 0.1749079 -0.574872968 -0.012734195 -0.4241459 -0.1622339
## 3602 0.1749079 1.206360577 0.876674262 0.3272519 -0.9022913
## 3603 0.1749079 0.285032881 1.122527006 0.3272519 0.5778235
## 3604 1.2544421 -0.544162045 -0.012734195 -0.4241459 -0.1622339
## 3605 1.2544421 0.622853037 0.139116029 -0.4241459 -0.1622339
## 3606 0.1749079 -0.780636153 -0.945528430 -1.1755437 -1.6423486
## 3607 1.2544421 0.622853037 0.139116029 -0.4241459 -0.1622339
## 3608 1.2544421 1.359915193 3.436435186 1.0786497 1.3178809
## 3609 1.2544421 0.100767342 2.004704499 3.3328431 2.0579382
## 3610 1.2544421 1.974133657 0.377737810 0.3272519 0.5778235
## 3611 1.2544421 -0.329185582 0.030651583 -0.4241459 -0.1622339
## 3612 1.2544421 0.438587497 1.194836636 -0.4241459 1.3178809
## 3613 0.1749079 1.006739576 2.026397389 -0.4241459 1.3178809
## 3614 0.1749079 0.438587497 -0.063350937 -0.4241459 -0.1622339
## 3615 1.2544421 1.482758886 0.377737810 0.3272519 1.3178809
## 3616 1.2544421 0.868540422 -0.099505752 -0.4241459 -0.1622339
## 3617 1.2544421 -0.329185582 0.117423140 -0.4241459 -0.1622339
## 3618 0.1749079 0.438587497 -0.265817902 -0.4241459 0.5778235
## 3619 1.2544421 1.022095038 0.182501808 -0.4241459 0.5778235
## 3620 1.2544421 0.377165651 -0.251355976 -0.4241459 -0.1622339
## 3621 0.1749079 -0.267763736 -0.489977757 -1.1755437 -0.9022913
## 3622 0.1749079 1.430550316 0.182501808 -0.4241459 0.5778235
## 3623 1.2544421 0.285032881 0.384968773 0.3272519 0.5778235
## 3624 1.2544421 1.298493347 0.905598114 0.3272519 2.0579382
## 3625 1.2544421 0.592142113 -0.251355976 -0.4241459 0.5778235
## 3626 0.1749079 -0.630152630 -0.808140132 -1.1755437 -0.9022913
## 3627 -0.9046263 -0.452029275 -0.200739235 -1.1755437 -0.9022913
## 3628 1.2544421 1.667024425 0.377737810 0.3272519 1.3178809
## 3629 1.2544421 -0.083498197 -0.424899090 -1.1755437 -0.1622339
## 3630 0.1749079 0.714985806 0.110192177 0.3272519 0.5778235
## 3631 0.1749079 0.377165651 -0.005503232 -0.4241459 0.5778235
## 3632 1.2544421 2.158399196 0.414181864 0.3272519 1.3178809
## 3633 0.1749079 2.741906737 0.992369671 0.3272519 1.3178809
## 3634 0.1749079 0.592142113 0.544049961 0.3272519 -0.1622339
## 3635 1.2544421 0.131478266 1.288839156 0.3272519 -0.9022913
## 3636 1.2544421 1.206360577 0.891136188 0.3272519 1.3178809
## 3637 0.1749079 1.052805961 4.521079645 2.5814453 2.7979956
## 3638 1.2544421 4.431007512 0.623590554 -0.4241459 0.5778235
## 3639 1.2544421 3.509679816 2.084245093 -0.4241459 2.0579382
## 3640 0.1749079 1.206360577 1.737158866 4.0842409 1.3178809
## 3641 1.2544421 -0.022076350 0.544049961 1.0786497 -0.1622339
## 3642 0.1749079 -0.022076350 0.760978853 0.3272519 -0.1622339
## 3643 1.2544421 -0.083498197 -0.034427084 -1.1755437 -0.1622339
## 3644 1.2544421 -0.283119198 -0.200739235 -0.4241459 0.5778235
## 3645 -0.9046263 -0.405962890 1.303301082 0.3272519 -0.1622339
## 3646 1.2544421 4.123898280 0.934521966 -0.4241459 0.5778235
## 3647 1.2544421 0.162189189 0.377737810 -0.4241459 0.5778235
## 3648 1.2544421 3.356125200 0.934521966 -0.4241459 -0.1622339
## 3649 -0.9046263 -0.421318352 1.484075159 0.3272519 0.5778235
## 3650 1.2544421 -0.022076350 0.045113509 -0.4241459 -0.1622339
## 3651 1.2544421 0.100767342 0.377737810 -0.4241459 -0.1622339
## 3652 0.1749079 -0.547233137 -0.526132573 -0.4241459 -0.1622339
## 3653 1.2544421 2.588352121 1.151450858 -0.4241459 1.3178809
## 3654 1.2544421 -0.513451121 -0.482746794 -0.4241459 -0.1622339
## 3655 1.2544421 -0.022076350 0.037882546 0.3272519 0.5778235
## 3656 1.2544421 1.206360577 -0.179046346 -0.4241459 0.5778235
## 3657 1.2544421 2.127688273 1.368379750 -0.4241459 0.5778235
## 3658 1.2544421 4.216031050 0.941752929 -0.4241459 0.5778235
## 3659 1.2544421 2.281242889 0.883905225 0.3272519 0.5778235
## 3660 1.2544421 2.281242889 0.876674262 -0.4241459 -0.1622339
## 3661 1.2544421 1.660882240 0.384968773 -0.4241459 1.3178809
## 3662 1.2544421 4.277452896 0.941752929 -0.4241459 0.5778235
## 3663 1.2544421 -0.083498197 -0.265817902 -0.4241459 -0.1622339
## 3664 1.2544421 0.438587497 -0.129441939 1.0786497 2.0579382
## 3665 1.2544421 -0.083498197 -0.265817902 -0.4241459 -0.1622339
## 3666 1.2544421 3.460542339 0.594666702 -0.4241459 0.5778235
## 3667 1.2544421 1.390626116 0.045113509 -0.4241459 -0.9022913
## 3668 1.2544421 1.974133657 1.404534565 1.0786497 2.0579382
## 3669 1.2544421 3.202570584 0.384968773 1.0786497 2.0579382
## 3670 1.2544421 3.356125200 0.457278404 -0.4241459 0.5778235
## 3671 1.2544421 1.390626116 0.956214855 0.3272519 1.3178809
## 3672 1.2544421 1.974133657 1.534691900 0.3272519 1.3178809
## 3673 1.2544421 -0.114209120 0.037882546 0.3272519 -0.1622339
## 3674 1.2544421 0.438587497 -0.207970198 -1.1755437 -0.1622339
## 3675 0.1749079 3.202570584 2.351790726 2.5814453 2.7979956
## 3676 1.2544421 -0.605583891 -0.858756874 -1.9269415 -0.9022913
## 3677 1.2544421 -0.390607429 -0.106736715 -1.1755437 -0.1622339
## 3678 1.2544421 0.991384115 -0.106736715 -0.4241459 -0.1622339
## 3679 1.2544421 2.588352121 0.319890106 -0.4241459 2.0579382
## 3680 1.2544421 1.206360577 0.471740330 0.3272519 1.3178809
## 3681 1.2544421 2.434797505 0.312659143 -0.4241459 0.5778235
## 3682 1.2544421 -0.052787274 -0.403206201 -1.1755437 -0.9022913
## 3683 1.2544421 0.730341268 0.507895145 1.0786497 0.5778235
## 3684 1.2544421 1.206360577 0.471740330 1.0786497 1.3178809
## 3685 1.2544421 2.434797505 3.277353999 1.0786497 2.0579382
## 3686 1.2544421 1.206360577 0.471740330 1.0786497 1.3178809
## 3687 1.2544421 2.281242889 3.349663629 0.3272519 2.0579382
## 3688 1.2544421 0.407876574 1.303301082 0.3272519 0.5778235
## 3689 1.2544421 0.745696729 1.238222415 0.3272519 0.5778235
## 3690 1.2544421 1.203289485 0.688669222 -0.4241459 0.5778235
## 3691 1.2544421 0.899251345 0.037882546 -0.4241459 0.5778235
## 3692 1.2544421 0.899251345 0.037882546 0.3272519 1.3178809
## 3693 0.1749079 0.285032881 0.544049961 0.3272519 1.3178809
## 3694 1.2544421 0.223611035 -0.121198641 0.3272519 -0.1622339
## 3695 1.2544421 2.127688273 0.601897665 -0.4241459 1.3178809
## 3696 0.1749079 0.438587497 -0.236894050 -0.4241459 0.5778235
## 3697 1.2544421 0.223611035 -0.121198641 0.3272519 -0.1622339
## 3698 1.2544421 0.085411881 0.182501808 0.3272519 0.5778235
## 3699 1.2544421 2.281242889 1.628694420 1.8300475 2.7979956
## 3700 1.2544421 2.741906737 0.392199736 -0.4241459 1.3178809
## 3701 1.2544421 0.070056419 0.196963734 0.3272519 0.5778235
## 3702 1.2544421 1.052805961 -0.092274789 -0.4241459 0.5778235
## 3703 0.1749079 0.991384115 -0.041658047 -0.4241459 0.5778235
## 3704 0.1749079 -0.126493489 -0.555056425 -1.1755437 -0.9022913
## 3705 1.2544421 2.741906737 0.392199736 -0.4241459 0.5778235
## 3706 1.2544421 2.127688273 0.168039881 -0.4241459 0.5778235
## 3707 1.2544421 -0.022076350 0.088499288 -0.4241459 0.5778235
## 3708 1.2544421 -0.022076350 0.081268325 0.3272519 0.5778235
## 3709 1.2544421 0.254321958 -0.424899090 -1.9269415 -0.1622339
## 3710 0.1749079 0.714985806 0.905598114 1.0786497 1.3178809
## 3711 1.2544421 1.359915193 0.977907744 1.0786497 0.5778235
## 3712 1.2544421 1.359915193 0.992369671 0.3272519 1.3178809
## 3713 1.2544421 0.300388343 -0.387442701 -0.4241459 -0.1622339
## 3714 1.2544421 2.361091289 0.384968773 1.0786497 2.0579382
## 3715 1.2544421 0.315743805 -0.598442203 -1.1755437 -0.1622339
## 3716 1.2544421 0.807118576 0.139116029 0.3272519 0.5778235
## 3717 1.2544421 2.127688273 0.601897665 -0.4241459 1.3178809
## 3718 1.2544421 2.588352121 0.384968773 -0.4241459 1.3178809
## 3719 1.2544421 0.377165651 -0.229663087 0.3272519 0.5778235
## 3720 1.2544421 0.991384115 1.267146267 0.3272519 0.5778235
## 3721 0.1749079 0.929962268 0.977907744 1.0786497 1.3178809
## 3722 1.2544421 1.605602579 0.732055000 -0.4241459 -0.1622339
## 3723 0.1749079 0.822474037 -0.077812863 -0.4241459 -0.1622339
## 3724 0.1749079 0.837829499 -0.077812863 -0.4241459 -0.1622339
## 3725 1.2544421 -0.083498197 0.081268325 -0.4241459 -0.1622339
## 3726 -0.9046263 -0.789849430 -0.829833021 -0.4241459 -0.9022913
## 3727 1.2544421 2.127688273 0.601897665 -0.4241459 0.5778235
## 3728 1.2544421 0.346454728 -0.612904129 -1.1755437 -0.9022913
## 3729 1.2544421 0.119193896 -0.612904129 -1.1755437 -0.9022913
## 3730 1.2544421 -0.022076350 -0.106736715 0.3272519 0.5778235
## 3731 1.2544421 -0.022076350 -0.106736715 -0.4241459 0.5778235
## 3732 1.2544421 0.008634573 0.037882546 0.3272519 -0.1622339
## 3733 1.2544421 1.206360577 0.341582995 -0.4241459 -0.1622339
## 3734 1.2544421 1.252426962 0.146346992 -0.4241459 -0.1622339
## 3735 1.2544421 0.285032881 0.001727731 -0.4241459 -0.1622339
## 3736 1.2544421 1.052805961 -0.193508272 0.3272519 -0.1622339
## 3737 1.2544421 0.530720267 -0.157353456 -0.4241459 0.5778235
## 3738 1.2544421 -0.697716661 -0.865987837 -1.9269415 -0.9022913
## 3739 0.1749079 0.576786652 -0.157353456 0.3272519 1.3178809
## 3740 1.2544421 -0.267763736 -0.359820422 0.3272519 0.5778235
## 3741 1.2544421 0.592142113 -0.157353456 0.3272519 0.5778235
## 3742 1.2544421 1.359915193 0.377737810 -0.4241459 0.5778235
## 3743 1.2544421 -0.215555166 -0.829833021 -1.9269415 -1.6423486
## 3744 1.2544421 0.113051712 -0.056119974 -0.4241459 1.3178809
## 3745 1.2544421 0.377165651 -0.461053905 -0.4241459 -0.1622339
## 3746 1.2544421 2.434797505 0.392199736 0.3272519 0.5778235
## 3747 1.2544421 0.039345496 0.182501808 -1.1755437 -0.9022913
## 3748 1.2544421 1.590247117 0.544049961 -0.4241459 0.5778235
## 3749 1.2544421 0.843971684 -0.316434644 -0.4241459 -0.1622339
## 3750 1.2544421 0.407876574 -0.294741755 -0.4241459 0.5778235
## 3751 1.2544421 0.377165651 -0.157353456 0.3272519 0.5778235
## 3752 1.2544421 -0.022076350 0.305428180 -0.4241459 -0.1622339
## 3753 1.2544421 -0.175630966 -0.330896570 0.3272519 0.5778235
## 3754 1.2544421 0.899251345 0.037882546 -0.4241459 0.5778235
## 3755 1.2544421 1.590247117 0.544049961 -0.4241459 -0.1622339
## 3756 1.2544421 0.500009344 -0.150122493 -0.4241459 0.5778235
## 3757 1.2544421 0.745696729 -0.193508272 -0.4241459 -0.1622339
## 3758 1.2544421 2.434797505 0.457278404 0.3272519 1.3178809
## 3759 1.2544421 0.407876574 -0.294741755 0.3272519 0.5778235
## 3760 0.1749079 0.500009344 -0.150122493 -0.4241459 0.5778235
## 3761 1.2544421 2.127688273 0.587435739 -0.4241459 0.5778235
## 3762 1.2544421 -0.421318352 -0.562287388 -1.1755437 -0.9022913
## 3763 1.2544421 0.745696729 0.037882546 -0.4241459 0.5778235
## 3764 1.2544421 0.561431190 -0.128429604 0.3272519 0.5778235
## 3765 1.2544421 0.561431190 -0.128429604 0.3272519 0.5778235
## 3766 1.2544421 0.561431190 -0.251355976 -0.4241459 -0.1622339
## 3767 1.2544421 0.070056419 0.110192177 0.3272519 -0.1622339
## 3768 1.2544421 3.049015969 0.392199736 -0.4241459 0.5778235
## 3769 1.2544421 2.281242889 0.428354552 -0.4241459 0.5778235
## 3770 1.2544421 0.561431190 -0.128429604 -0.4241459 -0.1622339
## 3771 1.2544421 2.342664735 0.182501808 -0.4241459 0.5778235
## 3772 1.2544421 1.390626116 0.045113509 -0.4241459 0.5778235
## 3773 1.2544421 -0.052787274 0.616359591 -0.4241459 -0.1622339
## 3774 1.2544421 1.359915193 0.045113509 0.3272519 1.3178809
## 3775 1.2544421 0.438587497 -0.034427084 -0.4241459 1.3178809
## 3776 1.2544421 1.022095038 0.124654103 -0.4241459 1.3178809
## 3777 1.2544421 0.684274883 -0.157353456 -0.4241459 0.5778235
## 3778 1.2544421 1.636313502 0.457278404 -0.4241459 1.3178809
## 3779 1.2544421 0.530720267 -0.294741755 -0.4241459 0.5778235
## 3780 1.2544421 0.377165651 0.905598114 0.3272519 1.3178809
## 3781 1.2544421 0.684274883 -0.157353456 -0.4241459 0.5778235
## 3782 1.2544421 0.899251345 -0.388744274 -0.4241459 -0.1622339
## 3783 1.2544421 4.277452896 1.845623312 0.3272519 0.5778235
## 3784 0.1749079 4.431007512 2.713338880 0.3272519 0.5778235
## 3785 0.1749079 4.277452896 2.713338880 0.3272519 1.3178809
## 3786 1.2544421 0.438587497 0.746516926 -0.4241459 1.3178809
## 3787 1.2544421 1.390626116 0.045113509 0.3272519 1.3178809
## 3788 1.2544421 4.123898280 2.207171465 0.3272519 1.3178809
## 3789 1.2544421 1.513469809 0.770306795 0.3272519 2.0579382
## 3790 1.2544421 2.741906737 0.399430699 -0.4241459 0.5778235
## 3791 -0.9046263 -0.789849430 -0.829833021 -1.1755437 -0.9022913
## 3792 1.2544421 2.281242889 0.912829077 0.3272519 1.3178809
## 3793 1.2544421 2.342664735 0.160808918 -0.4241459 0.5778235
## 3794 1.2544421 2.434797505 0.905598114 0.3272519 0.5778235
## 3795 1.2544421 2.741906737 0.739285963 -0.4241459 1.3178809
## 3796 1.2544421 1.513469809 0.630821517 -0.4241459 -0.1622339
## 3797 1.2544421 4.123898280 1.990242573 0.3272519 1.3178809
## 3798 1.2544421 0.008634573 -0.555056425 -1.1755437 -0.9022913
## 3799 1.2544421 1.820579041 0.905598114 0.3272519 0.5778235
## 3800 1.2544421 1.974133657 0.912829077 1.0786497 1.3178809
## 3801 0.1749079 2.588352121 0.905598114 1.0786497 2.7979956
## 3802 1.2544421 4.123898280 2.351790726 1.0786497 2.0579382
## 3803 0.1749079 0.714985806 -0.236894050 -0.4241459 -0.1622339
## 3804 1.2544421 2.496219351 -0.157353456 0.3272519 2.0579382
## 3805 1.2544421 0.745696729 0.160808918 -0.4241459 -0.1622339
## 3806 1.2544421 2.124617181 0.399430699 0.3272519 0.5778235
## 3807 1.2544421 2.281242889 0.153577955 0.3272519 1.3178809
## 3808 0.1749079 0.714985806 -0.229663087 0.3272519 0.5778235
## 3809 1.2544421 2.281242889 0.139116029 0.3272519 1.3178809
## 3810 1.2544421 3.356125200 0.638052481 0.3272519 2.0579382
## 3811 1.2544421 2.434797505 0.544049961 -0.4241459 1.3178809
## 3812 1.2544421 0.377165651 -0.200739235 -0.4241459 -0.1622339
## 3813 1.2544421 3.970343664 2.207171465 1.0786497 2.0579382
## 3814 1.2544421 0.730341268 -0.222432124 0.3272519 0.5778235
## 3815 1.2544421 1.114227808 -0.034427084 0.3272519 1.3178809
## 3816 1.2544421 0.285032881 -0.215201161 0.3272519 0.5778235
## 3817 1.2544421 3.509679816 2.040859315 0.3272519 1.3178809
## 3818 1.2544421 2.895461353 2.055321241 0.3272519 2.0579382
## 3819 1.2544421 2.588352121 0.356044921 -0.4241459 0.5778235
## 3820 1.2544421 0.315743805 -0.251355976 -0.4241459 -0.1622339
## 3821 1.2544421 2.281242889 0.139116029 -0.4241459 0.5778235
## 3822 1.2544421 2.127688273 0.139116029 -0.4241459 0.5778235
## 3823 1.2544421 -0.237052813 0.037882546 0.3272519 0.5778235
## 3824 1.2544421 1.390626116 0.045113509 -0.4241459 0.5778235
## 3825 1.2544421 0.285032881 -0.222432124 -0.4241459 -0.1622339
## 3826 1.2544421 2.895461353 2.055321241 1.8300475 2.7979956
## 3827 1.2544421 0.960673192 -0.179046346 -0.4241459 0.5778235
## 3828 1.2544421 -0.190986428 0.037882546 -0.4241459 0.5778235
## 3829 0.1749079 1.943422734 1.390072639 1.0786497 2.0579382
## 3830 1.2544421 1.605602579 1.628694420 0.3272519 2.0579382
## 3831 1.2544421 1.206360577 0.544049961 -0.4241459 0.5778235
## 3832 1.2544421 0.714985806 1.006831597 0.3272519 1.3178809
## 3833 1.2544421 3.202570584 0.442816478 -0.4241459 1.3178809
## 3834 1.2544421 2.895461353 2.171016650 1.0786497 2.7979956
## 3835 1.2544421 2.895461353 2.171016650 1.0786497 2.7979956
## 3836 -1.9841605 -0.175630966 0.587435739 2.5814453 -0.9022913
## 3837 -1.9841605 -0.937261861 -0.771985317 -0.4241459 -0.9022913
## 3838 0.1749079 -0.667005737 -0.692444723 -1.1755437 -0.9022913
## 3839 -0.9046263 -0.098853658 1.267146267 0.3272519 -0.1622339
## 3840 1.2544421 3.509679816 4.701853722 3.3328431 2.0579382
## 3841 0.1749079 -0.734569768 -0.865987837 -1.1755437 -0.9022913
## 3842 0.1749079 -0.789849430 -0.461053905 -0.4241459 -0.1622339
## 3843 0.1749079 -0.114209120 -0.215201161 -0.4241459 -0.1622339
## 3844 0.1749079 0.285032881 1.628694420 4.0842409 0.5778235
## 3845 1.2544421 0.285032881 -0.092274789 -0.4241459 -0.1622339
## 3846 0.1749079 -0.390607429 -0.468284868 -0.4241459 0.5778235
## 3847 0.1749079 -0.682361199 -0.374282348 0.3272519 -0.1622339
## 3848 0.1749079 -0.636294814 -0.497208720 -0.4241459 -0.9022913
## 3849 0.1749079 -0.789849430 -0.706906649 -0.4241459 -0.1622339
## 3850 0.1749079 -0.246266090 -0.432130053 -0.4241459 0.5778235
## 3851 0.1749079 -0.329185582 -0.106736715 -0.4241459 -0.1622339
## 3852 0.1749079 -0.283119198 -0.432130053 0.3272519 0.5778235
## 3853 0.1749079 -0.789849430 -0.656289908 -0.4241459 -0.1622339
## 3854 0.1749079 -0.881982200 -0.750292428 -1.1755437 -0.9022913
## 3855 0.1749079 -0.820560353 -0.793678206 -0.4241459 -0.9022913
## 3856 -0.9046263 -0.820560353 -0.793678206 -0.4241459 -0.9022913
## 3857 -0.9046263 -0.713072122 -0.743061465 -0.4241459 -0.9022913
## 3858 0.1749079 0.054700958 0.066806399 -0.4241459 -0.1622339
## 3859 0.1749079 0.054700958 0.068686449 -0.4241459 0.5778235
## 3860 1.2544421 -0.574872968 -0.714137612 -1.1755437 -0.9022913
## 3861 -1.9841605 -0.789849430 -0.280279829 -0.4241459 -0.9022913
## 3862 -1.9841605 -0.805204892 -0.518901610 -0.4241459 -0.9022913
## 3863 -1.9841605 -0.820560353 -0.410871021 -0.4241459 -1.6423486
## 3864 -1.9841605 -0.805204892 -0.280279829 -0.4241459 -0.9022913
## 3865 -1.9841605 -0.974114969 -0.106736715 1.0786497 -0.1622339
## 3866 0.1749079 0.592142113 1.100834117 0.3272519 0.5778235
## 3867 1.2544421 -0.544162045 -0.410437164 -1.1755437 -0.1622339
## 3868 0.1749079 0.807118576 3.342432666 1.8300475 2.7979956
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## 4070 -0.9046263 -0.528806583 -0.106736715 -0.4241459 1.3178809
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## 4771 0.1749079 0.131478266 0.110192177 1.0786497 2.0579382
## 4772 -0.9046263 -0.298474659 -0.323665607 0.3272519 0.5778235
## 4773 1.2544421 0.991384115 1.050217375 0.3272519 2.0579382
## 4774 0.1749079 -0.083498197 -0.186277309 -0.4241459 -0.1622339
## 4775 -0.9046263 0.131478266 0.182501808 1.0786497 1.3178809
## 4776 0.1749079 0.585999929 1.719804555 1.0786497 1.3178809
## 4777 -0.9046263 0.361810189 1.701004051 1.8300475 0.5778235
## 4778 0.1749079 -0.006720889 0.760978853 1.0786497 1.3178809
## 4779 -0.9046263 -0.329185582 0.471740330 0.3272519 0.5778235
## 4780 -0.9046263 -0.482740198 0.182501808 -0.4241459 0.5778235
## 4781 -0.9046263 -0.313830121 -0.345358496 0.3272519 1.3178809
## 4782 0.1749079 -0.605583891 -0.612904129 -0.4241459 -0.9022913
## 4783 -1.9841605 -0.298474659 0.544049961 0.3272519 -0.1622339
## 4784 -0.9046263 -0.359896505 0.030651583 1.0786497 0.5778235
## 4785 -0.9046263 -0.298474659 0.290966253 1.8300475 2.0579382
## 4786 -0.9046263 -0.998683708 -0.873218800 -1.1755437 -1.6423486
## 4787 -0.9046263 -0.835915815 -0.800909169 -0.4241459 -0.9022913
## 4788 1.2544421 -0.344541044 -0.656289908 -1.1755437 -0.9022913
## 4789 1.2544421 -0.513451121 -0.128429604 0.3272519 0.5778235
## 4790 0.1749079 -0.713072122 -0.728599538 -0.4241459 0.5778235
## 4791 0.1749079 -0.329185582 -0.005503232 0.3272519 -0.1622339
## 4792 1.2544421 2.895461353 2.402407468 0.3272519 3.5380530
## 4793 0.1749079 -0.897337661 -0.865987837 -1.9269415 -0.9022913
## 4794 0.1749079 -0.774493969 -0.721368575 -0.4241459 -0.9022913
## 4795 -1.9841605 -0.329185582 1.484075159 0.3272519 0.5778235
## 4796 -0.9046263 -0.713072122 -0.771985317 -0.4241459 -0.9022913
## 4797 -1.9841605 -0.974114969 -0.815371095 -0.4241459 -0.9022913
## 4798 -1.9841605 -0.989470431 -0.757523391 -0.4241459 -0.9022913
## 4799 0.1749079 -0.854342369 -0.468284868 0.3272519 -0.1622339
## 4800 0.1749079 -0.759138507 -0.649058945 -0.4241459 -0.9022913
## 4801 0.1749079 -0.667005737 -0.771985317 -0.4241459 -0.9022913
## 4802 1.2544421 0.116122804 -0.388744274 0.3272519 0.5778235
## 4803 -1.9841605 -0.974114969 -0.829833021 -0.4241459 -1.6423486
## 4804 -1.9841605 -1.127669585 -0.822602058 -0.4241459 -0.9022913
## 4805 0.1749079 -0.636294814 -0.627366056 -1.1755437 -0.9022913
## 4806 0.1749079 -0.347612136 -0.446591979 0.3272519 0.5778235
## 4807 0.1749079 -0.605583891 -0.793678206 -0.4241459 -0.9022913
## 4808 0.1749079 -0.482740198 -0.583980277 -0.4241459 -0.9022913Con la finalidad de que las diferencias en las dimensiones no afecte de cálculo de la distancias, se realiza la estandarización de las variables.
3.1.1 Método Elbow (del codo)
## Identificando la cantidad de clusters
fviz_nbclust(datavivienda_ac, kmeans, method = "wss") +
geom_vline(xintercept = 4, linetype = 2)
Se genera un gráfico que utiliza el método del codo para seleccionar el número de clusters adecuado, en este caso, según la gráfica anterior, 4 clusters.
# 4 Clusters
num_clusters <- 4
clustering_result1 <- kmeans(datavivienda_ac, centers = num_clusters)
clustering_result1## K-means clustering with 4 clusters of sizes 1347, 729, 2197, 535
##
## Cluster means:
## estrato preciom areaconst habitaciones banios
## 1 -1.1554757 -0.7236465 -0.5603795 -0.4302821 -0.7479066
## 2 1.1078387 1.8854132 1.3382209 0.3643579 1.3117899
## 3 0.4918399 -0.2093305 -0.3484831 -0.3300930 -0.2194982
## 4 -0.6201135 0.1124949 1.0184775 1.9424060 0.9969588
##
## Clustering vector:
## [1] 3 3 3 1 3 4 2 4 4 3 4 4 3 1 3 1 2 3 1 3 3 1 1 2 1 1 3 1 2 2 1 2 3 2 2 1 1
## [38] 2 1 2 2 2 1 1 1 3 2 2 1 2 1 2 3 3 1 2 3 2 2 1 2 2 2 2 3 1 2 2 2 2 2 2 2 3
## [75] 2 4 1 4 1 1 1 1 1 1 1 1 1 1 4 1 4 1 4 1 3 3 3 3 3 4 1 1 4 4 4 4 4 3 2 2 3
## [112] 2 2 3 3 4 3 3 3 3 3 3 3 3 3 3 3 3 2 2 2 2 3 3 2 2 3 2 3 2 3 4 1 4 1 1 1 1
## [149] 1 1 2 3 3 3 3 3 3 4 3 1 3 1 3 2 3 1 3 3 3 3 2 3 3 3 3 3 3 2 3 3 3 3 3 3 3
## [186] 1 1 1 1 1 1 1 1 3 1 3 1 4 1 4 1 1 1 1 3 3 4 1 4 4 1 2 1 1 1 1 1 1 1 1 1 1
## [223] 1 1 1 1 1 1 1 1 1 3 1 4 1 1 1 3 2 2 3 3 3 2 1 1 4 1 3 1 1 3 3 1 1 1 1 1 1
## [260] 1 1 1 1 1 1 3 3 1 1 1 4 1 1 1 1 1 3 1 1 3 3 1 3 3 4 3 1 3 1 3 1 3 1 3 4 3
## [297] 3 1 3 1 1 3 1 1 1 1 1 1 1 1 1 1 3 1 3 1 4 1 1 4 1 1 1 3 1 4 4 1 4 3 4 1 3
## [334] 3 1 1 1 1 1 1 3 1 1 1 3 1 3 3 3 4 3 3 1 4 4 4 1 4 4 3 3 3 3 3 3 1 3 3 3 3
## [371] 3 4 3 1 3 1 3 3 3 1 3 3 3 1 3 3 3 1 3 3 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 1 3
## [408] 3 3 3 2 3 3 1 1 1 4 1 4 1 1 1 1 3 3 3 3 4 4 3 3 3 1 1 3 3 3 3 4 3 3 3 1 3
## [445] 3 2 3 3 1 1 1 1 1 1 1 4 1 1 1 1 1 1 1 4 1 1 1 1 1 4 1 1 1 4 4 4 4 4 1 1 1
## [482] 1 1 1 4 4 1 1 1 1 1 1 3 3 4 4 4 4 1 1 1 3 1 1 3 1 1 1 1 3 1 3 1 1 1 1 1 1
## [519] 3 3 1 1 1 3 3 3 1 3 3 3 1 3 1 1 1 1 3 1 1 3 3 3 3 1 3 3 4 3 3 3 3 1 1 1 4
## [556] 2 3 1 2 3 2 3 3 3 3 3 2 3 3 3 3 3 3 2 3 2 3 3 3 2 2 2 2 3 3 2 3 2 3 2 2 3
## [593] 2 3 2 2 2 3 2 2 3 3 3 2 2 3 2 2 2 3 2 2 3 2 2 2 2 2 2 3 2 2 2 2 2 3 2 2 2
## [630] 3 2 3 3 3 2 3 2 2 2 2 2 3 3 2 2 2 2 3 2 2 2 3 2 2 4 2 2 2 3 2 3 2 3 2 3 3
## [667] 2 2 4 2 3 3 2 2 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 3 2 3 2 2 2 3 3 3 2 2 3 3 2
## [704] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 2 3 3 3 2 2 2
## [741] 3 2 2 3 2 2 3 2 3 3 3 3 3 3 3 3 3 3 2 3 3 3 2 2 1 3 3 2 2 2 3 3 2 3 3 2 3
## [778] 3 3 3 4 3 2 3 3 3 2 3 3 3 3 3 3 3 3 3 3 3 2 3 3 3 2 2 2 3 3 3 2 2 3 2 2 2
## [815] 3 3 2 3 2 3 3 3 3 3 3 3 3 3 3 3 2 3 3 3 3 3 3 3 3 2 3 2 3 2 3 3 2 3 3 3 3
## [852] 3 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 3 2 3 3 3 3 3 2 3 3
## [889] 3 2 3 3 3 2 2 2 3 2 2 3 3 3 3 3 3 3 3 3 3 2 3 2 3 3 3 3 3 3 3 3 1 1 3 3 3
## [926] 3 3 3 3 3 2 2 2 2 2 2 2 2 2 3 3 1 1 1 1 1 1 1 1 1 1 4 1 1 1 4 1 1 3 1 1 1
## [963] 1 2 2 2 2 2 4 4 2 2 4 2 2 2 2 3 4 3 1 1 4 1 1 4 4 3 4 1 4 4 1 1 4 4 4 1 1
## [1000] 1 1 1 1 1 1 1 1 1 1 1 4 1 3 3 3 3 2 2 3 3 3 3 3 2 3 3 2 3 3 3 3 3 3 2 2 3
## [1037] 3 1 3 3 3 3 3 3 3 3 3 2 3 3 3 3 2 3 3 2 3 2 3 2 1 4 4 4 4 1 4 3 4 3 4 3 3
## [1074] 3 3 4 1 3 4 3 3 3 3 3 3 1 3 1 1 3 4 1 3 3 3 3 4 1 4 4 4 4 1 4 1 4 3 3 4 3
## [1111] 3 3 3 1 4 1 3 1 4 3 4 1 1 4 3 4 4 4 1 4 3 3 4 3 3 1 2 2 3 3 3 3 4 1 1 1 1
## [1148] 1 1 1 1 1 1 3 4 1 1 1 4 1 3 4 1 1 1 1 1 4 4 1 1 1 1 1 4 3 3 1 1 1 1 1 1 1
## [1185] 1 1 4 4 4 1 4 1 1 4 1 1 4 4 1 1 1 1 1 1 1 1 4 4 4 1 1 4 4 4 4 3 1 4 4 1 4
## [1222] 1 3 1 1 1 3 3 3 1 1 1 1 4 1 1 1 4 1 1 1 3 1 1 4 3 1 1 1 1 1 1 1 1 1 1 3 1
## [1259] 1 3 1 1 3 3 1 1 1 1 1 3 3 1 1 1 1 1 1 1 3 4 4 4 4 1 1 1 4 1 1 4 1 1 4 1 4
## [1296] 4 1 3 3 3 3 3 3 3 4 3 4 3 3 3 3 3 3 3 4 3 4 4 2 3 4 3 3 3 4 4 3 2 3 3 3 3
## [1333] 3 2 3 3 2 3 2 4 3 3 4 4 4 2 3 3 4 3 3 2 3 3 3 2 3 3 3 4 3 3 3 2 4 2 3 2 3
## [1370] 3 2 3 3 3 1 3 2 4 3 3 2 3 3 3 1 3 3 3 3 3 3 3 2 3 3 3 3 3 3 3 3 3 3 3 3 3
## [1407] 1 3 3 1 3 3 3 3 3 3 3 3 4 3 3 3 3 2 3 3 3 3 3 3 3 1 3 3 3 3 3 3 3 3 3 3 3
## [1444] 3 3 3 3 2 3 2 3 1 3 3 3 3 3 3 3 3 4 2 2 3 3 2 2 2 2 4 2 3 4 3 3 3 3 4 2 4
## [1481] 3 4 1 3 2 3 3 3 3 1 4 4 4 1 2 4 1 1 1 4 4 4 3 4 4 4 4 1 1 4 4 1 1 1 1 1 1
## [1518] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 3 4 4 4 3 1 4 3 3 3 4 4 4 1 3 3 1 1 1 4
## [1555] 4 4 4 3 2 3 4 1 1 3 4 4 4 4 4 4 4 1 3 4 3 4 3 4 3 3 4 3 4 3 1 3 1 2 4 4 1
## [1592] 3 4 3 3 3 3 3 1 1 3 1 3 1 1 1 3 3 3 1 3 1 3 3 3 2 2 3 3 3 3 3 3 3 3 3 3 3
## [1629] 3 3 3 2 3 3 2 3 3 2 2 3 2 3 2 1 2 3 3 3 3 1 1 1 3 4 1 1 1 3 3 1 1 1 1 1 4
## [1666] 3 4 4 4 1 1 1 1 3 3 1 1 4 3 4 3 3 1 1 1 1 1 1 3 1 3 1 1 1 1 1 4 3 1 1 1 1
## [1703] 1 1 1 1 1 3 3 3 1 1 1 1 1 1 3 3 1 1 1 1 1 1 1 1 1 1 3 1 3 3 3 1 1 1 4 1 4
## [1740] 4 1 4 1 1 3 1 1 1 4 3 1 3 3 3 4 1 4 4 3 2 4 4 2 1 4 4 3 4 4 3 3 4 3 1 3 3
## [1777] 1 3 4 1 3 2 3 1 3 3 3 4 3 4 4 4 4 1 3 4 2 3 1 3 1 1 4 1 2 3 1 2 3 3 3 3 3
## [1814] 2 2 3 3 2 2 2 2 4 2 3 3 3 3 3 2 2 3 2 2 3 2 2 2 3 1 1 1 4 1 1 1 1 4 4 1 1
## [1851] 1 1 3 2 2 3 2 3 1 4 4 1 1 1 1 1 1 4 1 4 4 4 3 3 4 3 3 3 3 3 3 4 3 3 3 3 3
## [1888] 4 3 3 4 3 3 3 3 1 3 3 3 3 3 1 3 3 3 2 2 4 3 4 3 3 3 3 3 2 1 3 3 2 3 4 3 3
## [1925] 4 4 4 2 1 3 3 3 3 3 2 3 3 3 3 4 4 3 3 4 2 3 3 3 3 4 3 3 4 3 3 4 4 3 3 3 4
## [1962] 3 1 4 4 4 4 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 3 3 3 3 3 3 3 3 3 1
## [1999] 1 3 3 3 3 3 3 3 3 1 3 1 1 3 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [2036] 3 1 3 3 3 3 3 3 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 1 3 3 3 3 3 3
## [2073] 3 3 3 3 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 1 3 3
## [2110] 3 3 3 4 3 1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 1 4 1 1
## [2147] 1 3 3 3 1 3 3 3 3 3 3 3 3 4 3 2 3 3 3 1 4 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [2184] 3 3 3 3 1 3 4 1 3 3 3 3 3 3 3 4 3 4 3 3 3 1 1 3 1 1 3 3 3 3 3 3 3 3 3 3 3
## [2221] 3 3 3 1 3 3 3 3 3 3 3 3 1 3 3 1 3 2 3 3 3 3 3 1 3 3 3 3 1 3 1 1 1 3 3 1 1
## [2258] 3 3 3 3 1 1 1 3 3 1 3 1 3 3 3 3 3 3 3 3 3 3 1 4 4 1 1 1 1 1 1 4 4 1 4 1 4
## [2295] 1 1 1 4 4 4 4 4 2 1 4 1 1 1 1 1 1 1 1 3 1 1 1 4 4 4 1 1 1 1 1 4 4 1 1 1 1
## [2332] 4 1 1 1 4 3 4 1 1 1 1 1 1 1 1 4 4 1 1 1 4 3 3 4 1 1 1 1 3 1 4 4 3 4 1 1 1
## [2369] 1 1 1 3 3 1 2 3 2 3 3 3 3 3 3 3 3 3 3 3 2 3 1 3 3 1 3 3 3 2 2 3 3 3 2 3 3
## [2406] 3 3 3 2 3 3 2 2 1 2 3 3 3 3 3 3 1 2 3 3 3 2 3 3 3 3 3 3 3 3 2 3 3 2 3 2 3
## [2443] 3 3 3 3 3 3 3 3 3 3 1 3 3 3 3 3 3 2 2 2 3 4 3 3 3 3 3 3 3 3 3 2 2 3 3 3 3
## [2480] 3 3 3 2 2 3 3 2 2 2 2 3 1 1 1 1 1 2 4 1 1 1 1 1 3 1 1 1 1 1 3 3 3 3 4 3 3
## [2517] 3 3 3 3 3 3 3 3 3 3 1 3 3 3 3 3 3 3 3 3 3 3 3 3 1 1 1 1 4 1 1 1 1 1 1 1 1
## [2554] 1 1 1 1 1 1 4 4 1 1 1 1 1 4 4 1 1 1 1 1 1 1 2 3 1 2 3 3 3 3 3 1 1 1 1 1 1
## [2591] 1 1 1 1 1 1 4 4 4 1 1 4 3 1 4 4 1 4 4 1 3 1 3 3 3 3 3 1 3 3 3 3 3 3 3 3 3
## [2628] 3 3 3 3 3 3 2 1 1 3 1 1 1 4 4 1 1 1 1 1 4 1 3 3 3 2 3 3 3 2 2 2 3 2 2 3 3
## [2665] 2 3 3 2 3 2 3 3 2 3 3 3 3 2 2 3 2 3 3 3 3 2 2 3 3 2 3 2 2 3 2 1 2 2 2 3 3
## [2702] 3 3 2 3 3 3 3 2 3 3 3 3 3 3 3 2 2 3 3 3 2 3 3 3 3 3 2 3 3 2 3 2 2 3 3 2 2
## [2739] 2 3 2 2 2 2 2 2 2 2 3 3 3 3 2 3 2 3 3 1 4 4 4 2 1 4 3 3 4 3 1 3 3 3 1 4 1
## [2776] 3 3 3 4 3 1 1 4 3 3 1 1 3 4 3 1 4 3 3 3 3 3 3 1 3 3 3 3 3 3 3 3 3 1 3 3 1
## [2813] 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 1 4 4 4 3 4 4 1 1 1 3 3 3 3 4 3 3
## [2850] 3 3 1 4 1 2 2 2 2 2 2 3 2 3 3 2 3 2 3 3 3 3 2 3 2 3 2 2 3 3 3 2 2 3 3 2 2
## [2887] 2 2 2 3 2 2 3 2 3 2 2 2 2 2 3 3 2 2 3 2 2 3 3 2 2 2 2 2 2 2 2 2 3 2 2 3 2
## [2924] 3 2 2 3 3 3 3 2 2 3 2 3 3 2 2 2 2 3 2 3 2 2 2 2 3 2 2 2 3 3 3 2 2 2 2 2 2
## [2961] 3 2 2 2 3 2 2 2 3 2 3 3 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 3 3 2 3 2 3
## [2998] 2 3 2 2 2 2 4 2 2 2 2 3 3 2 3 2 3 3 3 3 3 1 3 3 3 3 3 2 2 2 3 2 2 3 2 2 2
## [3035] 3 2 3 2 2 3 3 3 2 2 2 3 2 3 2 3 3 2 2 2 3 3 2 2 2 3 3 3 3 3 3 3 3 2 3 3 3
## [3072] 3 2 2 3 3 3 3 3 3 3 2 2 3 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 3 3 3 3 2 3 3 3
## [3109] 2 2 2 3 3 2 3 2 3 3 2 2 3 3 3 2 3 3 3 2 3 3 3 2 2 2 2 2 2 2 3 2 2 2 2 2 2
## [3146] 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 2 2 3 1 1 4 1 1 1 3 3 4 1 1 1 1
## [3183] 3 1 4 4 3 1 3 3 4 4 4 4 3 4 3 1 3 4 3 3 4 3 1 1 1 1 4 3 4 4 1 4 1 3 3 3 1
## [3220] 1 1 3 1 3 1 3 4 3 4 1 1 1 1 1 1 1 1 1 1 1 3 1 1 3 3 1 1 1 3 1 1 3 1 1 3 1
## [3257] 1 1 1 1 1 3 3 3 1 1 3 3 4 1 4 1 4 4 4 3 4 1 4 1 1 1 4 1 1 1 1 1 1 1 1 1 1
## [3294] 1 4 3 3 1 3 3 3 3 3 3 3 3 4 3 3 3 3 3 3 2 3 3 3 3 3 3 4 3 3 3 3 3 3 3 3 3
## [3331] 3 3 1 3 3 3 3 3 1 3 1 3 3 3 3 1 3 3 3 3 3 2 3 1 1 1 1 1 4 1 1 4 1 1 1 1 4
## [3368] 1 4 1 1 1 1 1 1 3 2 4 1 4 4 4 4 4 4 3 1 1 3 3 4 1 4 4 4 4 1 3 4 4 1 4 4 3
## [3405] 3 1 1 3 3 4 1 3 3 3 1 3 3 4 3 3 1 4 4 4 2 3 4 4 2 4 3 3 4 3 3 3 2 4 4 3 3
## [3442] 3 1 1 1 2 1 1 4 4 1 4 4 4 4 4 1 4 3 4 1 3 4 4 4 4 3 1 1 1 3 3 3 3 3 3 3 3
## [3479] 3 1 3 1 1 3 1 1 1 3 3 1 1 1 3 3 1 3 1 1 1 1 3 1 3 3 3 3 3 3 3 3 4 1 1 4 4
## [3516] 1 4 4 3 1 1 1 4 3 3 1 3 1 3 4 4 3 4 1 4 3 3 3 3 3 3 4 3 3 3 3 3 3 3 3 3 4
## [3553] 4 3 3 1 3 3 3 3 3 1 2 2 3 3 1 4 3 3 4 3 2 2 3 3 2 4 2 2 3 4 2 2 2 2 2 3 3
## [3590] 2 2 3 3 2 3 2 3 3 4 2 3 3 4 3 3 1 3 2 4 2 3 2 2 3 2 3 3 3 3 3 3 2 3 2 3 3
## [3627] 1 2 3 3 3 2 2 3 3 2 4 2 2 4 3 3 3 3 4 2 3 2 4 3 3 3 2 3 3 3 2 2 2 2 2 2 3
## [3664] 2 3 2 3 2 2 2 2 2 3 3 2 3 3 3 2 2 2 3 2 2 2 2 2 2 2 2 3 2 4 3 2 3 3 3 2 2
## [3701] 3 3 3 3 2 2 3 3 3 4 2 2 3 2 3 3 2 2 3 2 4 2 3 3 3 1 2 3 3 3 3 3 3 3 3 3 3
## [3738] 3 3 3 3 2 3 3 3 2 3 2 3 3 3 3 3 3 2 3 3 2 3 3 2 3 3 3 3 3 3 2 2 3 2 2 3 2
## [3775] 3 2 3 2 3 2 3 3 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 3 2 2 2 2 3 2 3 2 2 3 2 2 2
## [3812] 3 2 3 2 3 2 2 2 3 2 2 3 2 3 2 3 3 2 2 2 2 2 2 2 4 1 3 4 2 3 3 3 4 3 3 3 3
## [3849] 3 3 3 3 3 3 3 1 1 3 3 3 1 1 1 1 1 2 3 4 2 2 3 4 4 4 4 4 4 3 1 4 1 4 4 3 3
## [3886] 3 4 3 3 3 4 3 4 4 4 1 1 3 1 1 1 3 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4 1
## [3923] 4 3 3 3 3 4 3 3 3 4 3 4 4 3 4 4 1 3 4 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [3960] 3 3 3 3 3 3 3 3 3 3 4 4 1 2 2 3 3 1 4 3 3 4 4 1 1 3 1 1 1 1 1 3 1 1 3 3 3
## [3997] 1 3 1 3 3 1 1 3 3 3 3 1 3 1 1 1 1 3 3 3 3 1 1 1 3 3 1 3 1 1 3 3 3 1 3 1 3
## [4034] 3 1 3 1 3 1 1 1 3 1 1 1 1 1 3 3 1 3 3 1 1 1 3 4 1 1 1 3 1 3 3 3 1 1 3 1 3
## [4071] 3 3 1 3 4 3 1 1 3 3 1 1 3 1 3 1 1 3 3 3 1 1 1 1 3 1 1 1 4 1 3 1 3 1 3 1 4
## [4108] 3 1 3 1 3 1 1 1 1 1 1 1 3 3 1 1 3 1 3 3 3 1 3 1 3 3 4 1 3 3 3 3 1 3 1 3 1
## [4145] 3 1 3 3 1 3 3 3 1 3 1 1 3 3 1 1 1 1 4 4 4 1 1 1 3 3 3 3 3 3 3 3 1 1 3 1 3
## [4182] 1 1 1 4 1 1 3 1 1 3 3 3 3 3 1 1 1 4 1 3 1 1 4 4 1 3 3 3 1 3 1 1 3 4 3 3 3
## [4219] 3 1 3 3 3 1 3 3 3 1 1 3 3 1 1 1 1 3 1 3 1 1 3 3 1 1 1 1 3 1 3 2 2 4 1 3 4
## [4256] 3 3 1 1 1 3 1 4 1 3 4 1 1 3 1 1 3 3 1 1 1 1 1 1 3 1 3 3 1 3 3 3 3 3 1 3 3
## [4293] 1 1 1 1 1 1 1 3 1 3 3 3 1 1 3 3 3 3 1 1 3 3 3 1 3 3 3 3 1 3 1 3 1 3 3 3 3
## [4330] 3 1 1 1 1 1 1 3 1 3 1 1 3 1 1 1 1 3 3 1 1 3 3 3 1 1 1 3 3 1 3 1 3 1 3 3 1
## [4367] 3 3 1 3 1 3 3 3 1 3 1 1 3 3 3 1 1 3 3 1 1 3 1 1 1 1 3 1 1 1 1 1 3 3 1 1 3
## [4404] 3 3 3 3 1 1 3 1 3 1 1 1 3 1 1 3 1 3 1 1 1 1 3 1 3 1 1 3 1 1 1 3 1 1 1 1 3
## [4441] 1 1 3 3 1 3 3 3 1 1 3 3 1 1 3 1 1 3 2 1 3 3 3 3 1 3 1 1 3 3 1 1 1 3 1 1 3
## [4478] 3 3 1 1 1 3 3 1 1 1 1 3 3 3 1 3 3 3 1 1 1 1 1 1 1 3 3 3 1 3 1 3 1 3 1 3 3
## [4515] 1 1 1 3 1 3 3 1 3 3 1 1 1 1 1 3 1 1 1 3 3 1 1 1 3 1 1 3 1 1 3 3 1 1 1 1 3
## [4552] 1 3 1 3 3 3 1 1 1 1 3 1 3 3 3 1 1 3 3 3 3 1 3 1 3 1 1 3 3 3 1 3 3 3 3 3 1
## [4589] 1 1 1 3 1 1 3 3 3 1 3 1 3 3 3 3 3 3 1 1 1 1 3 3 1 3 1 3 3 1 1 1 4 4 3 4 1
## [4626] 4 3 4 2 3 3 3 3 3 3 3 3 3 3 1 1 3 3 3 3 3 3 4 3 1 1 3 3 3 3 1 3 3 1 3 3 3
## [4663] 3 2 3 1 2 3 4 4 4 4 1 1 1 1 1 1 1 1 1 1 1 4 1 1 1 1 1 1 1 1 1 1 4 1 3 1 4
## [4700] 4 3 4 1 4 4 4 1 3 3 4 4 4 4 4 1 1 1 3 4 1 1 3 4 1 1 3 1 3 1 1 1 3 1 1 3 3
## [4737] 3 3 3 4 2 1 3 3 1 2 2 2 4 4 1 1 1 4 4 1 4 4 2 4 3 1 3 2 2 1 1 1 3 2 4 1 2
## [4774] 3 4 4 4 4 4 1 3 3 1 4 4 1 1 3 3 3 3 2 3 3 4 1 1 1 3 3 3 3 1 1 3 3 3 3
##
## Within cluster sum of squares by cluster:
## [1] 1370.325 2944.858 2810.543 2279.233
## (between_SS / total_SS = 60.9 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault"## Grafica con el Metodo 1
fviz_cluster(clustering_result1, data = datavivienda_ac, stand = FALSE,
ellipse.type = "convex", geom = "point",
palette = "jco", main = "Método Elbow")
Método del codo (Elbow method); es una técnica comúnmente utilizada para determinar el número óptimo de clusters en un conjunto de datos mediante la evaluación de la suma de cuadrados dentro de los grupos (WSS) en función del número de clusters.
Los centroides de los clusters muestran las características promedio de cada cluster: * El cluster 1 tiene valores bajos en todas las características. * El cluster 2 tiene valores altos en todas las características. * El cluster 3 tiene valores bajos en estrato, precio y área de construcción, pero valores moderados en habitaciones y baños. * El cluster 4 tiene un valor bajo en estrato pero valores altos en precio, área de construcción, habitaciones y baños.
3.1.2 Método silhouette (de la silueta)
## Metodo 2
fviz_nbclust(datavivienda_ac, kmeans, method = "silhouette")
Se genera un gráfico que utiliza el método de la silueta para seleccionar el número de clusters adecuado, en este caso, según la gráfica anterior, 2 clusters.
# 2 clusters
num_clusters <- 2
clustering_result2 <- kmeans(datavivienda_ac, centers = num_clusters)
print(clustering_result2)## K-means clustering with 2 clusters of sizes 1554, 3254
##
## Cluster means:
## estrato preciom areaconst habitaciones banios
## 1 0.6354813 1.0417054 0.975576 0.7677431 1.0954827
## 2 -0.3034843 -0.4974831 -0.465902 -0.3666481 -0.5231654
##
## Clustering vector:
## [1] 2 2 2 2 2 1 1 1 1 2 1 1 2 2 2 2 1 2 2 2 1 2 2 1 2 2 2 2 1 1 2 1 1 1 1 2 2
## [38] 1 2 1 1 1 2 2 2 1 1 1 2 1 2 1 1 1 2 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 1 1 2
## [75] 1 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 1 2 1 2 1 1 2 2 2 1 2 2 1 2 2 1 2 2 1 1 2
## [112] 1 1 2 2 1 1 2 2 2 1 2 1 1 1 1 2 2 1 1 1 1 1 2 1 1 1 1 2 1 1 2 2 1 2 2 2 2
## [149] 2 2 1 2 2 2 2 2 2 1 2 2 2 2 2 1 1 2 2 1 1 2 1 1 1 2 2 2 2 1 2 1 2 2 2 2 1
## [186] 2 2 2 2 2 2 2 2 2 2 1 2 1 2 1 2 2 2 2 2 2 1 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2
## [223] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 2 1 1 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2
## [260] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 1 2
## [297] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 1 2 2 1 2 1 2 2
## [334] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 1 1 1 2 1 1 2 2 2 2 2 2 2 2 2 2 2
## [371] 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2
## [408] 2 2 2 1 2 2 2 2 2 1 2 1 2 2 2 2 2 2 2 1 1 1 2 2 1 2 2 2 2 2 1 1 2 2 2 2 2
## [445] 2 1 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 1 2 1 2 2 2
## [482] 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 1 1 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2
## [519] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 1 1 2 2 2 2 2 2 2 1
## [556] 1 2 2 1 1 1 2 2 2 2 2 1 2 1 1 2 2 1 1 1 1 2 2 2 1 1 1 1 2 1 1 2 1 2 1 1 1
## [593] 1 2 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1
## [630] 1 1 2 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 2 1
## [667] 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 2 1 1 1 1 1
## [704] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1
## [741] 1 1 1 1 1 1 1 1 1 2 2 1 2 2 2 1 1 1 1 2 1 2 1 1 2 1 1 1 1 1 2 2 1 1 1 1 2
## [778] 2 2 1 1 1 1 2 1 2 1 1 1 2 1 1 2 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1
## [815] 1 2 1 2 1 1 1 2 2 2 1 1 1 2 2 2 1 2 2 1 2 2 2 2 2 1 2 1 2 1 2 1 1 2 2 2 2
## [852] 2 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 2 2 2 2 1 1 1 1 1 2 2 2 2 2 1 2 2
## [889] 2 1 1 2 2 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 1 2 1 2 2 2 2 2 2 2 1 2 2 2 2 1
## [926] 2 2 1 2 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2
## [963] 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 2 2 1 2 2 1 1 2 1 2 1 1 2 2 1 1 1 2 2
## [1000] 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 1 1 1 1 2 2 2 2 1 2 2 1 2 2 2 2 1 1 1 1 2
## [1037] 2 2 2 2 2 1 2 2 2 2 2 1 2 2 2 2 1 2 1 1 1 1 2 1 2 1 1 2 1 2 1 2 1 1 1 2 2
## [1074] 2 1 1 2 2 1 1 2 1 2 2 2 2 2 2 2 2 1 2 2 1 2 2 2 2 2 1 1 1 2 1 2 2 2 2 1 1
## [1111] 2 2 2 2 1 2 1 2 1 1 1 2 2 1 2 1 1 2 2 1 2 2 1 2 2 2 1 1 2 2 2 2 1 2 2 2 2
## [1148] 2 2 2 2 2 2 2 2 2 2 2 1 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [1185] 2 2 2 1 2 2 1 2 2 1 2 2 2 1 2 2 2 2 2 2 2 2 2 1 1 2 2 1 1 1 2 2 2 2 1 2 1
## [1222] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2
## [1259] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 2 2 2 1 2 2 2 2 2 1 2 1
## [1296] 2 2 2 2 2 2 2 2 1 2 2 1 2 2 2 2 2 2 2 1 2 1 1 1 2 1 2 2 2 1 1 2 1 1 2 2 2
## [1333] 1 1 2 2 1 2 1 1 2 1 1 1 1 1 2 1 1 2 2 1 2 2 2 1 2 2 2 1 2 2 2 1 1 1 2 1 2
## [1370] 1 1 2 2 2 2 2 1 1 2 2 1 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2
## [1407] 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2
## [1444] 2 2 2 2 1 2 1 2 2 2 2 2 2 2 2 2 2 1 1 1 2 1 1 1 1 1 1 1 2 1 2 2 2 1 1 1 1
## [1481] 2 1 2 2 1 2 2 2 2 2 2 1 1 2 1 1 2 2 2 2 2 1 2 1 1 1 2 2 2 1 1 2 2 2 2 2 2
## [1518] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 1 1 1 1 2 1 2 1 2 1 1 1 2 2 1 2 2 2 1
## [1555] 1 1 1 1 1 2 1 2 2 1 1 1 1 1 1 1 1 2 2 1 2 1 2 1 2 2 1 2 1 2 2 2 2 1 1 1 2
## [1592] 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 2 2 2 2 2 1 1 2 2 2 2
## [1629] 2 2 2 1 2 2 1 2 2 1 1 2 1 2 1 2 1 1 1 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 1
## [1666] 2 1 1 1 2 2 2 2 2 1 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [1703] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1
## [1740] 1 2 2 2 2 2 2 2 2 1 2 2 2 2 2 1 2 1 2 1 1 1 1 1 2 1 1 2 1 1 2 2 1 2 2 2 2
## [1777] 2 1 1 2 2 1 2 2 2 1 2 1 2 1 1 1 1 2 2 1 1 2 2 2 2 2 1 2 1 2 2 1 2 2 2 2 1
## [1814] 1 1 2 2 1 1 1 1 1 1 2 2 1 2 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 2 2 2 2 1 2 2 2
## [1851] 2 2 1 1 1 1 1 1 2 2 1 2 2 2 2 2 2 1 2 1 2 1 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2
## [1888] 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 2 1 2 2 2 2 2 1 2 2 2 1 2 1 2 2
## [1925] 1 1 1 1 2 2 2 2 2 2 1 2 2 2 2 1 1 2 1 1 1 2 2 2 1 1 2 2 1 2 2 1 1 2 2 2 1
## [1962] 2 2 1 1 1 1 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2
## [1999] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 1 2 2 2 2 2 2 2 2 2 2 2 2
## [2036] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [2073] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [2110] 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 2 1 2 2
## [2147] 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 1 2 2 2 2 1 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2
## [2184] 2 2 2 1 2 2 1 2 2 2 1 1 1 2 2 1 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [2221] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [2258] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2
## [2295] 2 2 2 1 1 2 1 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 1 2 2 2 2 2 1 1 2 2 2 2
## [2332] 1 2 2 2 1 2 1 2 2 2 2 2 2 2 2 1 1 2 2 2 2 2 2 1 2 2 2 2 2 2 1 1 2 1 2 2 2
## [2369] 2 2 2 2 2 2 1 2 1 2 2 2 2 2 1 1 1 2 2 2 1 2 2 2 2 2 1 2 2 1 1 2 1 2 1 2 2
## [2406] 2 2 2 1 1 2 1 1 2 1 1 2 2 2 2 1 2 1 2 2 2 1 2 1 2 1 1 2 2 2 1 1 2 1 2 1 1
## [2443] 2 2 1 2 2 2 2 1 2 2 2 2 1 2 2 2 2 1 1 1 2 1 2 2 2 1 2 2 2 1 2 1 1 2 2 2 1
## [2480] 2 1 2 1 1 1 1 1 1 1 1 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2
## [2517] 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [2554] 2 2 2 2 2 2 1 1 2 2 2 2 2 1 2 2 2 2 2 2 2 2 1 1 2 1 2 1 2 1 1 2 2 2 2 2 2
## [2591] 2 2 2 2 2 2 1 1 2 2 2 1 2 2 1 1 2 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [2628] 2 2 2 2 2 2 1 2 2 2 2 2 2 1 2 2 2 2 2 2 1 2 2 2 2 1 1 2 2 1 1 1 1 1 1 2 2
## [2665] 1 1 2 1 2 1 1 2 1 1 2 1 2 1 1 2 1 2 2 2 2 1 1 2 1 1 1 1 1 2 1 2 1 1 1 2 2
## [2702] 2 2 1 2 2 2 2 1 1 1 1 2 2 2 2 1 1 2 2 2 1 2 2 2 2 2 1 2 1 1 1 1 1 2 2 1 1
## [2739] 1 2 1 1 1 1 1 1 1 1 2 2 2 2 1 2 1 2 2 2 2 2 1 1 2 2 1 2 1 2 2 2 2 1 2 1 2
## [2776] 2 2 2 1 2 2 2 1 2 2 2 2 2 1 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 2
## [2813] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 1 1 1 1 1 1 2 2 2 2 2 2 1 1 1 1
## [2850] 2 2 2 1 2 1 1 1 1 1 1 2 1 2 2 1 2 1 2 1 2 2 1 1 1 1 1 1 1 2 1 1 1 2 1 1 1
## [2887] 1 1 1 2 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 2 1 1 1 1
## [2924] 2 1 1 1 2 1 1 1 1 1 1 2 2 1 1 1 1 2 1 1 1 1 1 1 2 1 1 1 2 1 1 1 1 1 1 1 1
## [2961] 2 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1
## [2998] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 2 1 2 2 2 2 2 1 1 1 1 2 1 1 1 1 1 1
## [3035] 2 1 1 1 1 2 1 1 1 1 1 2 1 2 1 1 1 1 1 1 2 1 1 1 1 2 2 2 1 1 1 1 2 1 1 1 1
## [3072] 2 1 1 1 1 2 2 2 1 2 1 1 2 1 1 1 1 2 2 1 2 2 1 2 2 2 1 1 1 1 1 2 2 1 1 1 1
## [3109] 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [3146] 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 2 2 2 2 2 2 2 1 1 2 2 2 2
## [3183] 2 2 1 1 2 2 2 2 1 1 1 1 2 1 1 2 2 1 2 2 1 2 2 2 2 2 1 2 1 1 2 1 2 2 1 2 2
## [3220] 2 2 2 2 2 2 2 1 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [3257] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 2 1 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2
## [3294] 2 1 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 1 1 2 1 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2
## [3331] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 1 2 2 2 2 1
## [3368] 2 1 2 2 2 2 2 2 1 1 2 2 1 1 2 1 1 1 2 2 2 1 1 1 2 1 1 2 1 2 1 1 1 2 1 1 2
## [3405] 2 2 2 2 2 1 2 2 2 2 2 1 1 1 2 2 2 1 1 1 1 2 2 1 1 1 1 1 1 2 2 1 1 1 1 1 2
## [3442] 1 2 2 2 1 2 2 1 1 2 2 1 1 1 1 2 1 2 1 2 2 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 1
## [3479] 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 1
## [3516] 2 2 1 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 2 1 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 1
## [3553] 1 2 2 2 2 2 2 2 2 2 1 1 2 2 2 1 1 2 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 1 2 2
## [3590] 1 1 2 2 1 2 1 2 1 1 1 2 1 1 2 2 2 2 1 1 1 2 1 1 2 1 2 2 2 1 2 2 1 1 1 1 2
## [3627] 2 1 2 1 2 1 1 1 1 1 1 1 1 1 1 2 2 2 2 1 1 1 1 2 2 2 1 2 1 1 1 1 1 1 1 1 2
## [3664] 1 2 1 2 1 1 1 1 1 2 2 1 2 2 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 2 1 2 2 1 1 1
## [3701] 1 1 1 2 1 1 1 1 2 1 1 1 2 1 2 1 1 1 1 1 1 1 2 2 2 2 1 2 2 1 2 2 1 1 2 1 1
## [3738] 2 1 2 1 1 2 1 2 1 2 1 2 1 1 2 1 1 1 1 2 1 1 2 1 2 1 1 1 2 2 1 1 2 1 1 2 1
## [3775] 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 2 1 1 1 1 2 1 1 1 1 1 1 1 1
## [3812] 2 1 1 1 1 1 1 1 2 1 1 1 1 2 1 1 2 1 1 1 1 1 1 1 2 2 2 2 1 2 2 2 1 2 2 2 2
## [3849] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 1 1 1 2 1 1 1 1 1 1 2 2 1 2 1 1 2 1
## [3886] 2 1 2 2 1 1 2 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2
## [3923] 1 2 2 2 2 1 2 2 2 1 1 1 1 2 1 1 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [3960] 2 2 2 2 2 2 2 2 2 2 1 1 2 1 1 2 2 2 1 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [3997] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2
## [4034] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [4071] 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1
## [4108] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 1 2 2 2 2 2 2
## [4145] 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 1 1 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2
## [4182] 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 1 2 2 2 1 2 2 2 2 2 2 2 2 2 1 2 2 2
## [4219] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 2 2 1
## [4256] 2 2 2 2 2 2 2 1 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [4293] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [4330] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [4367] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [4404] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [4441] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [4478] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [4515] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [4552] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [4589] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 2
## [4626] 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 1 2 2 2 2 2 2 2 2
## [4663] 2 1 2 2 1 2 2 2 1 1 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 1 2 2 2 1
## [4700] 1 2 1 2 2 1 1 2 1 2 1 1 1 1 1 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1
## [4737] 2 2 2 1 1 2 1 1 2 1 1 1 1 1 2 2 2 1 2 2 1 2 1 1 2 2 2 1 1 2 2 2 2 1 1 2 1
## [4774] 2 1 1 1 1 2 2 2 2 2 2 1 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2
##
## Within cluster sum of squares by cluster:
## [1] 8461.097 5860.674
## (between_SS / total_SS = 40.4 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault"## Grafica con el Metodo 2
fviz_cluster(clustering_result2, data = datavivienda_ac, stand = FALSE,
ellipse.type = "convex", geom = "point",
palette = "jco", main = "Método Silhouette")
Este método evalúa la calidad de un clustering asignando un coeficiente de silueta a cada punto de datos. El coeficiente de silueta varía entre -1 y 1, donde valores más altos indican que el punto está bien clasificado en su cluster y mal clasificado en otros clusters. El número óptimo de clusters se elige maximizando el valor promedio del coeficiente de silueta.
3.1.3 Método Clústeres K-means
## Metodo 3
res.nbclust <- NbClust(datavivienda_ac, distance = "euclidean", min.nc = 2, max.nc=10, method = "complete", index = "all")
## *** : The Hubert index is a graphical method of determining the number of clusters.
## In the plot of Hubert index, we seek a significant knee that corresponds to a
## significant increase of the value of the measure i.e the significant peak in Hubert
## index second differences plot.
## 
## *** : The D index is a graphical method of determining the number of clusters.
## In the plot of D index, we seek a significant knee (the significant peak in Dindex
## second differences plot) that corresponds to a significant increase of the value of
## the measure.
##
## *******************************************************************
## * Among all indices:
## * 6 proposed 2 as the best number of clusters
## * 2 proposed 3 as the best number of clusters
## * 3 proposed 4 as the best number of clusters
## * 1 proposed 6 as the best number of clusters
## * 10 proposed 9 as the best number of clusters
## * 2 proposed 10 as the best number of clusters
##
## ***** Conclusion *****
##
## * According to the majority rule, the best number of clusters is 9
##
##
## *******************************************************************print(res.nbclust)## $All.index
## KL CH Hartigan CCC Scott Marriot TrCovW
## 2 2.1608 117.1554 1498.8722 -73.0646 785.8518 5.874603e+17 10755813
## 3 5.1514 826.1108 709.6001 -76.3126 5028.7059 5.469086e+17 7307928
## 4 0.2556 868.4262 16.1812 -86.1675 7181.7517 6.213167e+17 5023801
## 5 1.1305 657.4219 12.7293 -94.9613 7397.0336 9.282975e+17 5008021
## 6 1.4121 529.7669 71.1950 -101.5517 7480.7761 1.313667e+18 4941816
## 7 5.2199 459.7878 219.3006 -105.2303 8218.4161 1.533733e+18 4921393
## 8 0.0258 443.3421 2795.8633 -104.4094 9008.9548 1.699520e+18 4790887
## 9 14.6119 963.1614 37.8678 -62.3890 13987.7825 7.636714e+17 3392651
## 10 1.1329 866.9259 42.4495 -66.3280 14350.5320 8.742894e+17 3355649
## TraceW Friedman Rubin Cindex DB Silhouette Duda Pseudot2 Beale
## 2 23463.044 0.3761 1.0244 0.2431 0.6039 0.6827 0.7616 1502.0392 0.9796
## 3 17885.119 3.9556 1.3439 0.2341 1.3186 0.3690 0.6309 506.0527 1.8289
## 4 15583.722 5.8604 1.5423 0.2657 1.3228 0.3113 0.9779 12.7738 0.0708
## 5 15531.408 5.9633 1.5475 0.2741 1.1974 0.3099 1.5943 -2.2365 -1.0000
## 6 15490.354 6.0122 1.5516 0.2813 1.0165 0.3094 0.8560 50.2954 0.5247
## 7 15264.048 6.6239 1.5746 0.2822 1.2550 0.3015 0.7109 228.5114 1.2703
## 8 14597.272 7.1801 1.6465 0.2952 1.2618 0.2512 0.5361 3401.3462 2.7074
## 9 9224.351 11.5577 2.6056 0.2286 1.1893 0.3370 0.9672 37.8245 0.1061
## 10 9152.133 11.9316 2.6262 0.2451 1.1681 0.3372 0.6156 19.3564 1.8932
## Ratkowsky Ball Ptbiserial Frey McClain Dunn Hubert SDindex Dindex
## 2 0.0814 11731.5219 0.2282 10.0273 0.0010 0.1075 2e-04 1.5811 1.9329
## 3 0.2662 5961.7062 0.5058 -0.4141 0.2360 0.0154 1e-04 2.0539 1.7016
## 4 0.2869 3895.9305 0.5319 -1.0245 0.2465 0.0179 1e-04 2.0237 1.6083
## 5 0.2576 3106.2816 0.5322 -1.3769 0.2465 0.0185 1e-04 1.8190 1.6066
## 6 0.2358 2581.7257 0.5322 -0.1559 0.2465 0.0189 1e-04 1.5240 1.6051
## 7 0.2206 2180.5783 0.5333 0.2433 0.2471 0.0190 1e-04 1.6435 1.5970
## 8 0.2141 1824.6590 0.5366 0.8132 0.2501 0.0200 1e-04 1.7498 1.5652
## 9 0.2601 1024.9279 0.5995 -0.2133 0.6438 0.0095 1e-04 1.5993 1.2550
## 10 0.2473 915.2133 0.6007 -0.1895 0.6436 0.0102 1e-04 1.6140 1.2524
## SDbw
## 2 1.4242
## 3 1.4016
## 4 1.2134
## 5 1.0459
## 6 0.7326
## 7 0.8135
## 8 0.7579
## 9 0.7286
## 10 0.7218
##
## $All.CriticalValues
## CritValue_Duda CritValue_PseudoT2 Fvalue_Beale
## 2 0.8459 873.8196 0.4285
## 3 0.8098 203.2180 0.1037
## 4 0.7948 145.6061 0.9965
## 5 0.2177 21.5613 1.0000
## 6 0.7659 91.3923 0.7577
## 7 0.7947 145.2125 0.2738
## 8 0.8431 731.3555 0.0189
## 9 0.8172 249.3384 0.9910
## 10 0.5502 25.3445 0.0985
##
## $Best.nc
## KL CH Hartigan CCC Scott Marriot TrCovW
## Number_clusters 9.0000 9.0000 9.000 9.000 9.000 9.000000e+00 3
## Value_Index 14.6119 963.1614 2757.996 -62.389 4978.828 1.046467e+18 3447885
## TraceW Friedman Rubin Cindex DB Silhouette Duda
## Number_clusters 9.000 9.0000 9.0000 9.0000 2.0000 2.0000 4.0000
## Value_Index 5300.704 4.3776 -0.9385 0.2286 0.6039 0.6827 0.9779
## PseudoT2 Beale Ratkowsky Ball PtBiserial Frey McClain
## Number_clusters 4.0000 2.0000 4.0000 3.000 10.0000 2.0000 2.000
## Value_Index 12.7738 0.9796 0.2869 5769.816 0.6007 10.0273 0.001
## Dunn Hubert SDindex Dindex SDbw
## Number_clusters 2.0000 0 6.000 0 10.0000
## Value_Index 0.1075 0 1.524 0 0.7218
##
## $Best.partition
## [1] 1 2 2 2 2 1 1 1 1 2 1 1 3 2 2 2 3 3 2 2 3 2 2 3 2 2 2 2 3 3 2 4 3 4 3 2 2
## [38] 3 2 3 3 3 2 2 2 3 3 3 2 3 2 3 3 2 2 3 3 3 4 2 3 3 3 3 3 2 3 3 3 3 3 3 3 2
## [75] 3 1 2 1 2 2 2 2 2 2 2 2 2 2 1 2 1 2 1 2 2 3 2 2 2 1 2 2 1 1 1 1 1 2 3 3 2
## [112] 4 3 2 3 1 3 2 2 2 3 2 3 3 3 3 3 2 3 3 3 3 3 2 3 3 3 3 2 3 3 1 1 1 2 1 2 2
## [149] 2 2 5 3 1 2 3 2 2 1 2 2 2 2 2 3 3 2 2 3 3 2 3 3 3 2 2 2 2 4 2 2 3 2 2 2 3
## [186] 2 2 2 2 2 2 2 2 2 2 3 2 1 2 3 2 2 2 2 2 2 1 1 1 1 2 3 2 2 2 2 2 2 2 2 2 2
## [223] 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 3 5 4 3 2 3 3 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2
## [260] 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 3 3 1 2 2 2 2 2 2 2 2 2 4 2
## [297] 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 1 1 2 1 2 2 2 2 2 1 1 2 1 2 1 2 2
## [334] 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 6 2 2 2 1 1 1 2 1 3 2 2 2 2 2 2 2 2 2 2 2
## [371] 2 6 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 3 2 2 2 2 3 2 2 2 2 2
## [408] 2 2 2 3 2 2 2 1 2 1 2 1 2 2 2 2 2 2 2 3 3 1 2 2 3 2 2 2 2 2 3 1 2 3 2 2 2
## [445] 2 3 2 2 2 2 2 2 1 2 1 1 2 2 2 2 2 2 2 1 2 2 1 2 2 1 1 2 2 1 1 1 1 1 2 2 2
## [482] 2 1 2 1 1 2 2 2 2 2 2 2 1 1 1 1 1 2 2 2 1 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 2
## [519] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 1 3 2 2 2 2 2 2 2 1
## [556] 3 2 2 4 3 3 2 2 3 2 2 4 2 3 3 3 2 3 3 3 3 2 2 2 3 3 4 4 2 3 3 2 4 2 5 3 3
## [593] 3 2 4 4 3 3 4 3 3 2 3 4 3 3 4 4 3 3 4 3 3 4 4 3 4 5 4 3 3 3 3 3 4 2 3 3 3
## [630] 3 3 3 3 3 3 3 3 5 3 3 4 3 3 4 5 3 3 2 4 3 4 3 3 5 4 3 3 3 2 4 3 3 3 3 2 3
## [667] 3 3 3 3 3 2 4 3 3 3 3 4 3 3 3 3 3 4 3 3 3 3 4 3 3 3 4 3 3 3 3 2 4 3 3 3 4
## [704] 3 4 3 3 3 3 7 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 3 3 4 3 3 3 4 2 2 2 4 4 3
## [741] 3 3 3 3 4 4 3 3 3 3 3 3 3 2 2 3 3 3 4 2 3 3 4 7 2 3 3 4 3 4 2 2 3 3 3 4 3
## [778] 2 3 3 3 3 3 2 3 2 3 3 3 3 3 3 3 3 3 3 3 2 5 3 3 3 4 4 3 3 3 3 3 4 3 4 4 3
## [815] 3 2 4 2 3 3 3 3 3 2 3 3 3 2 2 3 5 2 3 3 2 2 2 2 2 3 2 4 2 3 2 3 5 2 2 2 2
## [852] 2 3 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 2 2 2 2 3 3 3 3 3 2 2 2 2 2 4 3 2
## [889] 3 3 3 2 2 3 3 4 3 3 4 3 3 2 2 2 2 3 2 2 2 4 3 3 2 2 2 2 2 2 2 3 2 2 2 3 3
## [926] 2 3 3 2 3 3 4 4 4 3 4 4 3 4 3 3 2 2 2 2 2 2 2 2 2 2 1 2 1 2 1 2 1 1 1 2 1
## [963] 2 3 5 4 3 4 3 3 4 4 4 3 4 4 4 2 3 3 2 2 1 2 2 6 1 1 1 1 1 6 2 2 1 1 1 2 2
## [1000] 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 3 3 3 3 2 2 2 2 3 2 2 4 2 2 2 2 3 3 4 3 2
## [1037] 2 2 2 2 2 3 2 2 2 2 2 3 3 3 3 2 3 2 3 3 3 3 2 3 2 1 1 1 1 2 1 2 1 1 3 1 2
## [1074] 2 1 6 2 2 3 3 2 3 2 2 2 2 2 2 2 2 3 2 2 3 2 2 1 2 1 1 1 1 2 6 2 1 1 2 1 3
## [1111] 2 1 2 2 3 2 3 1 1 1 3 2 2 1 1 1 1 1 1 1 2 2 1 1 2 2 5 4 2 2 2 3 1 2 2 2 2
## [1148] 2 2 2 2 2 2 2 1 2 2 1 1 2 2 1 2 2 2 1 2 1 1 2 2 1 2 2 1 2 1 2 2 2 2 1 2 2
## [1185] 2 1 1 1 1 2 1 1 2 1 2 2 1 1 2 2 2 2 2 2 2 2 1 3 1 2 2 4 1 1 1 2 2 1 6 2 1
## [1222] 2 2 2 2 1 2 2 1 2 2 2 1 1 2 2 2 1 2 2 2 2 2 2 4 2 2 2 2 2 2 2 2 2 2 2 2 2
## [1259] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 6 1 2 2 2 6 2 2 1 1 1 1 2 1
## [1296] 1 1 2 3 3 3 3 3 3 1 2 1 3 2 1 3 1 2 2 4 2 1 3 4 3 6 3 2 2 6 1 1 4 3 2 2 2
## [1333] 1 3 2 2 3 2 4 3 1 3 8 3 4 4 2 3 6 2 2 3 2 2 2 4 2 2 2 3 3 3 2 4 3 4 3 3 2
## [1370] 3 3 2 2 2 2 2 4 1 2 2 4 3 2 2 1 3 2 2 2 3 2 2 7 2 3 2 2 3 3 2 2 2 3 2 2 2
## [1407] 1 2 2 1 2 2 2 2 2 2 2 2 5 2 2 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 2 2 2
## [1444] 2 2 2 1 3 2 5 2 2 2 2 2 2 2 2 2 2 1 4 3 3 3 3 4 4 3 6 4 2 3 2 2 3 2 3 4 1
## [1481] 2 3 2 2 4 2 2 2 3 2 1 6 1 2 4 1 2 2 2 1 1 6 2 1 4 1 1 2 2 4 1 2 2 2 2 2 2
## [1518] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 3 3 1 3 3 2 1 2 3 2 4 6 6 2 2 1 2 2 2 4
## [1555] 1 3 4 3 4 2 1 2 2 1 4 6 6 6 6 4 4 2 2 6 2 1 2 6 2 2 6 2 4 2 2 2 2 3 3 3 2
## [1592] 3 4 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 3 3 2 2 2 2 2 3 3 2 3 3 2
## [1629] 3 2 2 4 2 2 3 2 2 3 3 2 3 2 3 2 3 3 1 2 2 2 2 2 2 1 2 2 1 2 2 2 2 1 1 2 1
## [1666] 2 1 1 1 1 1 2 2 1 1 2 2 1 2 1 2 2 2 2 2 2 2 2 3 2 3 2 2 2 2 2 1 2 2 1 2 2
## [1703] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 1 2 4
## [1740] 1 2 1 2 2 2 2 1 2 1 2 2 2 2 2 1 2 3 1 1 4 1 3 2 2 6 1 1 6 6 2 2 6 2 2 2 2
## [1777] 1 3 1 2 1 4 2 2 2 3 2 1 3 6 1 1 3 2 1 1 1 2 2 2 2 2 1 2 5 2 2 3 2 2 2 2 3
## [1814] 3 5 2 2 3 3 3 8 5 4 2 3 3 2 3 3 3 3 3 3 3 3 3 3 3 2 2 2 1 2 2 1 2 1 1 2 2
## [1851] 2 2 3 4 3 3 3 3 2 1 6 2 2 2 2 2 2 1 1 1 1 1 2 2 1 2 2 2 2 2 2 1 2 2 2 2 1
## [1888] 1 2 2 6 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 1 1 2 3 2 2 2 2 2 4 2 2 1 1 1 1 2 2
## [1925] 1 4 1 4 2 3 2 2 2 2 4 2 2 2 2 4 4 2 3 4 3 2 3 2 1 3 3 3 4 3 2 4 4 2 3 2 1
## [1962] 2 2 3 4 4 4 2 2 3 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 4 2 2 2 3 2 2 2 2 3 2
## [1999] 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 3 2 3 2 2 2 2 2 2 2 2 3 2 2 2
## [2036] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 2 3 2 2 2 2 2 2 2
## [2073] 2 2 2 2 2 2 3 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [2110] 2 2 2 1 2 2 2 2 2 2 2 2 2 3 2 2 2 3 2 2 2 2 3 2 3 2 2 2 2 2 2 6 1 1 6 3 2
## [2147] 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 4 3 3 2 2 1 3 2 2 2 2 3 2 2 2 2 3 2 2 2 3 2
## [2184] 2 3 2 3 2 2 3 2 2 3 3 3 3 2 3 3 3 3 2 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [2221] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 4 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [2258] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 1 2 1 1 1 2 2 2 2 2 1 1 2 1 2 1
## [2295] 2 2 2 6 3 1 6 1 1 1 1 2 2 2 2 1 2 2 2 2 2 2 2 1 1 1 2 2 2 1 2 6 6 2 2 2 2
## [2332] 1 2 2 2 3 2 1 2 2 2 2 2 2 2 2 1 6 2 2 2 1 2 2 1 2 2 2 2 2 2 6 6 2 6 2 2 2
## [2369] 2 2 2 2 2 2 4 2 4 2 2 2 2 3 3 3 3 2 2 3 3 3 2 2 3 2 3 2 2 4 3 2 3 2 3 2 2
## [2406] 2 2 2 3 3 2 3 3 2 3 3 2 2 3 2 3 2 4 3 2 2 3 2 3 2 3 3 2 2 2 4 3 2 3 2 4 3
## [2443] 2 2 3 2 2 3 2 3 3 2 2 2 3 2 2 2 2 3 3 3 2 3 3 2 2 3 2 2 2 3 2 3 3 2 2 2 3
## [2480] 2 3 2 3 3 3 3 4 3 3 3 2 2 2 2 2 2 4 1 1 2 2 2 2 2 2 2 2 2 2 2 1 2 2 3 2 2
## [2517] 2 2 2 3 2 2 2 3 2 2 2 2 2 2 2 2 2 2 2 3 2 2 3 2 2 2 2 2 1 2 2 2 2 2 2 1 2
## [2554] 1 2 2 2 1 2 1 1 2 2 2 2 2 1 1 2 2 2 2 2 2 2 4 2 2 3 2 3 3 3 3 2 2 2 2 2 2
## [2591] 2 2 2 2 2 2 4 1 1 2 2 1 2 2 1 4 2 1 1 1 2 1 2 2 2 2 2 2 2 2 2 2 2 2 3 2 3
## [2628] 2 2 2 2 2 2 3 1 2 1 2 1 2 1 1 2 2 1 2 2 1 2 2 2 2 4 3 2 2 4 3 4 3 3 4 2 2
## [2665] 3 3 2 3 3 3 3 3 3 3 2 3 2 3 3 2 3 2 2 2 2 3 3 2 3 3 3 3 3 2 3 1 3 3 3 3 3
## [2702] 3 2 3 3 2 2 2 3 3 3 3 2 3 2 2 3 3 3 3 2 3 2 3 2 2 2 3 2 3 3 3 3 3 2 3 3 3
## [2739] 3 2 3 3 3 4 3 3 3 3 2 2 2 2 3 2 3 2 2 2 1 1 1 3 2 1 1 2 3 1 2 1 1 3 2 1 2
## [2776] 1 2 1 3 2 2 2 3 2 2 2 2 2 1 3 2 4 2 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 1 3 3 2
## [2813] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 4 1 1 2 1 1 2 2 2 2 2 2 3 4 1 3
## [2850] 2 2 2 6 2 3 7 4 4 3 4 2 4 3 2 3 2 3 2 3 2 2 3 3 4 3 4 4 3 2 3 3 4 2 3 4 4
## [2887] 4 4 7 2 4 3 3 4 2 3 4 4 3 4 3 3 3 4 3 3 4 2 2 5 4 3 3 3 3 4 3 3 2 4 3 3 3
## [2924] 2 3 3 3 2 3 3 3 3 3 3 2 2 5 4 3 3 2 3 3 3 3 5 3 2 3 4 3 2 3 3 5 3 4 3 4 3
## [2961] 2 5 3 3 2 3 3 4 3 3 3 3 3 3 3 4 4 3 3 4 7 3 4 4 5 3 3 3 3 3 4 2 2 3 3 3 3
## [2998] 4 3 4 3 4 4 1 4 3 3 4 3 3 3 2 3 3 3 3 2 3 2 2 2 2 2 3 3 3 3 2 3 3 3 3 4 3
## [3035] 2 4 3 3 3 3 3 3 4 4 3 2 3 3 3 3 3 3 3 3 2 3 3 3 3 2 3 3 3 3 3 3 3 3 3 3 3
## [3072] 2 3 3 3 3 3 3 3 3 2 3 3 2 3 3 3 3 2 2 3 2 2 3 3 3 2 3 3 3 3 3 2 2 3 3 3 3
## [3109] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 4 5 3 3 3 4 4 3 7 4 3 3 3 4
## [3146] 3 3 2 3 3 3 3 3 3 3 5 3 3 3 3 3 3 3 3 3 2 3 3 3 2 2 1 2 2 2 2 3 3 2 2 2 2
## [3183] 2 2 1 3 2 2 2 2 4 1 1 1 3 6 2 2 2 1 1 2 3 2 2 2 2 2 1 2 6 6 2 6 2 3 3 2 2
## [3220] 2 2 2 2 3 2 2 4 3 6 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [3257] 2 2 2 2 2 2 2 2 2 2 2 2 1 2 1 1 1 1 1 2 6 2 1 2 2 2 6 2 2 2 2 2 2 2 2 2 2
## [3294] 2 1 2 2 2 2 2 2 2 2 2 2 2 3 2 3 1 3 3 2 4 2 2 2 2 2 3 3 2 2 2 2 2 2 2 2 2
## [3331] 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 3 2 2 2 1 2 2 1 2 2 1 2 2 2 2 6
## [3368] 2 1 2 2 2 2 2 2 3 5 1 2 6 6 1 1 1 1 2 2 2 3 3 6 2 5 6 1 1 2 1 6 6 1 4 1 2
## [3405] 2 2 2 2 2 1 2 3 2 2 2 1 1 6 2 2 2 6 4 1 3 2 1 3 3 1 3 3 3 3 2 1 3 3 3 3 3
## [3442] 3 2 2 2 4 2 2 1 1 2 1 4 1 6 6 1 4 2 1 2 2 1 1 6 5 1 2 2 2 2 2 2 2 2 2 2 3
## [3479] 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 2 2 1 1
## [3516] 2 1 6 1 2 2 2 1 2 2 2 2 2 1 1 1 3 6 2 1 2 2 2 2 2 2 1 2 2 2 2 2 3 2 2 2 1
## [3553] 1 2 2 2 2 3 2 2 2 2 3 3 3 2 2 1 3 2 3 1 5 4 3 3 3 4 3 3 2 4 3 3 3 3 3 2 2
## [3590] 4 3 2 2 4 3 3 2 3 5 4 2 3 3 2 3 2 3 4 6 3 2 3 4 2 3 3 2 2 3 2 2 3 3 3 3 2
## [3627] 2 3 2 3 2 3 3 3 3 3 5 4 4 6 3 1 2 3 1 4 3 4 1 2 3 2 3 2 3 3 3 4 3 3 3 4 2
## [3664] 3 2 4 3 4 3 4 3 3 3 2 4 2 2 3 3 3 3 2 3 3 4 3 4 3 3 3 3 3 3 3 3 2 3 3 4 3
## [3701] 3 3 2 2 3 3 3 3 2 3 3 3 2 3 2 3 3 3 3 3 3 3 2 2 2 2 3 2 2 3 3 3 3 3 2 3 3
## [3738] 2 3 3 3 3 2 3 2 3 2 3 3 3 3 3 3 3 3 3 3 3 3 2 3 2 3 3 3 3 3 3 3 3 3 3 3 3
## [3775] 3 3 3 3 3 3 3 3 4 4 4 3 3 4 3 3 2 3 3 3 3 3 4 2 3 3 4 4 2 3 3 3 3 3 3 3 3
## [3812] 2 4 3 3 3 4 3 3 2 3 3 3 3 2 4 3 3 4 3 3 3 3 4 4 1 2 2 1 5 2 2 2 6 2 3 2 2
## [3849] 2 3 2 2 2 2 2 2 2 2 3 2 2 2 2 2 1 3 2 4 4 4 3 4 4 4 4 4 6 2 2 1 2 6 1 2 2
## [3886] 2 6 1 1 1 6 2 1 6 4 1 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2
## [3923] 4 2 2 2 2 1 2 2 2 1 1 6 6 2 1 1 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 3 2
## [3960] 2 2 2 1 2 2 2 2 3 2 6 1 2 3 3 2 3 2 3 1 3 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [3997] 2 2 2 2 2 2 2 2 2 3 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 2 2 2
## [4034] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 1 2 2 2 2 2 2 2 2 1
## [4071] 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 2 1 2 1 2 2 2 1 2 1
## [4108] 2 2 2 2 2 2 2 2 2 2 2 1 2 3 1 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 1 3 2 2 2 2 2
## [4145] 3 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2 4 4 1 2 2 2 2 2 3 3 2 2 2 2 2 2 2 2 2
## [4182] 2 2 2 4 2 2 3 2 1 3 3 1 2 2 2 2 2 4 2 1 2 2 1 3 2 2 3 2 2 2 2 2 2 6 2 2 2
## [4219] 2 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 4 4 1 2 2 4
## [4256] 2 2 2 2 2 2 2 4 2 2 4 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [4293] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [4330] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [4367] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [4404] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [4441] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [4478] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [4515] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [4552] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
## [4589] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 6 5 1 1 2
## [4626] 1 1 4 4 2 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 3 1 2 2 2 2 2 3 2 2 2 3 2 2 2 3
## [4663] 2 3 2 2 3 2 1 1 1 6 2 2 2 2 2 2 2 2 2 2 2 9 2 2 2 2 2 2 2 2 2 2 1 2 1 1 1
## [4700] 4 1 1 2 1 1 1 2 1 1 1 1 6 4 6 2 2 2 2 1 2 2 2 1 2 2 3 2 2 2 2 2 2 2 2 2 3
## [4737] 2 2 2 1 3 2 3 3 2 3 3 3 1 1 2 1 1 1 1 2 1 1 3 4 1 2 2 4 3 2 2 2 2 3 3 1 3
## [4774] 2 1 3 4 3 1 1 1 2 1 1 1 2 2 2 3 3 2 4 2 2 1 2 2 2 2 2 2 3 2 2 2 2 2 2## Grafica con el Metodo 3
num_clusters_optimo <- res.nbclust$Best.nc[1]
resultado_3 <- kmeans(datavivienda_ac, centers = num_clusters_optimo)
fviz_cluster(resultado_3, data = datavivienda_ac, stand = FALSE,
ellipse.type = "convex", geom = "point",
palette = "jco", main = "Visualización de Clústeres K-means")
- Implementa el método de la validación interna para determinar el número óptimo de clusters y realiza el clustering k-means con ese número óptimo de clusters. Se especifica la distancia euclidiana como medida de distancia, y se solicita calcular los índices para un rango de 2 a 10 clusters.
- El método de agrupamiento jerárquico completo (complete linkage) se utiliza para calcular las distancias entre los clusters.
- Se extrae el número óptimo de clusters seleccionado según el índice de validación interna.
- La visualización muestra los datos agrupados en clusters con los centroides representados como puntos.
Basándonos en los índices de Hubert y D, así como en la regla de la mayoría de los índices:
- Se propuso que 2 índices sugirieran 2 como el mejor número de grupos.
- 2 índices sugirieron 3 grupos como el mejor número.
- 3 índices sugirieron 4 grupos.
- 1 índice sugirió 6 grupos.
- 10 índices sugirieron 9 grupos como el mejor número.
- 2 índices sugirieron 10 grupos como el mejor número.
En conclusión, según la regla de la mayoría, el mejor número de grupos es 9.
3.2 Análisis de Correspondencia
Objetivo: Examinar la relación entre las variables categóricas (tipo de vivienda, zona y barrio), para identificar patrones de comportamiento de la oferta en mercado inmobiliario.
Utilizada para explorar la relación entre dos o más variables categóricas. Esta técnica se basa en la construcción de una tabla de contingencia que muestra la frecuencia de ocurrencia conjunta de las diferentes categorías de las variables involucradas. Luego, se calculan las inercias de estas tablas y se aplican métodos de reducción de dimensionalidad para visualizar la estructura de las asociaciones entre las categorías.
# Convertir variables tipo caracter a factor
vivienda_aco$tipo <- factor(vivienda_aco$tipo)
vivienda_aco$zona <- factor(vivienda_aco$zona)
vivienda_aco$barrio <- factor(vivienda_aco$barrio)
vivienda_aco$estrato <- factor(vivienda_aco$estrato)Al realizar el Chi-squared test en la sección de análisis exploratorio se determina que los atributos tipo-zona,estrato-tipo y estrato-zona se encuentran relacionados.
# Realiza el análisis de correspondencia
vivienda_aco2 <- MCA(vivienda_aco[, c("tipo", "zona", "estrato")], graph = TRUE)
print(vivienda_aco2)## **Results of the Multiple Correspondence Analysis (MCA)**
## The analysis was performed on 4808 individuals, described by 3 variables
## *The results are available in the following objects:
##
## name description
## 1 "$eig" "eigenvalues"
## 2 "$var" "results for the variables"
## 3 "$var$coord" "coord. of the categories"
## 4 "$var$cos2" "cos2 for the categories"
## 5 "$var$contrib" "contributions of the categories"
## 6 "$var$v.test" "v-test for the categories"
## 7 "$ind" "results for the individuals"
## 8 "$ind$coord" "coord. for the individuals"
## 9 "$ind$cos2" "cos2 for the individuals"
## 10 "$ind$contrib" "contributions of the individuals"
## 11 "$call" "intermediate results"
## 12 "$call$marge.col" "weights of columns"
## 13 "$call$marge.li" "weights of rows"El gráfico nos permite observar las relaciones de los atributos:
- El estrato 6 se encuentra ubicado en la Zona Oeste
- Los estratos 4 y 5 se encuentran en las Zona Sur y Zona Norte.
- El estrato 3 se encuentra aproximado a la Zona Centro y Zona Oriente.
De acuerdo con lo anterior:
- Una persona que quiera comprar vivienda en estrato 6 se aconseja la Zona Oeste.
- Una persona que quiera adquirir vivienda en los estratos mas bajos, se aconseja adqurirla en Zona Oriente y Centro.
# Tabla de contingencia (o matriz de frecuencias)
Eigenvalues <- factoextra::get_eigenvalue(vivienda_aco2)
head(Eigenvalues)## eigenvalue variance.percent cumulative.variance.percent
## Dim.1 0.5416488 20.31183 20.31183
## Dim.2 0.4594459 17.22922 37.54105
## Dim.3 0.3986773 14.95040 52.49145
## Dim.4 0.3333715 12.50143 64.99288
## Dim.5 0.3188668 11.95750 76.95039
## Dim.6 0.2679131 10.04674 86.99713- La primera dimensión (Dim.1) explica el 20.31% de la varianza total en los datos.
- La segunda dimensión (Dim.2) agrega otro 17.23%, sumando un total del 20.31% + 17.23% = 37.54% de varianza explicada.
- El tercer eje (Dim.3) contribuye con un 14.95% adicional de varianza, acumulando así el 52.49% de varianza explicada.
- Las primeras dimensiones explican una cantidad significativa de la variabilidad en los datos, mientras que las dimensiones subsiguientes explican menos variabilidad. Esto sugiere que las primeras dimensiones son importantes para comprender la estructura
fviz_screeplot(vivienda_aco2, addlabels = TRUE)
fviz_contrib(vivienda_aco2, choice = "var", axes = 1, top = 15)
El estrato 3 y la Zona Oriente contribuyen en mayor proporción a la primera Dimensión y las que menos contribuyen sonlos estratos 4,5,6, las Zonas Norte y Sur y, la vivienda de tipo apartamento.
fviz_contrib(vivienda_aco2, choice = "var", axes = 2, top = 15)
El estrato 4,6 y la Zona Oeste contribuyen en mayor proporción a la segunda Dimensión y las que menos contribuyen son los estratos 3,5, las Zonas Norte, Centro y, la vivienda de tipo apartamento y casa.
3.3 Análisis de Componentes Principales
Objetivo: Reducir la dimensionalidad del conjunto de datos y visualizar la estructura de las variables en componentes principales para identificar características clave que influyen en la variación de precios y oferta del mercado.
# Se excluyen los datos faltantes
vivienda_pca <- na.omit(vivienda)# Conversión de texto a númerico atributo zona
vivienda_pca = vivienda_pca %>% mutate(zona = replace(zona,
zona == "Zona Centro", 1))
vivienda_pca = vivienda_pca %>% mutate(zona = replace(zona,
zona == "Zona Norte", 2))
vivienda_pca = vivienda_pca %>% mutate(zona = replace(zona,
zona == "Zona Oeste", 5))
vivienda_pca = vivienda_pca %>% mutate(zona = replace(zona,
zona == "Zona Oriente",
4))
vivienda_pca = vivienda_pca %>% mutate(zona = replace(zona,
zona == "Zona Sur", 3))
vivienda_pca$zona = as.numeric(vivienda_pca$zona)# Conversión de texto a númerico atributo tipo
vivienda_pca <- vivienda_pca %>%
mutate(tipo = ifelse(tipo == "Casa", 1,
ifelse(tipo == "Apartamento", 2, tipo)))
vivienda_pca$tipo = as.numeric(vivienda_pca$tipo)
vivienda_pca$piso <- as.numeric(factor(vivienda_pca$piso, levels = unique(vivienda_pca$piso)))# Selección de variables
vivienda_pca <- select(vivienda_pca, -id, -latitud, -longitud, -barrio)# Estandarizar el conjunto de datos
vivienda_pca <- scale(vivienda_pca)# Aplicación Análisis de componentes principales
pca_resultados <- PCA(vivienda_pca, graph = TRUE)
summary(pca_resultados)##
## Call:
## PCA(X = vivienda_pca, graph = TRUE)
##
##
## Eigenvalues
## Dim.1 Dim.2 Dim.3 Dim.4 Dim.5 Dim.6 Dim.7
## Variance 3.962 1.868 0.835 0.771 0.472 0.369 0.307
## % of var. 44.024 20.759 9.280 8.572 5.247 4.101 3.411
## Cumulative % of var. 44.024 64.783 74.063 82.635 87.882 91.983 95.394
## Dim.8 Dim.9
## Variance 0.244 0.171
## % of var. 2.709 1.897
## Cumulative % of var. 98.103 100.000
##
## Individuals (the 10 first)
## Dist Dim.1 ctr cos2 Dim.2 ctr cos2 Dim.3
## 1 | 2.725 | 1.499 0.012 0.303 | -1.271 0.018 0.217 | -0.396
## 2 | 2.179 | -1.537 0.012 0.497 | -0.503 0.003 0.053 | 0.059
## 3 | 2.016 | -1.248 0.008 0.383 | -0.498 0.003 0.061 | 0.150
## 4 | 2.364 | -1.602 0.013 0.459 | -0.918 0.009 0.151 | 0.204
## 5 | 1.704 | -0.403 0.001 0.056 | -0.576 0.004 0.114 | 0.420
## 6 | 2.894 | 1.189 0.007 0.169 | -2.106 0.049 0.530 | 0.290
## 7 | 2.806 | 1.456 0.011 0.269 | -1.097 0.013 0.153 | 0.062
## 8 | 3.357 | 2.417 0.031 0.518 | -2.080 0.048 0.384 | 0.634
## 9 | 3.616 | 2.663 0.037 0.542 | -1.737 0.034 0.231 | 0.610
## 10 | 2.668 | -0.763 0.003 0.082 | 0.512 0.003 0.037 | -0.231
## ctr cos2
## 1 0.004 0.021 |
## 2 0.000 0.001 |
## 3 0.001 0.006 |
## 4 0.001 0.007 |
## 5 0.004 0.061 |
## 6 0.002 0.010 |
## 7 0.000 0.000 |
## 8 0.010 0.036 |
## 9 0.009 0.028 |
## 10 0.001 0.007 |
##
## Variables
## Dim.1 ctr cos2 Dim.2 ctr cos2 Dim.3 ctr
## zona | 0.167 0.707 0.028 | 0.580 17.983 0.336 | -0.588 41.344
## piso | -0.310 2.422 0.096 | 0.550 16.186 0.302 | 0.647 50.122
## estrato | 0.459 5.323 0.211 | 0.684 25.027 0.468 | -0.064 0.490
## preciom | 0.830 17.380 0.689 | 0.387 8.002 0.150 | 0.046 0.257
## areaconst | 0.871 19.140 0.758 | -0.101 0.550 0.010 | 0.088 0.938
## parqueaderos | 0.777 15.227 0.603 | 0.210 2.351 0.044 | 0.103 1.279
## banios | 0.871 19.164 0.759 | 0.038 0.078 0.001 | 0.119 1.691
## habitaciones | 0.641 10.370 0.411 | -0.457 11.166 0.209 | 0.148 2.607
## tipo | -0.638 10.267 0.407 | 0.590 18.658 0.349 | 0.103 1.272
## cos2
## zona 0.345 |
## piso 0.419 |
## estrato 0.004 |
## preciom 0.002 |
## areaconst 0.008 |
## parqueaderos 0.011 |
## banios 0.014 |
## habitaciones 0.022 |
## tipo 0.011 |El análisis de PCA realizado sobre los datos de vivienda muestra que las primeras dos componentes principales explican aproximadamente el 64.78% de la varianza total, mientras que las cuatro primeras explican alrededor del 82.64%. Esto sugiere que un conjunto reducido de componentes principales puede capturar la mayoría de la variabilidad en los datos.
Al observar los individuos (instancias de vivienda), podemos notar que se distribuyen en el espacio de las componentes principales de manera significativa. Por ejemplo, el primer individuo se encuentra predominantemente en la dirección positiva de la Dimensión 1 y en la dirección negativa de la Dimensión 2, mientras que el quinto individuo se sitúa en una posición diferente en este espacio.
Al examinar las variables originales en relación con las componentes principales, vemos que algunas variables como ‘preciom’, ‘areaconst’, ‘banios’ y ‘habitaciones’ tienen una alta contribución a la Dimensión 1, mientras que otras como ‘piso’, ‘estrato’ y ‘tipo’ tienen una influencia considerable en la Dimensión 2, es decir, las variables originales con cargas altas en las primeras componentes principales son consideradas como aquellas que tienen un impacto significativo en la variabilidad del precio y la oferta en el mercado. En este análisis, las variables como ‘preciom’, ‘areaconst’, ‘banios’ y ‘habitaciones’ muestran una contribución destacada. Esto sugiere que estas características pueden ser cruciales para entender y predecir la variación en los precios y la oferta de viviendas.