Trabajo Final
Bárbara Santana Rodríguez, Fernanda Pérez, Vanessa Moreta, Alberto Sandoval
2023-12-20
library(ggplot2)
library(readxl)
library(readr)
library(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
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## filter, lag## The following objects are masked from 'package:base':
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## intersect, setdiff, setequal, unionlibrary(rpart)
library(ROSE)## Warning: package 'ROSE' was built under R version 4.3.2## Loaded ROSE 0.0-4library(caret)## Warning: package 'caret' was built under R version 4.3.2## Loading required package: latticelibrary(mltools)## Warning: package 'mltools' was built under R version 4.3.2library(e1071)## Warning: package 'e1071' was built under R version 4.3.2##
## Attaching package: 'e1071'## The following object is masked from 'package:mltools':
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## skewnesssetwd("~/01_Master-BigData/A03_Tec-AnalisisDatos/00_TrabajoFinal")1. Análisis exploratorio
Carga de datos
obesidad = read.csv("ObesityDataSet_raw_and_data_sinthetic.csv")
#obesidad <- read.csv('ObesityDataSet_raw_and_data_sinthetic.csv')
head(obesidad)## Gender Age Height Weight family_history_with_overweight FAVC FCVC NCP
## 1 Female 21 1.62 64.0 yes no 2 3
## 2 Female 21 1.52 56.0 yes no 3 3
## 3 Male 23 1.80 77.0 yes no 2 3
## 4 Male 27 1.80 87.0 no no 3 3
## 5 Male 22 1.78 89.8 no no 2 1
## 6 Male 29 1.62 53.0 no yes 2 3
## CAEC SMOKE CH2O SCC FAF TUE CALC MTRANS
## 1 Sometimes no 2 no 0 1 no Public_Transportation
## 2 Sometimes yes 3 yes 3 0 Sometimes Public_Transportation
## 3 Sometimes no 2 no 2 1 Frequently Public_Transportation
## 4 Sometimes no 2 no 2 0 Frequently Walking
## 5 Sometimes no 2 no 0 0 Sometimes Public_Transportation
## 6 Sometimes no 2 no 0 0 Sometimes Automobile
## NObeyesdad
## 1 Normal_Weight
## 2 Normal_Weight
## 3 Normal_Weight
## 4 Overweight_Level_I
## 5 Overweight_Level_II
## 6 Normal_WeightDetalle de la base de datos
Esta base de datos contiene datos para la estimación de los niveles de obesidad en personas de los países de México, Perú y Colombia, con edades entre 14 y 61 años y diversos hábitos alimenticios y condición física.
Las variables incluidas de origen son:
Atributos relacionados con los hábitos alimenticios
- FAVC: Consumo frecuente de alimentos altamente calóricos
- FCVC: Frecuencia de consumo de verduras
- NCP: Número de comidas principales
- CAEC: Consumo de alimentos entre comidas
- CH20: Consumo diario de agua
- CALC: Consumo de alcohol
Atributos relacionados con la condición física
- SCC: Monitoreo del consumo de calorías
- FAF: Frecuencia de actividad física
- TUE: Tiempo de uso de dispositivos tecnológicos
- MTRANS: Transporte utilizado
Otras variables
- Género
- Edad
- Altura
- Peso
Variable de clase
- NObeyesdad: Insuficiencia de peso, Peso normal, Sobrepeso Nivel I, Sobrepeso Nivel II, Obesidad Tipo I, Obesidad Tipo II y Obesidad Tipo III
Por nuestra parte hemos usado la ecuación del Índice de Masa Corporal para incluir la variable IMC en la columna obesidad_imc, ya que consideramos que nos ayudará a la construcción del modelo requerido.
summary(obesidad)## Gender Age Height Weight
## Length:2111 Min. :14.00 Min. :1.450 Min. : 39.00
## Class :character 1st Qu.:19.95 1st Qu.:1.630 1st Qu.: 65.47
## Mode :character Median :22.78 Median :1.700 Median : 83.00
## Mean :24.31 Mean :1.702 Mean : 86.59
## 3rd Qu.:26.00 3rd Qu.:1.768 3rd Qu.:107.43
## Max. :61.00 Max. :1.980 Max. :173.00
## family_history_with_overweight FAVC FCVC
## Length:2111 Length:2111 Min. :1.000
## Class :character Class :character 1st Qu.:2.000
## Mode :character Mode :character Median :2.386
## Mean :2.419
## 3rd Qu.:3.000
## Max. :3.000
## NCP CAEC SMOKE CH2O
## Min. :1.000 Length:2111 Length:2111 Min. :1.000
## 1st Qu.:2.659 Class :character Class :character 1st Qu.:1.585
## Median :3.000 Mode :character Mode :character Median :2.000
## Mean :2.686 Mean :2.008
## 3rd Qu.:3.000 3rd Qu.:2.477
## Max. :4.000 Max. :3.000
## SCC FAF TUE CALC
## Length:2111 Min. :0.0000 Min. :0.0000 Length:2111
## Class :character 1st Qu.:0.1245 1st Qu.:0.0000 Class :character
## Mode :character Median :1.0000 Median :0.6253 Mode :character
## Mean :1.0103 Mean :0.6579
## 3rd Qu.:1.6667 3rd Qu.:1.0000
## Max. :3.0000 Max. :2.0000
## MTRANS NObeyesdad
## Length:2111 Length:2111
## Class :character Class :character
## Mode :character Mode :character
##
##
## Verificación de datos faltantes
colSums(is.na(obesidad))## Gender Age
## 0 0
## Height Weight
## 0 0
## family_history_with_overweight FAVC
## 0 0
## FCVC NCP
## 0 0
## CAEC SMOKE
## 0 0
## CH2O SCC
## 0 0
## FAF TUE
## 0 0
## CALC MTRANS
## 0 0
## NObeyesdad
## 0colSums(obesidad=="")## Gender Age
## 0 0
## Height Weight
## 0 0
## family_history_with_overweight FAVC
## 0 0
## FCVC NCP
## 0 0
## CAEC SMOKE
## 0 0
## CH2O SCC
## 0 0
## FAF TUE
## 0 0
## CALC MTRANS
## 0 0
## NObeyesdad
## 0La base de datos no presenta faltantes.
Observación de variables de interés
Observamos que tan solo el 2,08% de la poblacion que conforma la muestra es fumadora, por lo que, más adelante en el análisis, se deberá proceder a técnicas de oversampling que permitan ampliar el número de registros de las personas que fuman a través de métodos estadisticos.
Sucederá lo mismo con la población que cuenta las calorías, ya que tan solo un 4,54% de la muestra declara contarlas.
# Calcular las frecuencias de 'si' y 'no'
frecuencias_fuma <- table(obesidad$SMOKE)
print(frecuencias_fuma)##
## no yes
## 2067 44# Calcular los porcentajes
porcentajes_fuma <- prop.table(frecuencias_fuma) * 100
print(porcentajes_fuma)##
## no yes
## 97.91568 2.08432# Crear un gráfico de barras
barplot(porcentajes_fuma, main = "% de personas que fuman",
names.arg = c("No", "Sí"),
ylab = "Porcentaje",
col = c("red", "green"))
# Calcular las frecuencias de 'si' y 'no'
frecuencias_calorias <- table(obesidad$SCC)
print(frecuencias_calorias)##
## no yes
## 2015 96# Calcular los porcentajes
porcentajes_calorias <- prop.table(frecuencias_calorias) * 100
print(porcentajes_calorias)##
## no yes
## 95.452392 4.547608# Crear un gráfico de barras
barplot(porcentajes_calorias, main = "% de personas que cuentan calorias",
names.arg = c("No", "Sí"),
ylab = "Porcentaje",
col = c("red", "green"))
Nueva variable: IMC
Dado que contamos con datos de altura y peso, crearemos una nueva variable para conocer el IMC de cada una de las personas que componen la muestra por si puede ser de interés en algunos de los puntos.
# Crear una nueva columna 'IMC'
obesidad$IMC <- obesidad$Weight / ((obesidad$Height)^2)Transformaciones, escalado y normalización
Dado que se trata de una base de datos relacionada con la obesidad y tenemos a mano el peso y la altura, crearemos la variable IMC (Índice de Masa Corporal), para apoyar nuestro modelo.
Variables numéricas
Observamos que las variables como ‘Age’, ‘Height’, ‘Weight’, ‘NCP’, ‘TUE’, ‘CH2O’ y ‘IMC’ tienen escalas numéricas diferentes. Esta diferencia de escalas puede influir en el modelo de aprendizaje automático, dando más peso a las variables con valores más grandes.
Variables categóricas
La base de datos también contiene variables categóricas como ‘Gender’, ‘family_history_with_overweight’, ‘FAVC’, ‘FCVC’, ‘CAEC’, ‘SMOKE’, ‘SCC’, ‘FAF’, ‘MTRANS’, y ‘NObeyesdad’. Estas variables no tienen un orden natural, por lo que el modelo de aprendizaje automático no las interpretará correctamente sin una transformación adecuada.
Al escalar y normalizar las variables pretendemos:
- Mejorar la precisión del modelo: Al tener todas las variables en una escala similar, el modelo puede ajustar mejor los pesos de cada variable y obtener una predicción más precisa.
- Evitar el sesgo: Las variables con escalas más grandes no tendrán un peso desproporcionado en el modelo.
- Facilitar la comparación de variables: Permite comparar el impacto de diferentes variables en el modelo, independientemente de su escala original.
2. Modelos predictivos
Antes de comenzar con los modelos predictivos es necesario preparar nuestra base de datos.
Las variables que son categorias ordinales se transforman a dicotómicas (0/1) para poder tratarlas en nuestro análisis. Sin embargo, podría ser interesante pasar a numericas las variables categóricas nominales, como son las relacionadas con la frecuencia o el grado de obesidad, ya que claramente se puede observar un orden entre cada categoria y va de menos a más.
Factores
obesidad$Gender =factor(obesidad$Gender)
obesidad$family_history_with_overweight=factor(obesidad$family_history_with_overweight)
obesidad$FAVC=factor(obesidad$FAVC)
obesidad$SMOKE=factor(obesidad$SMOKE)
obesidad$SCC=factor(obesidad$SCC)
obesidad$MTRANS=factor(obesidad$MTRANS)Escalado
library("scales")##
## Attaching package: 'scales'## The following object is masked from 'package:readr':
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## col_factor"Escalado Age"## [1] "Escalado Age"obesidad$Age <- rescale(obesidad$Age)
"Escalado Height"## [1] "Escalado Height"obesidad$Height <- rescale(obesidad$Height)
"Escalado Weight"## [1] "Escalado Weight"obesidad$Weight <- rescale(obesidad$Weight)
"Escalado NCP"## [1] "Escalado NCP"obesidad$NCP <- rescale(obesidad$NCP)
"Escalado TUE"## [1] "Escalado TUE"obesidad$TUE <- rescale(obesidad$TUE)
"Escalado CH2O"## [1] "Escalado CH2O"obesidad$CH2O <- rescale(obesidad$CH2O)
"Escalado obesidad_imc"## [1] "Escalado obesidad_imc"obesidad$IMC <- (rescale(obesidad$obesidad_imc))Una vez tenemos transformadas nuestras variables procedemos a realizar one hot encoding para realizar esa transformación a dictomicas.
library(mltools)
library(data.table)##
## Attaching package: 'data.table'## The following objects are masked from 'package:dplyr':
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## between, first, last#Creamos una nueva base de datos con las variables recodificadas en dictotómicas (0/1) para conservar la base original.
obesidad_cod <- one_hot(as.data.table(obesidad))Lo que ahora debemos hacer es recodificar las categoricas que no pasamos a factor a valor numerico, como comentamos anteriormente.
# Codificamos
obesidad_cod$CAEC <- ifelse(obesidad_cod$CAEC == "no", 1,
ifelse(obesidad_cod$CAEC == "Sometimes", 2,
ifelse(obesidad_cod$CAEC == "Frequently", 3,
ifelse(obesidad_cod$CAEC == "Always", 4, NA))))#Codificamos
obesidad_cod$CALC <- ifelse(obesidad_cod$CALC == "no", 1,
ifelse(obesidad_cod$CALC == "Sometimes", 2,
ifelse(obesidad_cod$CALC == "Frequently", 3,
ifelse(obesidad_cod$CALC == "Always", 4, NA))))str(obesidad_cod)## Classes 'data.table' and 'data.frame': 2111 obs. of 26 variables:
## $ Gender_Female : int 1 1 0 0 0 0 1 0 0 0 ...
## $ Gender_Male : int 0 0 1 1 1 1 0 1 1 1 ...
## $ Age : num 0.149 0.149 0.191 0.277 0.17 ...
## $ Height : num 0.321 0.132 0.66 0.66 0.623 ...
## $ Weight : num 0.187 0.127 0.284 0.358 0.379 ...
## $ family_history_with_overweight_no : int 0 0 0 1 1 1 0 1 0 0 ...
## $ family_history_with_overweight_yes: int 1 1 1 0 0 0 1 0 1 1 ...
## $ FAVC_no : int 1 1 1 1 1 0 0 1 0 0 ...
## $ FAVC_yes : int 0 0 0 0 0 1 1 0 1 1 ...
## $ FCVC : num 2 3 2 3 2 2 3 2 3 2 ...
## $ NCP : num 0.667 0.667 0.667 0.667 0 ...
## $ CAEC : num 2 2 2 2 2 2 2 2 2 2 ...
## $ SMOKE_no : int 1 0 1 1 1 1 1 1 1 1 ...
## $ SMOKE_yes : int 0 1 0 0 0 0 0 0 0 0 ...
## $ CH2O : num 0.5 1 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 ...
## $ SCC_no : int 1 0 1 1 1 1 1 1 1 1 ...
## $ SCC_yes : int 0 1 0 0 0 0 0 0 0 0 ...
## $ FAF : num 0 3 2 2 0 0 1 3 1 1 ...
## $ TUE : num 0.5 0 0.5 0 0 0 0 0 0.5 0.5 ...
## $ CALC : num 1 2 3 3 2 2 2 2 3 1 ...
## $ MTRANS_Automobile : int 0 0 0 0 0 1 0 0 0 0 ...
## $ MTRANS_Bike : int 0 0 0 0 0 0 0 0 0 0 ...
## $ MTRANS_Motorbike : int 0 0 0 0 0 0 1 0 0 0 ...
## $ MTRANS_Public_Transportation : int 1 1 1 0 1 0 0 1 1 1 ...
## $ MTRANS_Walking : int 0 0 0 1 0 0 0 0 0 0 ...
## $ NObeyesdad : chr "Normal_Weight" "Normal_Weight" "Normal_Weight" "Overweight_Level_I" ...
## - attr(*, ".internal.selfref")=<externalptr>unique(obesidad_cod$NObeyesdad)## [1] "Normal_Weight" "Overweight_Level_I" "Overweight_Level_II"
## [4] "Obesity_Type_I" "Insufficient_Weight" "Obesity_Type_II"
## [7] "Obesity_Type_III"#Codificamos
obesidad_cod$NObeyesdad <- ifelse(obesidad_cod$NObeyesdad == "Insufficient_Weight", 1,
ifelse(obesidad_cod$NObeyesdad == "Normal_Weight", 2,
ifelse(obesidad_cod$NObeyesdad == "Overweight_Level_I", 3,
ifelse(obesidad_cod$NObeyesdad == "Overweight_Level_II", 4,
ifelse(obesidad_cod$NObeyesdad == "Obesity_Type_I", 5,
ifelse(obesidad_cod$NObeyesdad == "Obesity_Type_II", 6,
ifelse(obesidad_cod$NObeyesdad == "Obesity_Type_III", 7,NA)))))))2.1 Modelo que detecte si un usuario es fumador o no.
Oversampling en función de los usuarios que sí fuman
# Aplicar la transformación a factores a todas las variables en obesidad_cod
obesidad_cod <- data.frame(lapply(obesidad_cod, as.factor))
str(obesidad_cod)## 'data.frame': 2111 obs. of 26 variables:
## $ Gender_Female : Factor w/ 2 levels "0","1": 2 2 1 1 1 1 2 1 1 1 ...
## $ Gender_Male : Factor w/ 2 levels "0","1": 1 1 2 2 2 2 1 2 2 2 ...
## $ Age : Factor w/ 1402 levels "0","0.0212765957446809",..: 405 405 702 1022 579 1062 702 579 777 579 ...
## $ Height : Factor w/ 1574 levels "0","0.0119735849056603",..: 296 29 1307 1307 1203 296 10 408 1203 839 ...
## $ Weight : Factor w/ 1525 levels "0","0.00075973880597014",..: 246 174 383 644 693 142 160 142 246 288 ...
## $ family_history_with_overweight_no : Factor w/ 2 levels "0","1": 1 1 1 2 2 2 1 2 1 1 ...
## $ family_history_with_overweight_yes: Factor w/ 2 levels "0","1": 2 2 2 1 1 1 2 1 2 2 ...
## $ FAVC_no : Factor w/ 2 levels "0","1": 2 2 2 2 2 1 1 2 1 1 ...
## $ FAVC_yes : Factor w/ 2 levels "0","1": 1 1 1 1 1 2 2 1 2 2 ...
## $ FCVC : Factor w/ 810 levels "1","1.003566",..: 171 810 171 810 171 171 810 171 810 171 ...
## $ NCP : Factor w/ 635 levels "0","9.43333333333444e-05",..: 478 478 478 478 1 478 478 478 478 478 ...
## $ CAEC : Factor w/ 4 levels "1","2","3","4": 2 2 2 2 2 2 2 2 2 2 ...
## $ SMOKE_no : Factor w/ 2 levels "0","1": 2 1 2 2 2 2 2 2 2 2 ...
## $ SMOKE_yes : Factor w/ 2 levels "0","1": 1 2 1 1 1 1 1 1 1 1 ...
## $ CH2O : Factor w/ 1268 levels "0","0.000231500000000051",..: 550 1268 550 550 550 550 550 550 550 550 ...
## $ SCC_no : Factor w/ 2 levels "0","1": 2 1 2 2 2 2 2 2 2 2 ...
## $ SCC_yes : Factor w/ 2 levels "0","1": 1 2 1 1 1 1 1 1 1 1 ...
## $ FAF : Factor w/ 1190 levels "0","9.6e-05",..: 1 1190 1072 1072 1 1 590 1190 590 590 ...
## $ TUE : Factor w/ 1129 levels "0","3.65e-05",..: 841 1 841 1 1 1 1 1 841 841 ...
## $ CALC : Factor w/ 4 levels "1","2","3","4": 1 2 3 3 2 2 2 2 3 1 ...
## $ MTRANS_Automobile : Factor w/ 2 levels "0","1": 1 1 1 1 1 2 1 1 1 1 ...
## $ MTRANS_Bike : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 1 1 1 ...
## $ MTRANS_Motorbike : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 2 1 1 1 ...
## $ MTRANS_Public_Transportation : Factor w/ 2 levels "0","1": 2 2 2 1 2 1 1 2 2 2 ...
## $ MTRANS_Walking : Factor w/ 2 levels "0","1": 1 1 1 2 1 1 1 1 1 1 ...
## $ NObeyesdad : Factor w/ 7 levels "1","2","3","4",..: 2 2 2 3 4 2 2 2 2 2 ...#install.packages("ROSE")
# Carga el paquete
library(ROSE)
library(caret)
# Aplica SMOTE para el sobremuestreo
obesidad_over <- ROSE(SMOKE_yes ~ ., data = obesidad_cod, seed = 100, p = 0.3)$dataSplit de base de datos: train y test
# Fijar semilla para reproducibilidad
set.seed(100)
# Crear un índice para la división de datos
index <- createDataPartition(obesidad_over$SMOKE_yes, p = 0.7, list = FALSE, times = 1)
# Crear conjuntos de entrenamiento y prueba
obesidad_over_train <- obesidad_over[index, ]
obesidad_over_test <- obesidad_over[-index, ]# Fijar semilla para reproducibilidad
set.seed(100)
# Crear un índice para la división de datos
index <- createDataPartition(obesidad_cod$SMOKE_yes, p = 0.7, list = FALSE, times = 1)
# Crear conjuntos de entrenamiento y prueba
obesidad_train <- obesidad_over[index, ]
obesidad_test <- obesidad_over[-index, ]Modelo de regresión logistica con el dataset de entrenamiento
# Convertir variables a numéricas o enteras según la estructura actual
obesidad_over_train$Age <- as.numeric(obesidad_over_train$Age)
obesidad_over_train$Height <- as.numeric(obesidad_over_train$Height)
obesidad_over_train$Weight <- as.numeric(obesidad_over_train$Weight)
obesidad_over_train$FCVC <- as.numeric(obesidad_over_train$FCVC)
obesidad_over_train$NCP <- as.numeric(obesidad_over_train$NCP)
obesidad_over_train$CH2O <- as.numeric(obesidad_over_train$CH2O)
obesidad_over_train$FAF <- as.numeric(obesidad_over_train$FAF)
obesidad_over_train$TUE <- as.numeric(obesidad_over_train$TUE)
obesidad_over_train$CALC <- as.numeric(obesidad_over_train$CALC)
#y para el test
obesidad_over_test$Age <- as.numeric(obesidad_over_test$Age)
obesidad_over_test$Height <- as.numeric(obesidad_over_test$Height)
obesidad_over_test$Weight <- as.numeric(obesidad_over_test$Weight)
obesidad_over_test$FCVC <- as.numeric(obesidad_over_test$FCVC)
obesidad_over_test$NCP <- as.numeric(obesidad_over_test$NCP)
obesidad_over_test$CH2O <- as.numeric(obesidad_over_test$CH2O)
obesidad_over_test$FAF <- as.numeric(obesidad_over_test$FAF)
obesidad_over_test$TUE <- as.numeric(obesidad_over_test$TUE)
obesidad_over_test$CALC <- as.numeric(obesidad_over_test$CALC)
# Verifica la estructura actualizada
str(obesidad_over_train)## 'data.frame': 1479 obs. of 26 variables:
## $ Gender_Female : Factor w/ 2 levels "0","1": 2 2 1 1 1 1 1 2 2 2 ...
## $ Gender_Male : Factor w/ 2 levels "0","1": 1 1 2 2 2 2 2 1 1 1 ...
## $ Age : num 345 674 1394 685 76 ...
## $ Height : num 44 315 956 1386 705 ...
## $ Weight : num 8 512 520 735 91 ...
## $ family_history_with_overweight_no : Factor w/ 2 levels "0","1": 2 1 1 1 2 1 1 1 2 1 ...
## $ family_history_with_overweight_yes: Factor w/ 2 levels "0","1": 1 2 2 2 1 2 2 2 1 2 ...
## $ FAVC_no : Factor w/ 2 levels "0","1": 1 1 1 1 1 2 1 1 1 1 ...
## $ FAVC_yes : Factor w/ 2 levels "0","1": 2 2 2 2 2 1 2 2 2 2 ...
## $ FCVC : num 584 109 171 133 1 810 171 810 2 171 ...
## $ NCP : num 402 1 478 70 478 1 478 478 517 302 ...
## $ CAEC : Factor w/ 4 levels "1","2","3","4": 2 2 2 2 3 3 2 2 3 2 ...
## $ SMOKE_no : Factor w/ 2 levels "0","1": 2 2 2 2 2 2 2 2 2 2 ...
## $ SMOKE_yes : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 1 1 1 ...
## $ CH2O : num 247 550 409 550 1 ...
## $ SCC_no : Factor w/ 2 levels "0","1": 2 2 2 2 2 2 2 2 2 2 ...
## $ SCC_yes : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 1 1 1 ...
## $ FAF : num 127 1 536 1 1072 ...
## $ TUE : num 257 241 1 1008 841 ...
## $ CALC : num 2 1 1 2 2 3 1 2 2 2 ...
## $ MTRANS_Automobile : Factor w/ 2 levels "0","1": 1 1 2 1 1 1 1 1 1 2 ...
## $ MTRANS_Bike : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 1 1 1 ...
## $ MTRANS_Motorbike : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 1 1 1 ...
## $ MTRANS_Public_Transportation : Factor w/ 2 levels "0","1": 2 2 1 2 2 2 2 2 2 1 ...
## $ MTRANS_Walking : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 1 1 1 ...
## $ NObeyesdad : Factor w/ 7 levels "1","2","3","4",..: 1 5 4 4 1 2 5 7 1 5 ...# Ahora, ajustamos tel modelo con la nueva base de datos balanceada (obesidad_over)
modelo_rl_over <- glm(SMOKE_yes ~ FAVC_yes + FCVC + NCP + CAEC + CH2O + SCC_yes + FAVC_yes + TUE + CALC + MTRANS_Public_Transportation + MTRANS_Motorbike + MTRANS_Bike + MTRANS_Walking + family_history_with_overweight_yes + Age + NObeyesdad + Gender_Male + Gender_Female, family = "binomial"(link='logit'), data = obesidad_over_train)
# Muestra un resumen del modelo
summary(modelo_rl_over)##
## Call:
## glm(formula = SMOKE_yes ~ FAVC_yes + FCVC + NCP + CAEC + CH2O +
## SCC_yes + FAVC_yes + TUE + CALC + MTRANS_Public_Transportation +
## MTRANS_Motorbike + MTRANS_Bike + MTRANS_Walking + family_history_with_overweight_yes +
## Age + NObeyesdad + Gender_Male + Gender_Female, family = binomial(link = "logit"),
## data = obesidad_over_train)
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -6.954e+00 9.845e-01 -7.064 1.62e-12 ***
## FAVC_yes1 -1.304e+00 2.206e-01 -5.909 3.45e-09 ***
## FCVC 8.215e-04 3.014e-04 2.725 0.006421 **
## NCP -4.114e-05 4.554e-04 -0.090 0.928010
## CAEC2 -2.636e-01 7.887e-01 -0.334 0.738228
## CAEC3 1.124e+00 8.128e-01 1.383 0.166774
## CAEC4 1.333e+00 8.538e-01 1.561 0.118582
## CH2O -8.126e-04 2.013e-04 -4.038 5.40e-05 ***
## SCC_yes1 6.631e-01 3.372e-01 1.966 0.049249 *
## TUE 1.039e-03 1.910e-04 5.438 5.39e-08 ***
## CALC 1.635e+00 1.541e-01 10.615 < 2e-16 ***
## MTRANS_Public_Transportation1 4.943e-01 2.155e-01 2.294 0.021811 *
## MTRANS_Motorbike1 3.776e+00 7.731e-01 4.884 1.04e-06 ***
## MTRANS_Bike1 -8.023e+00 5.354e+02 -0.015 0.988044
## MTRANS_Walking1 1.185e+00 3.979e-01 2.980 0.002887 **
## family_history_with_overweight_yes1 1.643e-01 2.594e-01 0.633 0.526631
## Age 2.550e-03 2.882e-04 8.849 < 2e-16 ***
## NObeyesdad2 2.511e+00 4.006e-01 6.268 3.66e-10 ***
## NObeyesdad3 3.656e-01 4.715e-01 0.775 0.438131
## NObeyesdad4 1.260e+00 4.633e-01 2.720 0.006522 **
## NObeyesdad5 1.575e+00 4.662e-01 3.378 0.000729 ***
## NObeyesdad6 2.422e+00 4.971e-01 4.871 1.11e-06 ***
## NObeyesdad7 -1.204e+00 5.955e-01 -2.022 0.043212 *
## Gender_Male1 -6.989e-01 2.084e-01 -3.353 0.000799 ***
## Gender_Female1 NA NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1836.9 on 1478 degrees of freedom
## Residual deviance: 1196.0 on 1455 degrees of freedom
## AIC: 1244
##
## Number of Fisher Scoring iterations: 12Hemos bajado el umbral de la predicción a 0,3 ya que el nivel de especificidad era muy bajo, y lo que nos interesa es elevar este parámetro para asegurarnos una mayor adecuación del modelo a la hora de predecir si una persona es fumadora. Aunque esto hace que podamos estar detectando a personas como fumadoras cuando en la realidad no lo son. Sin embargo, consideramos más importante ser estrictos en intentar no perder a ninguna persona fumadora ya que este criterio podría ser relevante, por ejemplo, en sanidad, para campañas de concienciación.
De esta manera, obtenemos un accuracy del 84,3%, es decir, casi un 85% de predicciones correctas.
Vamos a conocer un poco más en detalle que métricas devuelve nuestro modelo:
La sensibilidad es la proporción de verdaderos positivos respecto al total de casos positivos reales. En este caso, el modelo identifica correctamente al 91,5% de las personas no fumadoras.
La especificidad es la proporción de verdaderos negativos respecto al total de casos negativos reales. En este caso, el modelo identifica correctamente al 68,5% de las personas no fumadoras.
Pos pred value representa la proporción de verdaderos positivos respecto al total de predicciones positivas. En este caso, el 86,4% de las personas predichas como fumadoras son realmente fumadoras.
Neg pred value representa la proporción de verdaderos negativos respecto al total de predicciones negativas. En este caso, el 78,4% de las personas predichas como no fumadoras son realmente no fumadoras.
Y finalmente, el balanced Accuracy es la media aritmética de la sensibilidad y la especificidad. Representa un resumen general del rendimiento del modelo, lo que nos da un 79,9%.
pred.train <- predict(modelo_rl_over,obesidad_over_train)## Warning in predict.lm(object, newdata, se.fit, scale = 1, type = if (type == :
## prediction from rank-deficient fit; attr(*, "non-estim") has doubtful casespred.train <- ifelse(pred.train > 0.1,1,0)
# Convertir la variable dependiente a factor con los mismos niveles que la predicción
obesidad_over_train$SMOKE_yes <- factor(obesidad_over_train$SMOKE_yes, levels = levels(factor(pred.train)))
# Matriz de confusión
conf_matrix <- confusionMatrix(factor(pred.train), obesidad_over_train$SMOKE_yes)
print(conf_matrix)## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 930 146
## 1 87 316
##
## Accuracy : 0.8425
## 95% CI : (0.8229, 0.8607)
## No Information Rate : 0.6876
## P-Value [Acc > NIR] : < 2.2e-16
##
## Kappa : 0.62
##
## Mcnemar's Test P-Value : 0.0001449
##
## Sensitivity : 0.9145
## Specificity : 0.6840
## Pos Pred Value : 0.8643
## Neg Pred Value : 0.7841
## Prevalence : 0.6876
## Detection Rate : 0.6288
## Detection Prevalence : 0.7275
## Balanced Accuracy : 0.7992
##
## 'Positive' Class : 0
## Y ahora vamos a ponerlo a prueba con el dataset de test (over), para comprobar que los resultados se asemejan a los del train.
Observamos que el nivel de precisión es algo menor, pero que sigue siendo muy elevado (81,5% concretamente). Con un balanced accuracy del 75,5% en el test frente al 79,9% del train. Por lo que seguimos considerando el modelo como óptimo.
# Predicción en la base de datos de prueba
pred.test <- predict(modelo_rl_over, obesidad_over_test)## Warning in predict.lm(object, newdata, se.fit, scale = 1, type = if (type == :
## prediction from rank-deficient fit; attr(*, "non-estim") has doubtful casespred.test <- ifelse(pred.test > 0.1, 1, 0)
# Convertir la variable dependiente a factor con los mismos niveles que la predicción
obesidad_over_test$SMOKE_yes <- factor(obesidad_over_test$SMOKE_yes, levels = levels(factor(pred.test)))
# Matriz de confusión en la base de datos de prueba
conf_matrix_test <- confusionMatrix(factor(pred.test), obesidad_over_test$SMOKE_yes)
print(conf_matrix_test)## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 397 79
## 1 38 118
##
## Accuracy : 0.8149
## 95% CI : (0.7824, 0.8444)
## No Information Rate : 0.6883
## P-Value [Acc > NIR] : 4.21e-13
##
## Kappa : 0.5425
##
## Mcnemar's Test P-Value : 0.0002173
##
## Sensitivity : 0.9126
## Specificity : 0.5990
## Pos Pred Value : 0.8340
## Neg Pred Value : 0.7564
## Prevalence : 0.6883
## Detection Rate : 0.6282
## Detection Prevalence : 0.7532
## Balanced Accuracy : 0.7558
##
## 'Positive' Class : 0
## Finalmente, podemos ver la matriz de confusión pintada para el test.
# Crear la matriz de confusión
conf_matrix_df <- as.data.frame(as.table(conf_matrix_test$table))
colnames(conf_matrix_df) <- c("Predicción", "Valor Real", "Conteo")
conf_matrix_df$Predicción <- factor(conf_matrix_df$Predicción, levels = c("0", "1"))
conf_matrix_df$`Valor Real` <- factor(conf_matrix_df$`Valor Real`, levels = c("0", "1"))
# Visualizar la matriz de confusión con ggplot2
ggplot(conf_matrix_df, aes(x = Predicción, y = `Valor Real`, fill = Conteo)) +
geom_tile(color = "white") +
scale_fill_gradient(low = "white", high = "steelblue") +
geom_text(aes(label = Conteo), vjust = 1) +
theme_minimal() +
labs(title = "Matriz de Confusión",
x = "Predicción",
y = "Valor Real")
2.2 Modelo que detecte si un usuario controla o no las calorías.
# Aquí también usamos el paquete ROSE cargada con anticipación, por lo que ya se debe de encontrar instalado y llamado con la función library.
# Aplica SMOTE para el sobremuestreo
obesidad_over <- ROSE(SCC_yes ~ ., data = obesidad_cod, seed = 100, p = 0.5)$data# Fijar semilla para reproducibilidad
set.seed(100)
# Crear un índice para la división de datos
index <- createDataPartition(obesidad_over$SMOKE_yes, p = 0.7, list = FALSE, times = 1)
# Crear conjuntos de entrenamiento y prueba
obesidad_over_train <- obesidad_over[index, ]
obesidad_over_test <- obesidad_over[-index, ]# Fijar semilla para reproducibilidad
set.seed(100)
# Crear un índice para la división de datos
index <- createDataPartition(obesidad_cod$SMOKE_yes, p = 0.7, list = FALSE, times = 1)
# Crear conjuntos de entrenamiento y prueba
obesidad_train <- obesidad_over[index, ]
obesidad_test <- obesidad_over[-index, ]Y ya realizamos el modelo de regresión logistica con el dataset de entrenamiento
# Convertir variables a numéricas o enteras según la estructura actual
obesidad_over_train$Age <- as.numeric(obesidad_over_train$Age)
obesidad_over_train$Height <- as.numeric(obesidad_over_train$Height)
obesidad_over_train$Weight <- as.numeric(obesidad_over_train$Weight)
obesidad_over_train$FCVC <- as.numeric(obesidad_over_train$FCVC)
obesidad_over_train$NCP <- as.numeric(obesidad_over_train$NCP)
obesidad_over_train$CH2O <- as.numeric(obesidad_over_train$CH2O)
obesidad_over_train$FAF <- as.numeric(obesidad_over_train$FAF)
obesidad_over_train$TUE <- as.numeric(obesidad_over_train$TUE)
obesidad_over_train$CALC <- as.numeric(obesidad_over_train$CALC)
#y para el test
obesidad_over_test$Age <- as.numeric(obesidad_over_test$Age)
obesidad_over_test$Height <- as.numeric(obesidad_over_test$Height)
obesidad_over_test$Weight <- as.numeric(obesidad_over_test$Weight)
obesidad_over_test$FCVC <- as.numeric(obesidad_over_test$FCVC)
obesidad_over_test$NCP <- as.numeric(obesidad_over_test$NCP)
obesidad_over_test$CH2O <- as.numeric(obesidad_over_test$CH2O)
obesidad_over_test$FAF <- as.numeric(obesidad_over_test$FAF)
obesidad_over_test$TUE <- as.numeric(obesidad_over_test$TUE)
obesidad_over_test$CALC <- as.numeric(obesidad_over_test$CALC)
# Verifica la estructura actualizada
str(obesidad_over_train)## 'data.frame': 1478 obs. of 26 variables:
## $ Gender_Female : Factor w/ 2 levels "0","1": 1 2 2 2 1 1 1 2 2 2 ...
## $ Gender_Male : Factor w/ 2 levels "0","1": 2 1 1 1 2 2 2 1 1 1 ...
## $ Age : num 910 304 662 486 315 ...
## $ Height : num 1363 480 558 588 467 ...
## $ Weight : num 1007 64 615 1342 183 ...
## $ family_history_with_overweight_no : Factor w/ 2 levels "0","1": 1 2 1 1 2 1 1 1 1 2 ...
## $ family_history_with_overweight_yes: Factor w/ 2 levels "0","1": 2 1 2 2 1 2 2 2 2 1 ...
## $ FAVC_no : Factor w/ 2 levels "0","1": 1 2 1 1 1 1 1 1 2 1 ...
## $ FAVC_yes : Factor w/ 2 levels "0","1": 2 1 2 2 2 2 2 2 1 2 ...
## $ FCVC : num 737 490 243 810 171 171 171 810 810 240 ...
## $ NCP : num 478 478 156 478 478 192 1 478 478 1 ...
## $ CAEC : Factor w/ 4 levels "1","2","3","4": 2 2 2 2 2 2 3 2 2 2 ...
## $ SMOKE_no : Factor w/ 2 levels "0","1": 2 2 2 2 2 2 2 2 2 2 ...
## $ SMOKE_yes : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 1 1 1 ...
## $ CH2O : num 1198 514 875 263 550 ...
## $ SCC_no : Factor w/ 2 levels "0","1": 2 2 2 2 2 2 2 2 2 2 ...
## $ SCC_yes : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 1 1 1 ...
## $ FAF : num 154 1072 45 409 1190 ...
## $ TUE : num 120 841 841 472 841 ...
## $ CALC : num 2 2 1 2 2 2 1 1 2 2 ...
## $ MTRANS_Automobile : Factor w/ 2 levels "0","1": 1 1 1 1 1 2 1 1 1 1 ...
## $ MTRANS_Bike : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 1 1 1 ...
## $ MTRANS_Motorbike : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 1 1 1 ...
## $ MTRANS_Public_Transportation : Factor w/ 2 levels "0","1": 2 2 2 2 2 1 2 2 1 2 ...
## $ MTRANS_Walking : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 1 2 1 ...
## $ NObeyesdad : Factor w/ 7 levels "1","2","3","4",..: 5 1 5 7 2 4 1 5 2 1 ...# Ahora, ajustamos tel modelo con la nueva base de datos balanceada (obesidad_over)
modelo_rl_over <- glm(SCC_yes ~ FAVC_yes + FCVC + NCP + CAEC + CH2O + SMOKE_yes + FAVC_yes + TUE + CALC + MTRANS_Walking + family_history_with_overweight_yes + Age + NObeyesdad + Gender_Male + Gender_Female, family = "binomial"(link='logit'), data = obesidad_over_train)
# Muestra un resumen del modelo
summary(modelo_rl_over)##
## Call:
## glm(formula = SCC_yes ~ FAVC_yes + FCVC + NCP + CAEC + CH2O +
## SMOKE_yes + FAVC_yes + TUE + CALC + MTRANS_Walking + family_history_with_overweight_yes +
## Age + NObeyesdad + Gender_Male + Gender_Female, family = binomial(link = "logit"),
## data = obesidad_over_train)
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.645e+00 5.798e-01 2.838 0.004542 **
## FAVC_yes1 -1.179e+00 2.014e-01 -5.852 4.86e-09 ***
## FCVC 2.493e-03 2.927e-04 8.516 < 2e-16 ***
## NCP 1.958e-03 4.372e-04 4.477 7.56e-06 ***
## CAEC2 -1.359e+00 3.520e-01 -3.862 0.000113 ***
## CAEC3 -6.644e-01 3.712e-01 -1.790 0.073437 .
## CAEC4 -4.073e-02 5.131e-01 -0.079 0.936727
## CH2O 5.554e-04 2.112e-04 2.630 0.008546 **
## SMOKE_yes1 2.305e+00 5.811e-01 3.966 7.31e-05 ***
## TUE -8.919e-04 2.053e-04 -4.345 1.39e-05 ***
## CALC -4.078e-01 1.563e-01 -2.609 0.009091 **
## MTRANS_Walking1 1.618e-01 3.297e-01 0.491 0.623518
## family_history_with_overweight_yes1 -7.631e-01 1.710e-01 -4.462 8.14e-06 ***
## Age -2.313e-03 2.810e-04 -8.231 < 2e-16 ***
## NObeyesdad2 1.799e+00 2.660e-01 6.761 1.37e-11 ***
## NObeyesdad3 2.978e+00 2.820e-01 10.561 < 2e-16 ***
## NObeyesdad4 9.674e-01 3.369e-01 2.872 0.004082 **
## NObeyesdad5 1.561e-02 4.065e-01 0.038 0.969359
## NObeyesdad6 7.807e-01 5.414e-01 1.442 0.149301
## NObeyesdad7 -1.767e+01 5.658e+02 -0.031 0.975090
## Gender_Male1 -1.495e+00 1.912e-01 -7.818 5.37e-15 ***
## Gender_Female1 NA NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 2048.4 on 1477 degrees of freedom
## Residual deviance: 1032.3 on 1457 degrees of freedom
## AIC: 1074.3
##
## Number of Fisher Scoring iterations: 17La probabilidad para acertar si una persona cuenta calorias con nuestro modelo es del 83,1%.
Vamos a conocer un poco más en detalle que métricas devuelve nuestro modelo:
La sensibilidad es del 83,6%.
La especificidad del 82,6%
Los pos pred value es del 82,2% y los neg pred value del 83,9%.
Finalmente, nos encontramos balanced Accuracy del 83,0%. Lo que nos indica que hemos logrado un modelo muy equilibrado entre la sensibilidad y la especificidad.
pred.train <- predict(modelo_rl_over,obesidad_over_train)## Warning in predict.lm(object, newdata, se.fit, scale = 1, type = if (type == :
## prediction from rank-deficient fit; attr(*, "non-estim") has doubtful casespred.train <- ifelse(pred.train > 0.4,1,0)
# Convertir la variable dependiente a factor con los mismos niveles que la predicción
obesidad_over_train$SCC_yes <- factor(obesidad_over_train$SCC_yes, levels = levels(factor(pred.train)))
# Matriz de confusión
conf_matrix <- confusionMatrix(factor(pred.train), obesidad_over_train$SCC_yes)
print(conf_matrix)## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 609 126
## 1 116 627
##
## Accuracy : 0.8363
## 95% CI : (0.8164, 0.8548)
## No Information Rate : 0.5095
## P-Value [Acc > NIR] : <2e-16
##
## Kappa : 0.6725
##
## Mcnemar's Test P-Value : 0.5629
##
## Sensitivity : 0.8400
## Specificity : 0.8327
## Pos Pred Value : 0.8286
## Neg Pred Value : 0.8439
## Prevalence : 0.4905
## Detection Rate : 0.4120
## Detection Prevalence : 0.4973
## Balanced Accuracy : 0.8363
##
## 'Positive' Class : 0
## Cuando lo probamos con el test, observamos métricas muy similares a esta, aunque ligeramente más bajas (alrededor de un 5% menos), sin embargo, seguimos obteniendo métricas muy balanceadas, lo que corrobora la adecuación de este modelo para detectar si las personas cuentan o no cuentan calorías.
# Predicción en la base de datos de prueba
pred.test <- predict(modelo_rl_over, obesidad_over_test)## Warning in predict.lm(object, newdata, se.fit, scale = 1, type = if (type == :
## prediction from rank-deficient fit; attr(*, "non-estim") has doubtful casespred.test <- ifelse(pred.test > 0.45, 1, 0)
# Convertir la variable dependiente a factor con los mismos niveles que la predicción
obesidad_over_test$SCC_yes <- factor(obesidad_over_test$SCC_yes, levels = levels(factor(pred.test)))
# Matriz de confusión en la base de datos de prueba
conf_matrix_test <- confusionMatrix(factor(pred.test), obesidad_over_test$SCC_yes)
print(conf_matrix_test)## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 266 57
## 1 56 254
##
## Accuracy : 0.8215
## 95% CI : (0.7894, 0.8506)
## No Information Rate : 0.5087
## P-Value [Acc > NIR] : <2e-16
##
## Kappa : 0.6428
##
## Mcnemar's Test P-Value : 1
##
## Sensitivity : 0.8261
## Specificity : 0.8167
## Pos Pred Value : 0.8235
## Neg Pred Value : 0.8194
## Prevalence : 0.5087
## Detection Rate : 0.4202
## Detection Prevalence : 0.5103
## Balanced Accuracy : 0.8214
##
## 'Positive' Class : 0
## # Crear la matriz de confusión
conf_matrix_df <- as.data.frame(as.table(conf_matrix_test$table))
colnames(conf_matrix_df) <- c("Predicción", "Valor Real", "Conteo")
conf_matrix_df$Predicción <- factor(conf_matrix_df$Predicción, levels = c("0", "1"))
conf_matrix_df$`Valor Real` <- factor(conf_matrix_df$`Valor Real`, levels = c("0", "1"))
# Visualizar la matriz de confusión con ggplot2
ggplot(conf_matrix_df, aes(x = Predicción, y = `Valor Real`, fill = Conteo)) +
geom_tile(color = "white") +
scale_fill_gradient(low = "white", high = "steelblue") +
geom_text(aes(label = Conteo), vjust = 1) +
theme_minimal() +
labs(title = "Matriz de Confusión",
x = "Predicción",
y = "Valor Real")
3. Modelo predictivo multiclase que obtenga el grado de obesidad
Procesamiento de Datos
Conversión de las variables categóricas a factores
obesidad$Gender <- as.factor(obesidad$Gender)
obesidad$family_history_with_overweight <- as.factor(obesidad$family_history_with_overweight)
obesidad$CAEC <- as.factor(obesidad$CAEC)
obesidad$NObeyesdad <- as.factor(obesidad$NObeyesdad)
obesidad$CALC <- as.factor(obesidad$CALC)
obesidad$SMOKE <- as.factor(obesidad$SMOKE)Librerías a usar
library(randomForest)## Warning: package 'randomForest' was built under R version 4.3.2## randomForest 4.7-1.1## Type rfNews() to see new features/changes/bug fixes.##
## Attaching package: 'randomForest'## The following object is masked from 'package:dplyr':
##
## combine## The following object is masked from 'package:ggplot2':
##
## marginlibrary(caret)
library(dplyr)División datos en “factores de obesidad” y “nivel de obesidad”
Dividimos el conjunto de datos en características (factores de obesidad) y la variable objetivo (nivel de obesidad) usando “createDataPartition, para tener una distribución de 70% de entrenamiento y 30% test
Además de dividir los datos en conjuntos de entrenamiento y prueba para que poder hacer el modelo de entrenamiento y posteriormente hacer su respectiva evaluación.
factores_obesidad <- obesidad[, -which(names(obesidad) == "NObeyesdad")]
nivel_obesidad <- obesidad$NObeyesdad
set.seed(50) # Para reproducibilidad
trn_indices_obesidad <- createDataPartition(nivel_obesidad, p=.7, list = FALSE)
factores_obesidad_trn <- factores_obesidad[trn_indices_obesidad,]
nivel_obesidad_trn <- nivel_obesidad[trn_indices_obesidad]
factores_obesidad_test <- factores_obesidad[-trn_indices_obesidad,]
nivel_obesidad_test <- nivel_obesidad[-trn_indices_obesidad]Modelo de Entrenamiento
Para este conjunto de entrenamiento usamos el modelo “Random Forest”, la variable “objetivo” es nivel_obesidad_trn
rf_modelo <- randomForest(x= factores_obesidad_trn, y = nivel_obesidad_trn)
rf_modelo##
## Call:
## randomForest(x = factores_obesidad_trn, y = nivel_obesidad_trn)
## Type of random forest: classification
## Number of trees: 500
## No. of variables tried at each split: 4
##
## OOB estimate of error rate: 4.46%
## Confusion matrix:
## Insufficient_Weight Normal_Weight Obesity_Type_I
## Insufficient_Weight 180 11 0
## Normal_Weight 3 192 0
## Obesity_Type_I 0 4 236
## Obesity_Type_II 0 1 1
## Obesity_Type_III 0 0 0
## Overweight_Level_I 0 16 0
## Overweight_Level_II 0 7 2
## Obesity_Type_II Obesity_Type_III Overweight_Level_I
## Insufficient_Weight 0 0 0
## Normal_Weight 0 0 3
## Obesity_Type_I 1 0 1
## Obesity_Type_II 205 1 0
## Obesity_Type_III 1 226 0
## Overweight_Level_I 0 0 182
## Overweight_Level_II 0 0 2
## Overweight_Level_II class.error
## Insufficient_Weight 0 0.057591623
## Normal_Weight 3 0.044776119
## Obesity_Type_I 4 0.040650407
## Obesity_Type_II 0 0.014423077
## Obesity_Type_III 0 0.004405286
## Overweight_Level_I 5 0.103448276
## Overweight_Level_II 192 0.054187192##Evaluación del Modelo
Use el conjunto de prueba, para medir la efectividad de la clasificación multiclase
predicciones <- predict(rf_modelo,factores_obesidad_test)Calcular presición del modelo
presicion <- sum(predicciones == nivel_obesidad_test)/length(nivel_obesidad_test)
presicion## [1] 0.9509494La presición del modelo es alta, esto indica que el modelo es muy efectivo para una correcta clasificación de los diferentes grados de obesidad
Reporte de clasificación
Use “confusionMatrix” para evaluar cuándo el modelo acierta o falla al predecir los diferentes tipos de obesidad, y así entender mejor cómo funciona el modelo para cada categoría de peso
confusionMatrix(predicciones, nivel_obesidad_test)## Confusion Matrix and Statistics
##
## Reference
## Prediction Insufficient_Weight Normal_Weight Obesity_Type_I
## Insufficient_Weight 79 2 0
## Normal_Weight 2 83 0
## Obesity_Type_I 0 0 102
## Obesity_Type_II 0 0 0
## Obesity_Type_III 0 0 0
## Overweight_Level_I 0 1 0
## Overweight_Level_II 0 0 3
## Reference
## Prediction Obesity_Type_II Obesity_Type_III Overweight_Level_I
## Insufficient_Weight 0 0 0
## Normal_Weight 0 0 13
## Obesity_Type_I 0 0 0
## Obesity_Type_II 89 0 0
## Obesity_Type_III 0 97 0
## Overweight_Level_I 0 0 69
## Overweight_Level_II 0 0 5
## Reference
## Prediction Overweight_Level_II
## Insufficient_Weight 0
## Normal_Weight 2
## Obesity_Type_I 1
## Obesity_Type_II 0
## Obesity_Type_III 0
## Overweight_Level_I 2
## Overweight_Level_II 82
##
## Overall Statistics
##
## Accuracy : 0.9509
## 95% CI : (0.9311, 0.9664)
## No Information Rate : 0.1661
## P-Value [Acc > NIR] : < 2.2e-16
##
## Kappa : 0.9427
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: Insufficient_Weight Class: Normal_Weight
## Sensitivity 0.9753 0.9651
## Specificity 0.9964 0.9689
## Pos Pred Value 0.9753 0.8300
## Neg Pred Value 0.9964 0.9944
## Prevalence 0.1282 0.1361
## Detection Rate 0.1250 0.1313
## Detection Prevalence 0.1282 0.1582
## Balanced Accuracy 0.9858 0.9670
## Class: Obesity_Type_I Class: Obesity_Type_II
## Sensitivity 0.9714 1.0000
## Specificity 0.9981 1.0000
## Pos Pred Value 0.9903 1.0000
## Neg Pred Value 0.9943 1.0000
## Prevalence 0.1661 0.1408
## Detection Rate 0.1614 0.1408
## Detection Prevalence 0.1630 0.1408
## Balanced Accuracy 0.9848 1.0000
## Class: Obesity_Type_III Class: Overweight_Level_I
## Sensitivity 1.0000 0.7931
## Specificity 1.0000 0.9945
## Pos Pred Value 1.0000 0.9583
## Neg Pred Value 1.0000 0.9679
## Prevalence 0.1535 0.1377
## Detection Rate 0.1535 0.1092
## Detection Prevalence 0.1535 0.1139
## Balanced Accuracy 1.0000 0.8938
## Class: Overweight_Level_II
## Sensitivity 0.9425
## Specificity 0.9853
## Pos Pred Value 0.9111
## Neg Pred Value 0.9908
## Prevalence 0.1377
## Detection Rate 0.1297
## Detection Prevalence 0.1424
## Balanced Accuracy 0.9639Un nivel de precisión alto, como el que se logró en el modelo indica que es muy eficaz en identificar correctamente los distintos grados de obesidad. En un contexto práctico, esto quiere decir que el modelo es confiable para su uso en aplicaciones de salud, donde se requiere predicciones muy precisas para un tratamiento o diagnóstico adecuado.
Con base a la matriz de confusión, el modelo muestra un buen desempeño en la mayoría de las clases, particularmente en “Obesity_Type_II” y “obesity_Type_II” donde alcanza una gran precisión. Sin embargo, en el caso de “Overweight_Level_I” podemos ver que el rendimiento es menor lo que indica que puede ser una oportunidad de mejora para esta categoría en específico.
install.packages("ggplot2")## Warning: package 'ggplot2' is in use and will not be installedlibrary(ggplot2)Gráfico “Distribución de Niveles de Obesidad
En el siguiente gráfico se se muestra la dsitribución de las frecuencias de diferentes niveles de obesidad en un conjunto de datos. Las barras representan el número de casos en cada categoría de obesidad.
df_predicciones <- data.frame(Predicciones = predicciones)
ggplot(data= df_predicciones, aes(x = Predicciones)) +
geom_bar() +
theme_minimal() +
labs(title = "Distribución de Niveles de Obesidad", x = "Niveles de Obesidad", y = "Frecuencia")
4. Clustering para segmentar a la población
##Carga de datos
#Cargamos librería dplyr
library(dplyr)
#Vamoa a llamar a la base de datos original para este proceso
df <- read.csv("ObesityDataSet_raw_and_data_sinthetic.csv")
set.seed(101)
datosCluster <- df
datosCluster <- as.data.frame(datosCluster)
datosCluster <- datosCluster %>% mutate(grupo = datosCluster$NObeyesdad)
datosCluster <- datosCluster %>% mutate(grupo = sample(x = datosCluster$NObeyesdad,
size = 2111,
replace = TRUE))colnames(datosCluster)## [1] "Gender" "Age"
## [3] "Height" "Weight"
## [5] "family_history_with_overweight" "FAVC"
## [7] "FCVC" "NCP"
## [9] "CAEC" "SMOKE"
## [11] "CH2O" "SCC"
## [13] "FAF" "TUE"
## [15] "CALC" "MTRANS"
## [17] "NObeyesdad" "grupo"Analizamos: * Peso * Edad * Consumo de Hipercalóricos * Consumo de Alcohol * Historia del Familia con Obesidad
ggplot(datosCluster, aes(Weight, Age, CALC, FAVC, family_history_with_overweight)) + geom_point(aes(col=NObeyesdad), size=2) + ggtitle("Grupos de pesos, desde normal hasta obesidad tipo II")## Warning: Duplicated aesthetics after name standardisation:
La función kmeans() del paquete stats lleva a cabo el clustering K-means. Entre sus parámetros más relevantes se encuentran: centers, que establece la cantidad K de clusters a generar, y nstart, que determina cuántas veces se repetirá el proceso, cada vez con una asignación inicial aleatoria diferente.
Se visualiza la asignación de cada observación a un cluster específico, y se indica mediante códigos de color el grupo real al que pertenece
datosCluster <- datosCluster %>% mutate(cluster = datosCluster$NObeyesdad)
datosCluster <- datosCluster %>% mutate(cluster = as.factor(datosCluster$NObeyesdad),
grupo = as.factor(grupo))
ggplot(data = datosCluster, aes(x = datosCluster$NObeyesdad, y = datosCluster$Age, color = grupo)) +
geom_text(aes(label = cluster), size = 2111) +
theme_bw() +
theme(legend.position = "none")## Warning: Use of `datosCluster$NObeyesdad` is discouraged.
## ℹ Use `NObeyesdad` instead.## Warning: Use of `datosCluster$Age` is discouraged.
## ℹ Use `Age` instead.
ggplot(data = datosCluster, aes(x = datosCluster$NObeyesdad, y = datosCluster$Weight, color = grupo)) +
geom_text(aes(label = cluster), size = 2111) +
theme_bw() +
theme(legend.position = "none")## Warning: Use of `datosCluster$NObeyesdad` is discouraged.
## ℹ Use `NObeyesdad` instead.## Warning: Use of `datosCluster$Weight` is discouraged.
## ℹ Use `Weight` instead.
El cluster agrupa correctamente a las poblaciones por tipo de peso conforme a la edad.
Compararemos también contra el peso.
table(datosCluster$cluster, datosCluster$NObeyesdad)##
## Insufficient_Weight Normal_Weight Obesity_Type_I
## Insufficient_Weight 272 0 0
## Normal_Weight 0 287 0
## Obesity_Type_I 0 0 351
## Obesity_Type_II 0 0 0
## Obesity_Type_III 0 0 0
## Overweight_Level_I 0 0 0
## Overweight_Level_II 0 0 0
##
## Obesity_Type_II Obesity_Type_III Overweight_Level_I
## Insufficient_Weight 0 0 0
## Normal_Weight 0 0 0
## Obesity_Type_I 0 0 0
## Obesity_Type_II 297 0 0
## Obesity_Type_III 0 324 0
## Overweight_Level_I 0 0 290
## Overweight_Level_II 0 0 0
##
## Overweight_Level_II
## Insufficient_Weight 0
## Normal_Weight 0
## Obesity_Type_I 0
## Obesity_Type_II 0
## Obesity_Type_III 0
## Overweight_Level_I 0
## Overweight_Level_II 290#Cargamos el paquete cluster
library(cluster)
clusplot(datosCluster, datosCluster$cluster, color=T, shade=T, labels=0, lines=0, main="CLUSTERING PLOT")
#datosCluster
tot.withinss <- vector(mode="character", length=10)
for (i in 1:10){
datosCluster <- kmeans(df[,2:4], center=i, nstart=1)
tot.withinss[i] <- datosCluster$tot.withinss
}
plot(1:10, tot.withinss, type="b", pch=19, main="ELBOW GRAPH")
#Cargamos factoextra
library(factoextra)## Warning: package 'factoextra' was built under R version 4.3.2## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBadatosCluster## K-means clustering with 10 clusters of sizes 250, 130, 31, 281, 265, 307, 68, 379, 171, 229
##
## Cluster means:
## Age Height Weight
## 1 20.88436 1.668716 59.93018
## 2 22.33460 1.768050 132.09186
## 3 19.95346 1.797914 151.90534
## 4 24.25520 1.714321 102.04575
## 5 20.24172 1.635861 47.84239
## 6 25.91319 1.749235 115.92699
## 7 36.45252 1.759276 108.36032
## 8 22.28682 1.717282 83.90888
## 9 38.33744 1.654059 79.33164
## 10 21.67885 1.676475 70.92254
##
## Clustering vector:
## [1] 1 1 10 8 8 5 1 5 1 10 4 8 1 7 1 10 4 8 8 10 8 9 1 8
## [25] 10 5 1 5 10 10 8 10 10 9 1 1 5 5 10 8 10 1 1 1 8 1 10 10
## [49] 1 5 1 5 5 1 1 1 10 1 10 1 5 1 1 1 1 10 8 4 6 1 8 5
## [73] 1 1 8 5 5 8 8 1 1 8 8 5 8 1 8 8 1 8 4 1 9 1 5 10
## [97] 1 5 5 10 1 10 1 1 9 1 1 8 4 8 10 1 5 5 1 1 8 8 5 10
## [121] 10 4 5 10 8 8 10 1 10 8 5 1 1 9 7 10 10 9 9 10 1 10 4 9
## [145] 10 10 5 9 1 8 8 1 1 9 4 1 5 1 9 8 10 9 1 10 9 2 10 8
## [169] 8 9 8 1 1 1 10 1 5 8 8 10 5 10 5 1 10 10 7 4 7 1 1 8
## [193] 8 10 8 8 10 7 5 1 8 9 4 8 10 8 4 10 1 1 6 5 1 1 5 10
## [217] 1 10 5 10 8 8 10 1 8 6 5 1 9 6 8 10 5 9 5 10 1 5 5 1
## [241] 1 10 1 4 5 5 1 5 10 8 10 8 9 5 1 8 8 6 8 8 10 10 10 5
## [265] 10 5 5 9 1 10 4 5 1 10 1 5 5 10 1 5 1 1 1 1 10 4 1 1
## [289] 5 8 10 1 1 10 6 1 5 8 8 10 10 1 5 5 8 6 1 5 10 1 1 1
## [313] 1 1 1 10 9 10 5 1 10 9 1 10 10 1 1 10 10 8 5 1 10 1 5 5
## [337] 1 1 1 5 10 5 4 10 3 1 5 4 8 2 10 1 5 5 1 1 1 1 7 5
## [361] 10 9 9 8 8 10 9 9 9 10 1 10 1 1 10 9 1 10 10 10 8 10 1 4
## [385] 1 5 5 9 4 1 5 5 10 8 1 5 1 1 2 1 10 8 4 6 9 8 10 1
## [409] 8 1 10 1 9 9 7 10 9 8 8 8 1 1 1 4 9 5 10 1 10 8 8 1
## [433] 10 1 8 8 1 1 1 1 1 5 1 5 1 5 8 8 4 1 10 1 10 5 10 10
## [457] 1 5 1 8 1 4 8 10 8 5 10 10 5 5 5 8 10 5 1 10 10 1 1 5
## [481] 5 1 5 1 9 10 10 4 8 5 8 10 9 1 10 1 5 5 4 2 6 2 3 2
## [505] 6 4 2 1 1 1 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
## [529] 5 5 5 1 1 1 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5
## [553] 5 5 5 5 5 5 1 1 1 5 5 5 1 1 1 1 1 1 5 5 5 5 5 5
## [577] 5 5 5 1 1 1 5 5 5 5 5 5 5 5 5 1 1 1 1 1 1 5 5 5
## [601] 5 5 5 5 5 5 5 1 5 1 5 5 5 5 5 5 5 1 5 5 5 5 5 5
## [625] 5 5 1 5 1 1 5 5 5 1 5 5 5 1 1 5 5 5 5 1 1 1 5 5
## [649] 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 1 1 1 5 5
## [673] 5 5 5 5 5 5 5 5 1 5 5 5 5 5 5 5 5 5 5 5 5 5 1 1
## [697] 1 5 5 5 1 1 1 1 1 1 5 5 5 5 5 5 5 5 5 1 1 1 5 5
## [721] 5 5 5 5 5 5 5 1 1 1 1 1 1 5 5 5 5 5 5 5 5 5 5 5
## [745] 5 8 10 8 10 10 8 9 8 10 8 10 9 10 10 1 1 8 10 10 10 10 8 8
## [769] 8 10 10 10 8 10 8 8 10 10 8 10 8 1 9 10 1 1 1 9 8 9 10 10
## [793] 10 1 1 8 9 8 8 8 10 10 1 8 8 10 10 8 10 10 10 8 8 9 8 8
## [817] 10 10 8 10 9 9 10 10 10 9 9 9 8 8 10 10 10 10 10 10 10 8 8 8
## [841] 8 8 8 10 10 10 8 8 8 8 10 8 8 8 10 10 10 8 8 10 8 1 10 10
## [865] 10 1 1 1 1 1 9 8 8 9 10 10 1 10 10 1 1 1 9 9 8 8 8 8
## [889] 8 8 10 10 1 8 8 10 10 8 10 10 10 8 9 9 8 8 10 8 10 10 9 10
## [913] 10 10 10 9 9 1 8 8 10 10 10 10 10 10 8 8 8 10 10 10 10 10 8 10
## [937] 10 8 8 8 10 10 10 8 8 10 8 10 9 10 10 5 1 1 1 9 8 9 10 10
## [961] 10 10 1 1 1 1 8 9 9 8 8 8 8 10 10 10 1 8 8 8 8 7 9 8
## [985] 8 8 10 9 9 1 1 8 10 10 8 8 8 8 8 8 8 8 8 8 8 10 4 4
## [1009] 8 8 8 9 8 9 9 8 8 9 8 10 1 1 1 8 8 9 9 9 9 4 4 10
## [1033] 10 8 9 8 8 8 9 4 9 9 9 10 10 4 8 8 8 4 4 8 9 8 8 4
## [1057] 8 8 10 9 9 8 9 9 8 8 4 9 8 10 9 10 8 1 8 8 8 8 8 8
## [1081] 8 8 8 4 8 8 9 8 9 9 8 9 8 1 1 8 9 9 4 10 8 9 8 8
## [1105] 9 4 9 9 10 9 8 8 4 8 9 8 4 8 10 9 8 9 8 8 8 8 4 9
## [1129] 8 8 8 10 9 9 1 1 8 10 10 8 8 8 8 8 8 8 8 8 8 8 10 4
## [1153] 8 8 8 8 9 8 9 9 8 8 9 8 1 1 1 1 8 8 9 9 9 9 4 4
## [1177] 10 10 8 9 8 8 8 9 4 9 9 9 10 10 8 8 8 8 4 4 8 9 8 9
## [1201] 4 8 8 10 9 9 8 9 9 4 4 4 7 9 8 9 9 8 8 4 8 8 8 9
## [1225] 4 4 8 8 4 9 8 9 8 4 7 4 4 7 8 8 8 9 9 8 8 4 4 8
## [1249] 4 6 8 8 4 4 4 4 4 4 8 8 4 6 6 9 9 4 9 9 4 4 7 8
## [1273] 8 8 8 4 4 8 4 4 4 7 7 9 8 9 9 8 8 4 4 8 8 8 8 9
## [1297] 9 4 4 8 8 8 8 7 7 9 9 4 4 9 9 8 8 4 4 9 7 4 4 7
## [1321] 7 8 8 8 8 9 9 8 8 8 8 4 4 8 8 6 6 8 8 4 4 4 4 4
## [1345] 4 8 8 4 4 6 6 9 9 4 4 9 9 4 4 7 7 8 8 8 8 8 8 4
## [1369] 4 8 8 4 4 4 4 4 4 4 7 7 7 9 8 8 8 9 9 9 9 8 8 8
## [1393] 8 4 4 8 8 8 8 8 8 9 9 4 4 4 4 8 8 8 8 4 4 9 9 8
## [1417] 8 9 9 8 8 4 4 7 7 4 4 4 4 7 7 8 8 8 8 8 8 9 9 9
## [1441] 9 8 8 8 8 4 4 4 4 8 8 4 4 6 6 8 8 4 8 4 4 4 4 4
## [1465] 4 4 4 4 4 4 4 8 8 8 8 4 4 6 6 6 6 9 9 9 9 4 4 9
## [1489] 9 9 9 4 4 4 4 7 4 8 8 4 8 8 8 8 8 4 4 4 4 8 8 4
## [1513] 4 6 6 7 7 2 6 6 6 6 6 6 6 6 2 6 6 7 4 6 6 4 4 6
## [1537] 6 4 4 2 6 6 7 6 6 6 6 6 6 6 6 7 7 6 6 4 4 6 6 6
## [1561] 6 7 7 7 4 2 2 6 6 6 6 7 6 6 6 6 6 6 6 6 6 6 6 2
## [1585] 6 6 6 6 6 7 7 4 7 6 6 6 6 4 4 4 4 6 6 4 4 2 2 7
## [1609] 7 6 6 6 6 6 6 6 6 7 7 6 6 4 4 6 6 6 6 7 7 7 4 2
## [1633] 2 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 2 2 6 6 6 6 7
## [1657] 7 4 4 6 6 6 6 4 4 4 4 6 6 6 6 4 4 4 4 2 2 6 6 6
## [1681] 6 7 7 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 6
## [1705] 6 6 6 4 4 4 4 6 6 6 6 6 6 6 6 6 6 7 7 4 7 4 4 2
## [1729] 2 2 2 6 6 6 6 6 6 6 6 7 7 6 6 6 6 6 6 6 6 6 6 6
## [1753] 6 6 6 6 6 6 6 6 6 6 6 6 2 6 2 6 6 6 6 6 6 6 6 7
## [1777] 7 7 7 4 4 7 7 6 6 6 6 6 6 6 6 4 4 4 4 4 4 4 4 4
## [1801] 4 2 3 6 4 4 6 6 2 6 6 2 6 2 3 2 6 6 6 4 4 2 2 4
## [1825] 4 3 3 6 6 4 4 2 2 6 6 2 2 2 3 2 2 6 6 4 4 2 2 4
## [1849] 4 4 4 2 2 2 3 6 6 4 4 4 4 6 6 2 6 2 2 6 6 6 6 2
## [1873] 2 6 6 2 2 3 3 2 2 6 6 6 6 6 6 4 4 4 4 2 2 2 2 4
## [1897] 4 3 3 6 6 4 4 2 2 6 6 2 2 3 3 2 2 6 6 4 4 2 2 4
## [1921] 4 4 4 2 2 3 3 6 6 4 4 4 4 6 6 6 6 2 2 6 6 6 6 2
## [1945] 2 6 6 2 2 3 3 2 2 6 6 6 6 6 6 4 4 4 4 2 2 2 2 4
## [1969] 4 4 4 3 2 3 3 6 6 6 6 4 4 4 4 2 2 2 2 6 6 6 6 2
## [1993] 2 2 2 2 2 3 3 2 2 2 2 6 6 6 6 4 4 4 4 2 2 2 2 4
## [2017] 4 4 4 4 4 4 4 2 2 2 2 3 3 3 3 6 6 6 6 4 4 4 4 4
## [2041] 4 4 4 6 6 6 6 2 2 6 6 2 2 2 2 6 6 6 6 6 6 6 6 2
## [2065] 2 2 2 6 6 6 6 2 2 2 2 3 3 3 3 2 2 2 2 6 6 6 6 6
## [2089] 6 6 6 6 6 6 6 4 4 4 4 4 4 4 4 2 2 2 2 2 2 2 2
##
## Within cluster sum of squares by cluster:
## [1] 7235.181 3484.833 1433.393 8964.851 7553.029 8002.879 4234.906
## [8] 10898.163 11189.663 4910.382
## (between_SS / total_SS = 95.6 %)
##
## Available components:
##
## [1] "cluster" "centers" "totss" "withinss" "tot.withinss"
## [6] "betweenss" "size" "iter" "ifault"datosCluster <- kmeans(df[,2:4], center=5, nstart=20)
fviz_silhouette(silhouette(datosCluster$cluster, dist(df[,2:4])), main="SILHOUETTE")## cluster size ave.sil.width
## 1 1 592 0.34
## 2 2 359 0.57
## 3 3 388 0.41
## 4 4 604 0.48
## 5 5 168 0.57
Dengrama
hObesity <- hclust(
dist(df[,1:10], method="canberra"),
method="complete"
)## Warning in dist(df[, 1:10], method = "canberra"): NAs introducidos por coerciónplot(hObesity, hang = -1, cex = 0.6, main ="DENDOGRAM")
hObesity <- hclust(
dist(df),
method="complete"
)## Warning in dist(df): NAs introducidos por coerciónplot(hObesity, hang = -1, cex = 0.6, main ="DENDOGRAM")
dbs <- df[, 2:4]
plot(dbs, main = "DENSITY POINTS")
Agrupación de poblaciones por edad, altura y peso.
plot## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '30'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '30'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '30'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '27'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '30'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '27'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '27'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '27'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '27'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '27'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '30'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '30'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '30'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '27'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '27'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '30'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '30'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '27'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '27'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '27'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '30'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '27'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '27'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '27'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '30'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '30'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '30'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '30'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '30'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '27'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '30'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '27'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '27'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '27'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '30'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '27'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '31'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '27'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '27'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '27'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '27'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '27'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '27'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '27'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '30'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '30'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '27'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '27'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '27'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '27'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '27'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '27'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '30'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '30'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '30'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '27'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '26'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '27'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '27'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '30'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '30'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '26'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '27'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '26'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '29'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '30'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '27'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '27'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '30'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '30'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '30'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '30'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '30'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '30'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '30'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '27'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '30'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '30'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '30'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '27'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '27'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '27'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '27'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '27'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '27'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '27'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '27'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '27'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '27'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '27'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '27'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '27'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '27'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '27'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '27'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '27'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '27'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '31'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '31'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '31'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '31'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '31'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '31'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '31'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '31'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '31'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '31'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '31'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '31'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '31'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '31'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '31'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '31'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '31'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '31'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '29'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '26'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '29'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '29'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '26'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '29'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '29'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '29'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '26'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '29'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '29'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '26'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '26'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '29'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '29'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '26'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '26'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '29'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '29'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '29'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '29'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '26'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '26'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '29'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '29'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '29'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '29'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '26'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '26'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '29'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '29'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '29'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '29'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '29'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '29'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '26'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '26'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '26'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '29'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '29'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '29'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '29'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '29'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '26'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '26'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '26'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '26'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '29'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '29'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '29'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '29'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '29'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '26'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '27'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '29'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '30'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '31'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '26'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '26'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '27'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '27'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '28'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '29'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '29'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '30'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '30'## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '31'
## Warning in grid.Call.graphics(C_points, x$x, x$y, x$pch, x$size): unimplemented
## pch value '31'
No se encuentra una agrupamiento tan diferenciador.
Tendencia del clustering
Para ilustrar la importancia de este pre-análisis inicial, se aplica clustering a un sets de datos. Se agrupan con hasta mas de 40 grupos.
obesidad <- df
datos_obesidad <- df
datos_obesidad <- datos_obesidad[, -1]
datos_obesidad <- datos_obesidad[, -4]
datos_obesidad <- datos_obesidad[, -4]
datos_obesidad <- datos_obesidad[, -6]
datos_obesidad <- datos_obesidad[, -6]
datos_obesidad <- datos_obesidad[, -7]
datos_obesidad <- datos_obesidad[, -9]
datos_obesidad <- datos_obesidad[, -9]
datos_obesidad <- datos_obesidad[, -9]
datos_obesidad## Age Height Weight FCVC NCP CH2O FAF TUE
## 1 21.00000 1.620000 64.00000 2.000000 3.000000 2.000000 0.000000 1.000000
## 2 21.00000 1.520000 56.00000 3.000000 3.000000 3.000000 3.000000 0.000000
## 3 23.00000 1.800000 77.00000 2.000000 3.000000 2.000000 2.000000 1.000000
## 4 27.00000 1.800000 87.00000 3.000000 3.000000 2.000000 2.000000 0.000000
## 5 22.00000 1.780000 89.80000 2.000000 1.000000 2.000000 0.000000 0.000000
## 6 29.00000 1.620000 53.00000 2.000000 3.000000 2.000000 0.000000 0.000000
## 7 23.00000 1.500000 55.00000 3.000000 3.000000 2.000000 1.000000 0.000000
## 8 22.00000 1.640000 53.00000 2.000000 3.000000 2.000000 3.000000 0.000000
## 9 24.00000 1.780000 64.00000 3.000000 3.000000 2.000000 1.000000 1.000000
## 10 22.00000 1.720000 68.00000 2.000000 3.000000 2.000000 1.000000 1.000000
## 11 26.00000 1.850000 105.00000 3.000000 3.000000 3.000000 2.000000 2.000000
## 12 21.00000 1.720000 80.00000 2.000000 3.000000 2.000000 2.000000 1.000000
## 13 22.00000 1.650000 56.00000 3.000000 3.000000 3.000000 2.000000 0.000000
## 14 41.00000 1.800000 99.00000 2.000000 3.000000 2.000000 2.000000 1.000000
## 15 23.00000 1.770000 60.00000 3.000000 1.000000 1.000000 1.000000 1.000000
## 16 22.00000 1.700000 66.00000 3.000000 3.000000 2.000000 2.000000 1.000000
## 17 27.00000 1.930000 102.00000 2.000000 1.000000 1.000000 1.000000 0.000000
## 18 29.00000 1.530000 78.00000 2.000000 1.000000 2.000000 0.000000 0.000000
## 19 30.00000 1.710000 82.00000 3.000000 4.000000 1.000000 0.000000 0.000000
## 20 23.00000 1.650000 70.00000 2.000000 1.000000 2.000000 0.000000 0.000000
## 21 22.00000 1.650000 80.00000 2.000000 3.000000 2.000000 3.000000 2.000000
## 22 52.00000 1.690000 87.00000 3.000000 1.000000 2.000000 0.000000 0.000000
## 23 22.00000 1.650000 60.00000 3.000000 3.000000 2.000000 1.000000 0.000000
## 24 22.00000 1.600000 82.00000 1.000000 1.000000 2.000000 0.000000 2.000000
## 25 21.00000 1.850000 68.00000 2.000000 3.000000 2.000000 0.000000 1.000000
## 26 20.00000 1.600000 50.00000 2.000000 4.000000 2.000000 3.000000 2.000000
## 27 21.00000 1.700000 65.00000 2.000000 1.000000 2.000000 1.000000 2.000000
## 28 23.00000 1.600000 52.00000 2.000000 4.000000 2.000000 2.000000 1.000000
## 29 19.00000 1.750000 76.00000 3.000000 3.000000 2.000000 3.000000 1.000000
## 30 23.00000 1.680000 70.00000 2.000000 3.000000 2.000000 2.000000 2.000000
## 31 29.00000 1.770000 83.00000 1.000000 4.000000 3.000000 0.000000 1.000000
## 32 31.00000 1.580000 68.00000 2.000000 1.000000 1.000000 1.000000 0.000000
## 33 24.00000 1.770000 76.00000 2.000000 3.000000 3.000000 1.000000 1.000000
## 34 39.00000 1.790000 90.00000 2.000000 1.000000 2.000000 0.000000 0.000000
## 35 22.00000 1.650000 62.00000 2.000000 4.000000 2.000000 2.000000 0.000000
## 36 21.00000 1.500000 65.00000 2.000000 3.000000 2.000000 2.000000 2.000000
## 37 22.00000 1.560000 49.00000 2.000000 3.000000 1.000000 2.000000 0.000000
## 38 21.00000 1.600000 48.00000 2.000000 3.000000 1.000000 1.000000 0.000000
## 39 23.00000 1.650000 67.00000 2.000000 3.000000 2.000000 1.000000 1.000000
## 40 21.00000 1.750000 88.00000 2.000000 3.000000 3.000000 3.000000 0.000000
## 41 21.00000 1.670000 75.00000 2.000000 3.000000 2.000000 1.000000 0.000000
## 42 23.00000 1.680000 60.00000 2.000000 4.000000 2.000000 0.000000 0.000000
## 43 21.00000 1.660000 64.00000 1.000000 3.000000 1.000000 0.000000 0.000000
## 44 21.00000 1.660000 62.00000 2.000000 3.000000 2.000000 1.000000 1.000000
## 45 21.00000 1.810000 80.00000 1.000000 3.000000 2.000000 2.000000 0.000000
## 46 21.00000 1.530000 65.00000 2.000000 3.000000 1.000000 0.000000 1.000000
## 47 21.00000 1.820000 72.00000 1.000000 3.000000 3.000000 2.000000 0.000000
## 48 21.00000 1.750000 72.00000 1.000000 3.000000 3.000000 2.000000 0.000000
## 49 20.00000 1.660000 60.00000 3.000000 3.000000 2.000000 1.000000 0.000000
## 50 21.00000 1.550000 50.00000 2.000000 3.000000 2.000000 0.000000 0.000000
## 51 21.00000 1.610000 54.50000 3.000000 3.000000 3.000000 0.000000 1.000000
## 52 20.00000 1.500000 44.00000 2.000000 3.000000 1.000000 0.000000 0.000000
## 53 23.00000 1.640000 52.00000 3.000000 1.000000 2.000000 2.000000 2.000000
## 54 23.00000 1.630000 55.00000 3.000000 3.000000 2.000000 2.000000 1.000000
## 55 22.00000 1.600000 55.00000 3.000000 4.000000 3.000000 2.000000 0.000000
## 56 23.00000 1.680000 62.00000 2.000000 4.000000 2.000000 0.000000 0.000000
## 57 22.00000 1.700000 70.00000 2.000000 3.000000 1.000000 0.000000 1.000000
## 58 21.00000 1.640000 65.00000 2.000000 3.000000 1.000000 0.000000 1.000000
## 59 17.00000 1.650000 67.00000 3.000000 1.000000 2.000000 1.000000 1.000000
## 60 20.00000 1.760000 55.00000 2.000000 4.000000 3.000000 2.000000 2.000000
## 61 21.00000 1.550000 49.00000 2.000000 3.000000 3.000000 3.000000 1.000000
## 62 20.00000 1.650000 58.00000 2.000000 3.000000 2.000000 3.000000 1.000000
## 63 22.00000 1.670000 62.00000 2.000000 1.000000 2.000000 0.000000 0.000000
## 64 22.00000 1.680000 55.00000 2.000000 3.000000 2.000000 0.000000 2.000000
## 65 21.00000 1.660000 57.00000 2.000000 3.000000 1.000000 1.000000 1.000000
## 66 21.00000 1.620000 69.00000 1.000000 3.000000 2.000000 0.000000 1.000000
## 67 23.00000 1.800000 90.00000 1.000000 3.000000 2.000000 0.000000 2.000000
## 68 23.00000 1.650000 95.00000 2.000000 3.000000 2.000000 0.000000 1.000000
## 69 30.00000 1.760000 112.00000 1.000000 3.000000 2.000000 0.000000 0.000000
## 70 23.00000 1.800000 60.00000 2.000000 3.000000 3.000000 0.000000 1.000000
## 71 23.00000 1.650000 80.00000 2.000000 3.000000 2.000000 0.000000 2.000000
## 72 22.00000 1.670000 50.00000 3.000000 3.000000 3.000000 2.000000 1.000000
## 73 24.00000 1.650000 60.00000 2.000000 3.000000 3.000000 1.000000 0.000000
## 74 19.00000 1.850000 65.00000 2.000000 3.000000 3.000000 2.000000 1.000000
## 75 24.00000 1.700000 85.00000 2.000000 3.000000 3.000000 0.000000 1.000000
## 76 23.00000 1.630000 45.00000 3.000000 3.000000 3.000000 2.000000 0.000000
## 77 24.00000 1.600000 45.00000 2.000000 3.000000 2.000000 1.000000 0.000000
## 78 24.00000 1.700000 80.00000 2.000000 3.000000 3.000000 0.000000 0.000000
## 79 23.00000 1.650000 90.00000 2.000000 3.000000 3.000000 0.000000 1.000000
## 80 23.00000 1.650000 60.00000 2.000000 3.000000 2.000000 0.000000 0.000000
## 81 19.00000 1.630000 58.00000 3.000000 3.000000 2.000000 0.000000 0.000000
## 82 30.00000 1.800000 91.00000 2.000000 3.000000 2.000000 0.000000 0.000000
## 83 23.00000 1.670000 85.50000 2.000000 3.000000 2.000000 0.000000 1.000000
## 84 19.00000 1.600000 45.00000 3.000000 3.000000 3.000000 2.000000 0.000000
## 85 25.00000 1.700000 83.00000 2.000000 3.000000 2.000000 0.000000 1.000000
## 86 23.00000 1.650000 58.50000 2.000000 3.000000 2.000000 0.000000 0.000000
## 87 21.00000 1.850000 83.00000 2.000000 1.000000 3.000000 1.000000 0.000000
## 88 19.00000 1.820000 87.00000 2.000000 3.000000 2.000000 0.000000 0.000000
## 89 22.00000 1.650000 65.00000 2.000000 3.000000 2.000000 1.000000 0.000000
## 90 29.00000 1.700000 78.00000 3.000000 3.000000 1.000000 2.000000 1.000000
## 91 25.00000 1.630000 93.00000 3.000000 4.000000 1.000000 2.000000 0.000000
## 92 20.00000 1.610000 64.00000 3.000000 3.000000 2.000000 0.000000 1.000000
## 93 55.00000 1.780000 84.00000 3.000000 4.000000 3.000000 3.000000 0.000000
## 94 20.00000 1.600000 57.00000 3.000000 3.000000 2.000000 1.000000 0.000000
## 95 24.00000 1.600000 48.00000 3.000000 3.000000 2.000000 2.000000 0.000000
## 96 26.00000 1.700000 70.00000 3.000000 1.000000 2.000000 2.000000 0.000000
## 97 23.00000 1.660000 60.00000 2.000000 3.000000 2.000000 3.000000 0.000000
## 98 21.00000 1.520000 42.00000 3.000000 1.000000 1.000000 0.000000 0.000000
## 99 21.00000 1.520000 42.00000 3.000000 1.000000 1.000000 0.000000 0.000000
## 100 23.00000 1.720000 70.00000 2.000000 3.000000 2.000000 3.000000 1.000000
## 101 21.00000 1.690000 63.00000 3.000000 1.000000 1.000000 0.000000 0.000000
## 102 22.00000 1.700000 66.40000 2.000000 3.000000 2.000000 0.000000 0.000000
## 103 21.00000 1.550000 57.00000 2.000000 4.000000 2.000000 2.000000 0.000000
## 104 22.00000 1.650000 58.00000 3.000000 4.000000 2.000000 1.000000 0.000000
## 105 38.00000 1.560000 80.00000 2.000000 3.000000 2.000000 0.000000 0.000000
## 106 25.00000 1.570000 55.00000 2.000000 1.000000 2.000000 2.000000 0.000000
## 107 25.00000 1.570000 55.00000 2.000000 1.000000 2.000000 2.000000 0.000000
## 108 22.00000 1.880000 90.00000 2.000000 3.000000 1.000000 0.000000 1.000000
## 109 22.00000 1.750000 95.00000 2.000000 3.000000 3.000000 3.000000 2.000000
## 110 21.00000 1.650000 88.00000 3.000000 1.000000 3.000000 2.000000 1.000000
## 111 21.00000 1.750000 75.00000 3.000000 3.000000 2.000000 0.000000 1.000000
## 112 22.00000 1.580000 58.00000 2.000000 1.000000 1.000000 0.000000 0.000000
## 113 18.00000 1.560000 51.00000 2.000000 4.000000 2.000000 1.000000 0.000000
## 114 22.00000 1.500000 49.00000 2.000000 1.000000 2.000000 3.000000 0.000000
## 115 19.00000 1.610000 62.00000 3.000000 1.000000 2.000000 1.000000 0.000000
## 116 17.00000 1.750000 57.00000 3.000000 3.000000 2.000000 0.000000 1.000000
## 117 15.00000 1.650000 86.00000 3.000000 3.000000 1.000000 3.000000 2.000000
## 118 17.00000 1.700000 85.00000 2.000000 3.000000 2.000000 1.000000 1.000000
## 119 23.00000 1.620000 53.00000 2.000000 3.000000 2.000000 1.000000 1.000000
## 120 19.00000 1.630000 76.00000 3.000000 3.000000 3.000000 2.000000 1.000000
## 121 23.00000 1.670000 75.00000 2.000000 3.000000 2.000000 0.000000 2.000000
## 122 23.00000 1.870000 95.00000 1.000000 3.000000 2.000000 0.000000 2.000000
## 123 21.00000 1.750000 50.00000 3.000000 4.000000 1.000000 1.000000 0.000000
## 124 24.00000 1.660000 67.00000 3.000000 1.000000 2.000000 1.000000 0.000000
## 125 23.00000 1.760000 90.00000 3.000000 3.000000 1.000000 0.000000 0.000000
## 126 18.00000 1.750000 80.00000 2.000000 3.000000 2.000000 0.000000 0.000000
## 127 19.00000 1.670000 68.00000 2.000000 3.000000 2.000000 1.000000 0.000000
## 128 19.00000 1.650000 61.00000 3.000000 1.000000 3.000000 1.000000 0.000000
## 129 20.00000 1.720000 70.00000 3.000000 3.000000 1.000000 0.000000 0.000000
## 130 27.00000 1.700000 78.00000 3.000000 3.000000 3.000000 1.000000 1.000000
## 131 20.00000 1.580000 53.00000 2.000000 4.000000 2.000000 1.000000 1.000000
## 132 23.00000 1.620000 58.00000 2.000000 3.000000 1.000000 1.000000 0.000000
## 133 19.00000 1.650000 56.00000 3.000000 3.000000 3.000000 1.000000 2.000000
## 134 61.00000 1.650000 66.00000 3.000000 3.000000 2.000000 1.000000 1.000000
## 135 30.00000 1.770000 109.00000 3.000000 3.000000 1.000000 2.000000 0.000000
## 136 24.00000 1.700000 75.00000 2.000000 3.000000 2.000000 1.000000 0.000000
## 137 25.00000 1.790000 72.00000 2.000000 3.000000 2.000000 1.000000 1.000000
## 138 44.00000 1.600000 80.00000 2.000000 3.000000 3.000000 0.000000 0.000000
## 139 31.00000 1.760000 75.00000 3.000000 3.000000 3.000000 3.000000 0.000000
## 140 25.00000 1.700000 68.00000 2.000000 3.000000 2.000000 0.000000 1.000000
## 141 23.00000 1.890000 65.00000 3.000000 3.000000 3.000000 1.000000 1.000000
## 142 25.00000 1.870000 66.00000 3.000000 3.000000 2.000000 2.000000 0.000000
## 143 23.00000 1.740000 93.50000 2.000000 3.000000 1.000000 1.000000 1.000000
## 144 34.00000 1.680000 75.00000 3.000000 1.000000 1.000000 0.000000 0.000000
## 145 22.00000 1.610000 67.00000 2.000000 4.000000 3.000000 2.000000 2.000000
## 146 21.00000 1.620000 70.00000 2.000000 1.000000 3.000000 1.000000 0.000000
## 147 24.00000 1.560000 51.00000 3.000000 3.000000 2.000000 2.000000 2.000000
## 148 36.00000 1.630000 80.00000 3.000000 3.000000 1.000000 0.000000 0.000000
## 149 27.00000 1.600000 61.00000 3.000000 3.000000 2.000000 0.000000 0.000000
## 150 32.00000 1.670000 90.00000 3.000000 1.000000 2.000000 2.000000 0.000000
## 151 25.00000 1.780000 78.00000 2.000000 1.000000 2.000000 2.000000 1.000000
## 152 30.00000 1.620000 59.00000 3.000000 3.000000 2.000000 2.000000 0.000000
## 153 38.00000 1.500000 60.00000 2.000000 1.000000 2.000000 0.000000 0.000000
## 154 34.00000 1.690000 84.00000 2.000000 3.000000 3.000000 2.000000 0.000000
## 155 22.00000 1.740000 94.00000 2.000000 3.000000 2.000000 0.000000 0.000000
## 156 31.00000 1.680000 63.00000 3.000000 1.000000 2.000000 1.000000 1.000000
## 157 35.00000 1.530000 45.00000 3.000000 3.000000 1.000000 0.000000 1.000000
## 158 21.00000 1.670000 60.00000 2.000000 3.000000 2.000000 2.000000 1.000000
## 159 40.00000 1.550000 62.00000 3.000000 3.000000 3.000000 0.000000 0.000000
## 160 27.00000 1.640000 78.00000 2.000000 1.000000 2.000000 0.000000 0.000000
## 161 20.00000 1.830000 72.00000 3.000000 3.000000 1.000000 2.000000 1.000000
## 162 55.00000 1.650000 80.00000 2.000000 3.000000 2.000000 1.000000 0.000000
## 163 21.00000 1.630000 60.00000 3.000000 3.000000 2.000000 2.000000 0.000000
## 164 25.00000 1.890000 75.00000 3.000000 3.000000 2.000000 3.000000 0.000000
## 165 35.00000 1.770000 85.00000 3.000000 3.000000 3.000000 2.000000 1.000000
## 166 30.00000 1.920000 130.00000 2.000000 3.000000 1.000000 1.000000 0.000000
## 167 29.00000 1.740000 72.00000 3.000000 3.000000 2.000000 0.000000 0.000000
## 168 20.00000 1.650000 80.00000 2.000000 3.000000 2.000000 1.000000 2.000000
## 169 22.00000 1.730000 79.00000 2.000000 1.000000 2.000000 1.000000 0.000000
## 170 45.00000 1.630000 77.00000 2.000000 3.000000 1.000000 0.000000 0.000000
## 171 22.00000 1.720000 82.00000 2.000000 1.000000 2.000000 2.000000 1.000000
## 172 18.00000 1.600000 58.00000 2.000000 3.000000 2.000000 1.000000 0.000000
## 173 23.00000 1.650000 59.00000 3.000000 1.000000 2.000000 1.000000 2.000000
## 174 18.00000 1.740000 64.00000 3.000000 3.000000 2.000000 0.000000 1.000000
## 175 21.00000 1.620000 70.00000 2.000000 1.000000 3.000000 1.000000 0.000000
## 176 38.00000 1.640000 59.80000 2.000000 3.000000 2.000000 2.000000 0.000000
## 177 18.00000 1.570000 48.00000 3.000000 1.000000 1.000000 1.000000 0.000000
## 178 22.00000 1.840000 84.00000 3.000000 3.000000 2.000000 3.000000 0.000000
## 179 26.00000 1.910000 84.00000 3.000000 3.000000 2.000000 2.000000 2.000000
## 180 21.00000 1.620000 70.00000 2.000000 1.000000 3.000000 1.000000 0.000000
## 181 18.00000 1.580000 48.00000 2.000000 3.000000 2.000000 1.000000 0.000000
## 182 23.00000 1.680000 67.00000 2.000000 3.000000 1.000000 0.000000 0.000000
## 183 22.00000 1.680000 52.00000 3.000000 3.000000 2.000000 0.000000 1.000000
## 184 23.00000 1.480000 60.00000 2.000000 1.000000 1.000000 0.000000 0.000000
## 185 21.00000 1.620000 70.00000 2.000000 1.000000 3.000000 1.000000 0.000000
## 186 31.00000 1.620000 68.00000 3.000000 3.000000 2.000000 1.000000 0.000000
## 187 39.00000 1.780000 96.00000 2.000000 3.000000 3.000000 1.000000 0.000000
## 188 25.00000 1.780000 98.00000 2.000000 3.000000 3.000000 3.000000 2.000000
## 189 35.00000 1.780000 105.00000 3.000000 1.000000 3.000000 3.000000 1.000000
## 190 33.00000 1.630000 62.00000 2.000000 3.000000 2.000000 1.000000 1.000000
## 191 20.00000 1.600000 56.00000 2.000000 3.000000 2.000000 1.000000 0.000000
## 192 26.00000 1.750000 80.00000 3.000000 1.000000 2.000000 2.000000 0.000000
## 193 20.00000 1.830000 85.00000 3.000000 3.000000 3.000000 3.000000 0.000000
## 194 20.00000 1.780000 68.00000 2.000000 1.000000 3.000000 2.000000 1.000000
## 195 23.00000 1.600000 83.00000 3.000000 3.000000 3.000000 3.000000 0.000000
## 196 19.00000 1.800000 85.00000 3.000000 3.000000 2.000000 1.000000 1.000000
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## 521 19.00000 1.556211 42.33977 3.000000 2.084600 2.137550 0.196152 0.062488
## 522 19.00000 1.564199 42.09606 3.000000 1.894384 2.456581 1.596576 0.997400
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## 530 21.37643 1.722527 50.83303 3.000000 3.285167 1.569082 0.545931 0.469735
## 531 19.72411 1.734832 50.00000 1.123939 4.000000 1.000000 1.303976 0.371941
## 532 23.00000 1.882779 64.10611 3.000000 3.000000 2.843777 1.488843 0.009254
## 533 22.85183 1.854592 63.61111 3.000000 3.691226 2.650989 1.228136 0.832400
## 534 23.00000 1.835643 58.85442 3.000000 3.000000 2.027984 1.661556 0.114716
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## 539 18.76603 1.579561 41.89020 2.027574 1.000000 1.636326 0.000000 1.906141
## 540 18.54053 1.564568 41.39738 2.658112 1.000000 1.298165 0.000000 1.639326
## 541 19.88036 1.670635 49.74293 2.886260 3.559841 1.632004 2.000000 1.000000
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## 554 16.30687 1.752755 50.00000 2.310423 3.558637 1.787843 1.926592 0.828549
## 555 16.19815 1.691007 52.62937 2.000000 2.000986 2.673835 0.992950 0.474836
## 556 18.00000 1.753349 51.45723 2.823179 3.000000 1.773236 1.252472 1.000000
## 557 18.00000 1.781543 50.86970 2.052932 3.000000 2.000000 0.520408 1.000000
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## 559 17.48687 1.836669 58.94335 2.767731 3.821168 2.000000 2.000000 0.556245
## 560 19.92063 1.768493 57.79038 2.000000 3.897078 2.622638 2.000000 1.894105
## 561 18.42662 1.777108 57.14592 2.000000 3.092116 2.426465 2.000000 1.839862
## 562 17.08287 1.640824 43.36500 2.815157 3.000000 2.911187 2.595128 1.380204
## 563 17.00043 1.584951 44.41180 2.737762 3.000000 2.310921 2.240714 1.592570
## 564 16.27043 1.818268 47.12472 3.000000 3.286431 2.148146 2.458237 1.273333
## 565 17.90811 1.793926 59.68259 2.568063 4.000000 2.000000 2.000000 0.220029
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## 567 19.32954 1.767335 55.70050 2.000000 4.000000 2.157395 2.000000 1.679149
## 568 22.37800 1.699568 54.98774 3.000000 3.000000 2.000000 0.139808 0.875464
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## 571 19.30044 1.739354 49.64961 3.000000 3.754599 1.692112 2.000000 1.000000
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## 579 19.00000 1.530875 42.00000 2.844607 1.273128 1.695510 0.260079 0.635867
## 580 17.00000 1.848294 59.40902 2.440040 3.000000 2.000000 2.784471 1.000000
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## 584 21.78535 1.675054 49.94523 2.929889 3.000000 2.792074 0.630944 1.366355
## 585 23.00000 1.717601 51.07392 2.000000 3.000000 1.426874 2.202080 2.000000
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## 591 20.40005 1.529724 40.34346 2.703436 2.884479 1.439962 0.144627 0.322307
## 592 19.55673 1.767563 56.30702 2.362918 4.000000 2.358172 2.000000 0.939819
## 593 17.70368 1.883364 60.00000 3.000000 3.626815 2.000000 2.011519 0.456462
## 594 18.27436 1.824655 58.62135 2.140840 4.000000 2.931438 2.000000 1.164457
## 595 18.00000 1.840138 60.00000 3.000000 4.000000 2.000000 2.000000 0.000000
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## 598 18.00000 1.710800 50.92538 2.000000 3.000000 2.000000 0.000000 1.593704
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## 605 19.00000 1.538398 42.00000 2.718970 1.473088 1.164644 1.235675 0.930926
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## 607 18.00000 1.717826 51.73250 1.133844 3.000000 1.325326 0.227985 1.708309
## 608 18.42494 1.753389 54.12192 2.000000 3.166450 2.278578 1.838881 2.000000
## 609 18.00000 1.701650 50.15771 1.757466 3.000000 1.153559 0.833976 1.616045
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## 616 20.34516 1.534385 41.96525 2.888530 1.000000 1.000000 0.000000 0.196224
## 617 20.51992 1.725548 49.81560 2.890535 3.907790 1.109115 1.548953 0.555468
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## 619 21.47850 1.686936 51.25606 3.000000 3.179995 1.910378 0.480614 0.625079
## 620 18.37256 1.589829 40.20277 2.000000 1.075553 1.000000 0.127425 1.679442
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## 623 18.00674 1.700000 50.00000 1.003566 3.238258 1.014634 0.783676 1.000000
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## 626 18.00000 1.788459 51.55259 2.897899 3.000000 1.835545 1.162519 1.000000
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## 658 19.05283 1.546551 42.06999 3.000000 1.735493 2.318736 1.193486 0.745680
## 659 19.59904 1.566501 41.70628 2.967853 1.000000 1.131185 0.000000 0.504176
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## 667 18.90944 1.732096 50.00000 1.053534 3.378859 1.000000 1.853425 0.861809
## 668 22.39650 1.869098 61.41114 3.000000 3.263201 2.233274 1.557737 0.000355
## 669 19.08432 1.851123 61.26479 3.000000 3.994588 2.548527 1.285976 0.267076
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## 673 18.03842 1.698914 51.69227 2.824559 3.000000 2.000000 0.533309 1.099764
## 674 18.87459 1.533609 41.66935 2.762325 1.163666 1.304910 0.252890 1.001405
## 675 19.21164 1.567981 41.93437 2.070964 1.000000 1.676975 0.000000 1.718513
## 676 18.98858 1.544263 41.53505 2.686010 1.000000 1.310074 0.000000 1.064700
## 677 19.40900 1.670552 49.80425 2.794197 3.409363 1.543021 2.000000 1.000000
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## 681 20.24224 1.756330 54.56734 2.000000 3.985250 2.654078 2.113151 2.000000
## 682 22.63702 1.703584 51.60709 2.559960 3.000000 1.990788 0.486006 1.561272
## 683 19.00718 1.690727 49.89572 1.212908 3.207071 1.029703 2.000000 1.000000
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## 687 25.38056 1.630379 46.06295 2.690754 3.037790 2.212296 1.616882 0.000000
## 688 22.86772 1.655413 50.42466 3.000000 3.642802 1.995177 0.118271 0.065515
## 689 17.72992 1.732862 51.21646 2.051283 2.645858 2.357520 0.291309 0.897942
## 690 16.83481 1.744020 50.00000 2.190050 3.420618 1.356405 1.351996 0.984680
## 691 17.52175 1.757958 52.09432 2.214980 2.641550 2.121251 0.998391 0.858820
## 692 18.00000 1.786758 51.52444 2.915480 3.000000 1.777486 1.077469 1.000000
## 693 18.00000 1.767058 51.13281 2.708965 3.000000 1.873004 1.217180 1.000000
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## 696 19.72925 1.793315 58.19515 2.508835 3.435905 2.076933 2.026668 1.443328
## 697 18.52583 1.776989 57.27595 2.000000 3.747163 2.575535 2.000000 1.843830
## 698 18.59561 1.609495 42.65656 2.896562 2.625475 2.839558 1.949667 1.253311
## 699 16.61311 1.777929 44.76202 2.911877 3.098399 2.196405 2.328147 1.550110
## 700 16.92879 1.710948 45.24863 2.910733 3.125440 2.204263 2.407906 1.403037
## 701 17.75831 1.854162 59.88132 2.966126 3.969810 2.000000 2.000088 0.378619
## 702 17.28295 1.821514 59.60503 2.613249 3.712183 2.000000 2.002997 0.174848
## 703 19.99315 1.762073 55.51107 2.000000 4.000000 2.542415 2.000000 1.807465
## 704 22.93561 1.732307 54.83558 3.000000 3.000000 2.003570 1.259550 0.417116
## 705 20.73847 1.759933 55.00342 2.627031 3.832911 2.993448 2.000000 1.425903
## 706 22.99368 1.741377 54.87711 3.000000 3.000000 2.009796 2.000000 0.071317
## 707 19.31715 1.731195 49.65090 2.919751 3.576103 1.949308 1.940182 1.000000
## 708 16.91100 1.748230 49.92845 2.494451 3.565440 1.491268 1.951027 0.956204
## 709 19.07103 1.756865 49.69967 1.694270 3.266644 1.095417 2.000000 1.000000
## 710 18.01957 1.701378 50.08847 1.601236 3.433908 1.055019 0.819269 1.030848
## 711 19.73597 1.699956 49.98297 1.204855 3.531038 1.134658 2.000000 1.000000
## 712 18.09408 1.723328 50.00000 1.052699 3.998618 1.000000 2.000000 1.000000
## 713 19.05494 1.585886 42.54179 2.910345 3.000000 1.000000 1.461005 0.000000
## 714 20.85012 1.524926 42.00000 2.866383 1.226342 1.000000 0.144950 0.000000
## 715 19.34926 1.523370 42.00000 2.913486 1.060796 1.596212 0.108948 0.773087
## 716 17.00000 1.844749 59.31352 2.432886 3.000000 2.000000 2.697949 1.000000
## 717 17.20392 1.853325 59.61948 2.883745 3.595761 2.000000 2.077653 0.714701
## 718 17.67106 1.854706 59.20945 2.707666 3.737914 2.026547 2.009397 0.613971
## 719 21.31091 1.720640 50.00000 2.919584 3.697831 1.147121 0.993058 0.089220
## 720 21.70835 1.704167 50.16575 2.969205 3.210430 2.765876 0.611037 1.300692
## 721 22.17692 1.717460 51.49196 2.486189 3.000000 1.064378 2.206055 1.958089
## 722 17.82344 1.708406 50.00000 1.642241 3.452590 1.099231 0.418875 1.000000
## 723 18.00000 1.763465 50.27905 1.567101 3.000000 1.994139 0.107981 1.000000
## 724 18.28109 1.700000 50.00000 1.036414 3.205587 1.745959 0.115974 1.000000
## 725 18.65691 1.574017 41.22017 1.649974 1.513835 1.549974 0.227802 1.972926
## 726 19.99454 1.537739 39.10180 1.118436 3.000000 1.997744 2.432443 1.626194
## 727 20.25562 1.534223 41.26860 2.673638 2.779379 1.249074 0.043412 0.403694
## 728 19.86589 1.760330 55.37070 2.120185 4.000000 2.582165 2.000000 1.510609
## 729 17.88807 1.841879 60.00000 3.000000 3.732126 2.000000 2.000934 0.384662
## 730 18.47056 1.856406 58.67396 2.342220 3.937099 2.311791 2.013377 1.128355
## 731 17.92550 1.829142 59.93301 2.860990 4.000000 2.000000 2.000000 0.007872
## 732 17.00075 1.822084 58.44305 2.559571 3.047959 2.000000 2.011646 0.588994
## 733 17.36213 1.806710 59.24351 2.424977 4.000000 2.000000 2.000000 0.039210
## 734 18.00000 1.707259 50.66446 1.786841 3.000000 1.546856 0.512094 1.608265
## 735 18.00000 1.708107 51.31466 1.303878 3.000000 1.755497 0.062932 1.672532
## 736 18.00000 1.739344 50.95144 1.889883 3.000000 1.959531 0.520407 1.151166
## 737 19.02949 1.573987 44.31625 2.984004 3.000000 1.015249 1.327833 0.000000
## 738 19.26908 1.580920 44.75394 3.000000 2.975362 1.246822 0.979701 0.000000
## 739 19.94624 1.603435 45.00000 3.000000 3.000000 2.487919 1.230441 0.000000
## 740 19.63943 1.535350 42.00000 3.000000 1.000000 1.496810 0.000000 0.513427
## 741 19.00000 1.531610 42.00000 2.749268 1.394539 1.322048 0.463949 0.800993
## 742 19.43471 1.525691 42.00000 3.000000 1.000000 1.764055 0.000000 0.560887
## 743 18.00000 1.719827 52.28983 1.202075 3.000000 1.927976 0.023574 1.747256
## 744 18.38138 1.722547 53.78398 2.000000 3.131032 2.072194 1.487987 2.000000
## 745 18.00000 1.738702 50.24868 1.871213 3.000000 1.283738 0.684879 1.487223
## 746 26.69858 1.816298 86.96376 2.341133 1.578521 2.000000 2.000000 0.554072
## 747 21.12584 1.638085 70.00000 2.000000 1.000000 2.115967 0.770536 0.000000
## 748 25.19163 1.813678 85.63779 1.450218 3.985442 2.147746 0.046836 1.000000
## 749 21.96346 1.697228 75.57710 2.204914 3.623364 1.815293 0.989316 0.000000
## 750 21.00000 1.617469 68.86979 1.206276 3.000000 2.406541 0.949840 0.479221
## 751 19.11498 1.855543 88.96552 2.000000 3.000000 1.015677 0.000000 0.374650
## 752 41.82357 1.721854 82.91958 2.816460 3.363130 2.722063 3.000000 0.265790
## 753 21.14243 1.855353 86.41339 2.000000 3.000000 1.345298 1.097905 1.000000
## 754 21.96243 1.696336 75.00000 2.000000 3.000000 1.825629 0.699592 0.142056
## 755 18.83631 1.751631 80.00000 2.000000 1.737620 2.207978 2.641072 0.707044
## 756 23.57265 1.698346 75.00000 2.000000 3.000000 2.000000 0.345684 1.415536
## 757 33.70075 1.642971 74.80316 3.000000 1.146052 1.074048 0.679935 0.000000
## 758 21.84502 1.613668 68.12695 1.758394 3.981997 2.174248 0.920476 1.358163
## 759 21.00000 1.605404 68.22651 2.000000 1.915400 3.000000 1.000000 0.000000
## 760 35.12540 1.529834 62.90394 2.000000 2.105616 1.456581 0.000000 0.997400
## 761 36.76965 1.550000 62.33772 2.392665 3.000000 2.951056 0.000000 0.369134
## 762 21.86893 1.731261 78.17571 2.577427 1.000000 2.000000 2.287423 0.000000
## 763 22.54921 1.629194 70.00000 2.000000 1.000000 2.803311 0.245354 0.000000
## 764 21.00000 1.620000 70.00000 2.000000 1.000000 3.000000 1.000000 0.000000
## 765 21.00000 1.620000 70.00000 2.000000 1.000000 3.000000 1.000000 0.000000
## 766 30.95896 1.633491 68.80369 2.052152 3.000000 1.972074 0.228307 0.000000
## 767 21.01738 1.752391 79.10964 3.000000 1.000000 2.000000 2.572230 0.000000
## 768 19.62357 1.818226 85.83303 2.954996 3.714833 2.430918 2.545931 0.469735
## 769 19.63795 1.809101 85.00000 3.000000 3.000000 2.229171 1.607953 0.628059
## 770 21.41364 1.709484 75.00000 2.000000 3.000000 2.843777 2.022315 0.009254
## 771 21.02963 1.607082 67.72222 2.000000 3.691226 3.000000 1.228136 0.335200
## 772 22.66760 1.718939 75.95147 2.000000 3.000000 2.000000 0.000000 2.000000
## 773 20.00000 1.831357 89.65256 2.555401 3.292386 3.000000 2.000000 0.315918
## 774 21.81119 1.600000 66.40141 2.108711 3.000000 2.746197 1.910432 0.000000
## 775 21.00000 1.754813 77.92920 2.915279 1.104642 1.530046 1.360635 0.000000
## 776 18.12821 1.778447 80.27381 1.570089 3.000000 2.000000 2.707882 0.000000
## 777 21.00000 1.709561 75.00000 2.000000 3.000000 1.636326 1.000000 0.000000
## 778 29.08107 1.674568 71.60262 2.000000 3.000000 1.701835 1.682271 0.000000
## 779 26.35892 1.755317 82.22879 1.943130 3.559841 2.367996 0.235530 0.879977
## 780 22.71725 1.708071 75.00000 2.714447 3.000000 3.000000 1.096818 1.893880
## 781 19.81695 1.806947 85.07959 2.000000 3.000000 2.292073 1.067817 0.196680
## 782 24.02397 1.599697 64.80802 2.903545 3.000000 1.549931 0.000000 0.273882
## 783 32.59313 1.721903 72.74890 2.000000 3.000000 1.000000 0.000000 1.339232
## 784 23.00000 1.712556 75.48076 3.000000 3.654061 1.229915 0.793489 1.597608
## 785 16.94149 1.551288 54.93242 1.753750 1.296156 2.000000 0.110174 1.944675
## 786 16.17299 1.603842 65.00000 2.543563 1.000000 2.000000 0.694281 1.056911
## 787 23.71259 1.588597 62.33900 2.397280 2.656588 2.061062 1.912981 1.887386
## 788 35.19409 1.673482 73.19359 3.000000 2.809716 1.591425 0.178023 0.000000
## 789 23.17298 1.858624 88.67550 2.000000 2.776840 1.278231 0.557130 1.000000
## 790 37.21816 1.593894 63.32063 2.374640 3.000000 2.000000 2.892922 0.480813
## 791 19.07644 1.620000 69.52962 2.278644 1.000000 2.628985 1.000000 1.285373
## 792 16.30687 1.616366 67.18313 1.620845 1.000000 2.000000 0.926592 1.657098
## 793 18.29723 1.637396 70.00000 2.000000 1.999014 2.326165 0.007050 0.000000
## 794 18.61076 1.550723 60.62832 2.823179 2.644692 1.226764 0.747528 0.008899
## 795 17.45108 1.600000 65.00000 3.000000 2.449723 2.000000 0.479592 1.720642
## 796 29.74050 1.820471 87.66883 3.000000 3.000000 1.174611 2.000000 0.000000
## 797 31.53939 1.657496 73.64163 2.000000 3.000000 1.000000 0.000000 1.112489
## 798 18.02646 1.752123 80.00000 2.000000 2.794156 2.377362 0.101236 0.105895
## 799 19.47554 1.857231 88.13878 2.061952 4.000000 2.426465 2.000000 0.160138
## 800 19.00000 1.760000 79.54500 2.000000 1.146794 3.000000 1.809745 1.690102
## 801 18.00000 1.644682 68.39213 2.000000 1.131695 1.344539 0.000000 1.592570
## 802 18.27043 1.737165 76.69977 2.838969 3.000000 2.425927 1.000000 1.453335
## 803 19.81623 1.507853 64.25938 2.568063 3.000000 1.817983 0.000000 0.000000
## 804 28.39124 1.810060 87.28678 3.000000 3.000000 1.205633 2.000000 0.000000
## 805 26.75852 1.801790 86.98120 2.652958 2.488189 2.000000 2.000000 0.096614
## 806 21.03379 1.625891 70.00000 2.000000 1.000000 2.008760 0.631190 0.000000
## 807 22.42981 1.640370 70.00000 2.000000 1.000000 2.069184 0.729898 0.000000
## 808 26.65042 1.791047 83.26312 1.277850 3.999591 2.495944 0.003420 1.000000
## 809 21.61825 1.679306 75.00000 2.000000 3.000000 1.957871 0.994592 0.117303
## 810 21.01254 1.615145 68.65335 1.729824 3.612941 2.043703 0.562118 0.426643
## 811 21.07119 1.616467 68.77185 1.452524 3.950553 2.109858 0.508847 1.194633
## 812 19.74120 1.816783 86.52280 2.000000 3.000000 2.177386 0.336814 0.004813
## 813 19.21638 1.812472 86.74829 2.000000 3.000000 2.168651 0.977998 0.142638
## 814 42.24475 1.768231 75.62931 3.000000 2.951837 2.112032 0.378683 0.000000
## 815 22.28308 1.870931 89.25164 2.000000 2.799979 1.081333 0.444347 1.000000
## 816 21.08651 1.863685 89.55885 2.000000 3.000000 1.005727 0.000000 0.798219
## 817 23.45160 1.670227 75.00000 2.000000 3.000000 2.000000 0.129163 1.983678
## 818 22.74028 1.717288 75.94816 2.000000 3.000000 2.000000 0.000000 2.000000
## 819 18.90025 1.750359 79.82873 2.000000 2.228113 2.045004 1.293665 0.961806
## 820 23.17031 1.707557 75.30670 2.303367 3.042774 1.277636 0.944982 0.366126
## 821 32.99712 1.672446 74.81271 2.948425 1.198643 1.000000 0.000000 0.173796
## 822 32.50114 1.675979 74.95975 2.291846 1.555557 1.000000 0.000000 0.388271
## 823 21.93883 1.611239 67.93965 1.906194 3.987707 2.597746 1.922234 1.376124
## 824 21.90953 1.611356 68.06609 1.834155 3.995957 2.632871 1.236114 1.980875
## 825 21.00000 1.620000 70.00000 2.000000 1.000000 3.000000 1.000000 0.000000
## 826 37.45575 1.508908 63.18385 2.048582 1.047197 2.000000 0.151360 0.225960
## 827 40.00000 1.561109 62.87179 2.948248 3.000000 2.429911 0.119640 0.360193
## 828 38.94328 1.554728 63.01165 2.869436 3.000000 2.972426 2.160790 0.305954
## 829 21.98734 1.730182 78.55444 2.293705 1.000000 2.000000 2.063943 0.000000
## 830 21.19822 1.743841 78.88036 2.510583 1.000000 2.000000 2.119682 0.000000
## 831 21.00000 1.620000 70.00000 2.000000 1.000000 3.000000 1.000000 0.000000
## 832 21.00000 1.620000 70.00000 2.000000 1.000000 3.000000 1.000000 0.000000
## 833 21.00000 1.620000 70.00000 2.000000 1.000000 3.000000 1.000000 0.000000
## 834 21.00000 1.620000 70.00000 2.000000 1.000000 3.000000 1.000000 0.000000
## 835 21.00000 1.620000 70.00000 2.000000 1.000000 3.000000 1.000000 0.000000
## 836 29.32038 1.642506 69.90671 2.366949 3.000000 1.926577 1.581242 0.000000
## 837 31.25559 1.693080 71.92738 2.615788 3.000000 1.771781 0.759422 0.686529
## 838 22.85177 1.752115 79.41460 3.000000 1.000000 2.000000 2.315983 0.000000
## 839 26.00000 1.745033 80.00000 2.217267 1.193589 2.000000 2.000000 0.000000
## 840 19.78929 1.820643 85.00000 3.000000 3.000000 2.759246 1.763277 0.453314
## 841 19.89588 1.807330 85.07380 2.801514 3.000000 2.734782 2.207881 0.143675
## 842 19.69380 1.800000 85.00000 2.188722 3.000000 2.721356 1.528968 1.000000
## 843 19.22631 1.814255 85.25563 2.971351 3.390143 2.133767 2.318492 0.678618
## 844 21.65223 1.700181 75.05718 2.086093 3.546352 2.081121 1.993666 0.673835
## 845 21.68741 1.604697 68.01647 1.901611 3.266501 2.926995 0.985872 0.307982
## 846 21.45546 1.611000 68.10787 1.977298 3.554974 2.217957 0.978120 0.459759
## 847 21.00000 1.754497 77.95692 2.446872 2.372311 1.810310 0.094893 1.650778
## 848 21.00000 1.752944 77.96553 2.839048 2.106010 1.639202 1.117311 0.967919
## 849 19.33740 1.859927 87.10583 2.212320 4.000000 2.374044 2.000000 0.622638
## 850 21.70164 1.896073 90.52446 2.427689 3.715306 2.876096 1.815768 0.426465
## 851 21.62025 1.605314 66.62165 2.357496 3.376717 2.184843 1.358185 0.014885
## 852 21.01257 1.758628 78.37004 3.000000 1.000000 2.000000 2.971832 0.000000
## 853 21.01662 1.755427 78.30008 3.000000 1.000000 2.000000 2.877473 0.000000
## 854 19.00000 1.779882 80.09189 1.078529 1.211606 2.568063 3.000000 0.817983
## 855 21.00000 1.712061 75.00000 2.000000 3.000000 1.333707 1.000000 0.000000
## 856 21.00000 1.676014 75.00000 2.000000 3.000000 1.164062 1.000000 0.000000
## 857 27.89978 1.700000 74.24400 2.000000 3.000000 2.000000 1.722053 0.000000
## 858 28.82522 1.765874 82.04505 1.064162 3.989550 2.028426 0.815170 0.894678
## 859 26.04708 1.745950 80.01857 1.993101 3.171082 2.364498 1.224743 0.022245
## 860 23.00000 1.690196 75.00000 2.620963 3.000000 2.824559 0.754599 2.000000
## 861 20.00000 1.817480 85.00000 2.951180 3.000000 3.000000 2.433918 0.561602
## 862 21.83300 1.580964 65.36394 2.021446 3.000000 1.077917 0.523847 0.808599
## 863 30.25574 1.652084 73.57598 2.000000 3.000000 1.000000 0.000000 0.018877
## 864 30.61359 1.645511 69.16898 2.000466 3.000000 1.131448 0.061366 0.000000
## 865 23.24541 1.707968 75.38372 2.562100 3.105007 1.172427 0.184917 0.923082
## 866 18.00000 1.456346 55.52348 2.000000 3.000000 1.040342 0.497373 1.783319
## 867 18.00000 1.498561 55.37651 2.000000 3.000000 1.274718 0.129902 0.978574
## 868 16.95050 1.603501 65.00000 2.960080 1.000000 2.000000 0.736032 1.344072
## 869 21.83706 1.558045 63.59763 2.539150 1.590982 1.977801 1.264616 0.000000
## 870 27.00000 1.550000 62.87735 2.244142 1.704828 1.000000 0.792929 0.395468
## 871 35.48360 1.647514 73.91692 3.000000 2.725012 1.622440 0.902661 0.000000
## 872 23.80144 1.855779 86.09852 2.000000 2.372339 1.675733 1.066241 1.000000
## 873 23.36721 1.853223 87.08327 2.000000 1.097312 1.328835 1.264257 1.000000
## 874 40.00000 1.570811 62.21157 2.253371 3.000000 2.756916 1.016042 0.213437
## 875 16.38009 1.617124 67.91356 2.851664 1.000000 2.000000 0.977929 1.765321
## 876 16.86598 1.644053 67.43959 1.314150 1.068196 1.364957 0.000000 0.057926
## 877 16.09323 1.608914 65.00000 1.321028 1.000000 2.000000 0.371452 0.965604
## 878 18.00000 1.647971 68.81889 2.000000 1.411685 1.859089 0.000000 1.306000
## 879 18.83919 1.624831 69.97561 2.253998 2.752318 2.328331 0.815509 0.024088
## 880 19.72652 1.508267 61.10403 2.778079 3.000000 1.696691 0.942240 0.879925
## 881 18.94710 1.518917 60.26743 2.838037 2.737571 1.144467 0.753782 1.286844
## 882 17.78118 1.600000 65.00000 3.000000 2.973504 2.000000 0.178976 0.166076
## 883 33.10058 1.838791 87.85785 2.814453 2.608055 1.859160 2.000000 0.516084
## 884 33.25102 1.730379 75.92052 2.013782 2.625942 1.045586 0.553305 0.480214
## 885 18.98512 1.759117 80.00000 2.000000 1.411808 2.651194 2.878414 0.953841
## 886 18.87192 1.755254 80.00000 2.000000 1.095223 2.474132 2.876696 0.793900
## 887 19.47853 1.804099 85.19628 2.459976 3.308460 2.078011 1.779646 0.871772
## 888 19.42972 1.813567 86.14490 2.643183 3.821461 2.397124 2.044165 0.471663
## 889 20.97925 1.756550 78.72170 2.000000 3.000000 2.813234 0.228753 2.000000
## 890 18.86915 1.756774 79.98979 2.000000 2.658639 2.781628 1.955992 1.409198
## 891 18.23609 1.620000 69.38990 2.223990 1.000000 2.203120 0.104451 1.899073
## 892 20.90139 1.709585 75.00000 2.104105 3.000000 1.871033 1.000000 0.000000
## 893 17.08525 1.535618 57.25912 1.972545 2.339614 1.711074 0.095517 1.191053
## 894 25.78592 1.818848 87.03240 2.286481 1.713762 1.797161 1.658698 0.926581
## 895 26.78784 1.817641 87.10732 2.971588 2.743277 1.394883 2.000000 0.470243
## 896 21.03751 1.636592 70.00000 2.000000 1.000000 2.881677 0.915699 0.000000
## 897 21.00829 1.621412 70.00000 2.000000 1.000000 2.795651 0.808730 0.000000
## 898 26.70371 1.802871 85.77001 2.872121 3.051804 2.111913 0.843709 0.153559
## 899 21.73150 1.696201 75.39919 2.109162 3.245148 1.971774 0.989335 0.000000
## 900 21.05289 1.694633 75.05220 2.178889 3.563744 1.853991 0.997731 0.000000
## 901 21.00000 1.618148 68.98140 1.142468 3.000000 2.197732 0.827506 0.572877
## 902 19.24106 1.856811 88.63362 2.047069 3.829101 1.641022 1.554817 0.248218
## 903 38.93945 1.738321 86.93485 2.843709 3.058539 1.130079 2.834373 0.044954
## 904 39.96547 1.739293 80.91438 2.416044 3.196043 1.352649 0.148628 1.082660
## 905 20.26193 1.807538 85.31612 2.000000 3.000000 1.968011 1.072662 0.776758
## 906 20.31094 1.849425 85.22812 2.146598 3.000000 2.100112 1.171160 0.833761
## 907 21.42054 1.712473 75.00000 2.000000 3.000000 1.362642 0.921268 0.139013
## 908 18.84552 1.753471 80.00000 2.000000 1.391778 2.645480 2.685087 0.975540
## 909 23.56214 1.717432 75.37124 2.000000 3.000000 2.000000 0.121585 1.967259
## 910 23.11833 1.677573 75.00000 2.000000 3.000000 2.000000 0.334579 1.905826
## 911 33.73271 1.679725 74.88522 3.000000 1.137150 1.000695 0.261274 0.000000
## 912 21.57129 1.600914 68.05890 1.766849 3.322522 2.616285 0.943058 0.256977
## 913 21.16557 1.617749 68.90814 1.188089 3.269088 2.039535 0.779686 1.043108
## 914 21.00000 1.610209 68.86501 1.910176 2.938135 2.943097 0.997202 0.207922
## 915 21.00000 1.612556 69.46346 2.000000 1.259628 3.000000 1.000000 0.000000
## 916 38.69226 1.548178 62.34144 2.956671 2.965494 2.868132 0.000000 0.549250
## 917 38.95287 1.568441 62.85507 2.002796 3.000000 2.526775 0.271174 0.806069
## 918 36.63146 1.532322 62.41723 2.288604 2.845307 2.638164 0.000000 0.990741
## 919 21.99612 1.730199 78.99706 2.277077 1.000000 2.000000 1.061743 0.000000
## 920 21.95131 1.730167 78.42931 2.138334 1.000000 2.000000 2.269058 0.000000
## 921 22.01823 1.627396 70.00000 2.000000 1.000000 2.976177 0.780117 0.000000
## 922 21.00000 1.620000 70.00000 2.000000 1.000000 3.000000 1.000000 0.000000
## 923 21.00000 1.620000 70.00000 2.000000 1.000000 3.000000 1.000000 0.000000
## 924 21.00000 1.620000 70.00000 2.000000 1.000000 3.000000 1.000000 0.000000
## 925 29.93446 1.638744 69.24235 2.029634 3.000000 1.827515 0.480206 0.000000
## 926 31.16657 1.680858 71.81338 2.048216 3.000000 1.305816 0.170452 0.276806
## 927 20.53461 1.758372 79.46951 2.855700 1.000000 2.663861 2.762711 0.783336
## 928 19.97166 1.822573 85.08436 2.995599 3.095663 2.568157 2.724300 0.330457
## 929 19.62700 1.815409 85.30215 2.987148 3.483449 2.359246 2.060415 0.598999
## 930 21.92939 1.698049 75.00000 2.000000 3.000000 2.763573 1.502711 0.127879
## 931 21.00944 1.606810 67.77391 2.000000 3.156309 3.000000 1.179592 0.086868
## 932 21.53823 1.610327 67.99978 1.887951 3.728377 2.682107 1.123931 0.492528
## 933 22.82843 1.710415 75.14286 2.786008 3.000000 2.526193 0.925118 2.000000
## 934 22.81466 1.716289 75.68843 2.000000 3.000000 2.000000 0.092344 1.466496
## 935 19.57668 1.834715 89.42920 2.342323 3.608850 2.878866 2.000000 0.208323
## 936 21.81465 1.611822 67.14037 1.874935 3.370362 2.558773 1.206121 0.271024
## 937 21.97977 1.600000 66.12696 2.213135 3.000000 2.046766 2.172546 0.000000
## 938 21.00000 1.753578 77.97917 2.273548 2.390070 1.648404 0.874643 1.102696
## 939 21.02850 1.742364 78.66462 2.780699 1.101404 1.579207 1.153775 0.000000
## 940 18.72104 1.775626 80.11349 1.687569 2.756405 2.079131 2.931527 0.681730
## 941 21.00000 1.714253 75.00000 2.000000 3.000000 1.081597 1.000000 0.000000
## 942 21.00000 1.693628 75.00000 2.000000 3.000000 1.833055 1.000000 0.000000
## 943 29.46317 1.659172 71.17000 2.000000 3.000000 1.281683 1.609801 0.000000
## 944 24.28486 1.776347 82.32905 1.989905 3.054899 2.080968 1.107543 0.939726
## 945 26.28842 1.767806 82.69469 1.947405 3.118013 2.136159 0.783963 0.888680
## 946 23.45532 1.702516 75.00000 2.162519 3.000000 2.152666 1.078074 1.502839
## 947 19.63720 1.814182 85.30103 2.923916 3.335876 2.372444 1.305633 0.311436
## 948 22.23984 1.599940 65.42394 2.994480 3.000000 1.706568 0.784216 0.150969
## 949 31.62638 1.666023 72.90619 2.000000 3.000000 1.000000 0.000000 1.301385
## 950 23.00000 1.701584 75.09357 3.000000 3.205009 2.643468 0.998039 1.898139
## 951 22.87466 1.713343 75.82812 2.507841 3.648194 1.279756 0.132629 1.827530
## 952 17.42027 1.489409 53.62060 1.836554 1.865238 2.000000 0.320209 1.969507
## 953 17.80783 1.518067 55.82212 1.773265 2.118153 1.075239 0.085388 1.915191
## 954 16.24058 1.616533 65.06294 2.388168 1.000000 1.438018 0.110887 1.165817
## 955 23.25246 1.589616 65.12732 2.286146 2.961113 2.657303 1.911080 1.618227
## 956 34.77290 1.675612 73.50123 3.000000 2.400943 1.509734 0.167125 0.000000
## 957 22.76623 1.874061 89.75430 2.000000 2.870005 1.150310 0.417724 1.000000
## 958 39.21451 1.580765 62.63138 2.487167 3.000000 2.396977 0.577063 0.435072
## 959 19.85897 1.620000 69.57532 2.185938 1.000000 2.813530 1.000000 1.110222
## 960 16.37001 1.613921 66.73877 2.206399 1.000000 2.000000 0.948930 1.772463
## 961 17.99272 1.618683 67.19358 1.952987 1.000000 1.334856 0.732276 1.890214
## 962 19.17993 1.637537 70.00000 2.000000 1.030416 2.118716 0.529259 0.000000
## 963 19.62155 1.566524 61.61600 2.908757 2.696051 1.622827 0.539952 0.001096
## 964 19.75580 1.542328 63.85619 2.628791 2.762883 1.512035 0.303722 0.003229
## 965 17.09902 1.600000 65.00000 3.000000 2.401341 2.000000 0.663896 1.753745
## 966 17.25813 1.600184 65.00000 2.749629 2.298612 2.000000 0.547515 1.619473
## 967 29.15391 1.773656 87.07023 1.595746 3.618722 1.274389 1.504003 0.370067
## 968 32.27887 1.646020 74.14744 2.885178 2.562895 1.017006 0.588673 0.916291
## 969 31.79394 1.650150 73.81073 2.372494 2.849848 1.028538 0.675983 0.303025
## 970 18.01433 1.751029 80.00000 2.000000 2.805436 2.122884 0.045651 0.017225
## 971 19.68500 1.838266 89.49690 2.153639 3.715148 2.703337 2.000000 0.226097
## 972 19.50639 1.824449 87.65603 2.793561 3.788602 2.429059 2.094542 0.393358
## 973 19.00000 1.760000 79.34922 2.000000 1.893811 3.000000 1.376229 1.801322
## 974 18.00000 1.622241 68.25025 2.000000 1.010319 1.319437 0.000000 1.626456
## 975 18.00315 1.729996 75.81686 2.992329 3.000000 2.004908 1.000000 1.405086
## 976 18.05239 1.725233 75.97071 2.927409 3.000000 2.209991 1.000000 0.797215
## 977 19.77432 1.541039 64.72695 2.706134 2.669766 1.979848 0.445238 0.908836
## 978 21.18035 1.773766 89.28282 2.010684 1.322087 2.000000 0.540397 0.973834
## 979 21.79372 1.754630 89.06823 2.000000 2.041558 2.387250 0.813917 0.000000
## 980 20.88016 1.674327 80.00000 2.000000 3.000000 2.000000 1.666390 1.443212
## 981 21.18354 1.720000 80.55588 2.000000 2.468421 2.000000 2.000000 1.000000
## 982 32.77449 1.913241 101.48205 2.000000 2.110937 2.175632 1.000000 0.000000
## 983 31.32761 1.737984 82.52311 2.300408 3.071028 1.738959 0.090147 0.000000
## 984 29.95620 1.703688 82.20798 2.119643 3.292956 1.723372 0.000000 0.987102
## 985 21.40342 1.716308 80.00000 2.000000 3.000000 2.000000 2.936551 1.409130
## 986 22.59144 1.650000 80.00000 2.000000 3.000000 2.000000 0.451078 2.000000
## 987 28.58394 1.578560 65.52274 2.000000 2.283673 1.970622 1.863258 1.581703
## 988 38.82519 1.780846 85.68775 2.901924 1.124977 2.763820 0.855400 0.999183
## 989 35.21717 1.823168 91.63026 2.000000 2.994800 1.290979 0.875990 0.854050
## 990 20.39267 1.525234 65.22025 2.451009 3.000000 2.000000 2.177243 1.323877
## 991 22.15485 1.481682 61.37387 2.000000 2.983297 1.453626 0.328960 0.509396
## 992 19.10880 1.768578 87.80331 2.754646 3.000000 2.957821 2.242754 0.786609
## 993 20.70768 1.569878 69.74332 2.417635 3.000000 1.937674 1.417035 1.000000
## 994 20.63469 1.568188 67.90402 2.512719 3.000000 1.131169 0.095389 1.000000
## 995 22.05215 1.792527 89.99442 1.771693 1.890213 2.000000 0.000000 1.365950
## 996 22.86978 1.795311 89.86878 1.572230 1.888067 2.000000 0.000000 0.552498
## 997 22.90999 1.700038 80.00000 2.000000 3.000000 2.000000 0.973114 1.540298
## 998 23.00000 1.668649 80.45834 2.000000 2.256119 1.142873 0.807076 1.611271
## 999 24.67981 1.700000 84.68755 2.000000 3.000000 2.020424 0.000000 1.000000
## 1000 23.88421 1.713825 83.95297 2.000000 2.664800 1.810738 0.809890 1.000000
## 1001 25.46141 1.700000 78.05597 2.661556 3.000000 3.000000 0.551810 0.658783
## 1002 31.33380 1.835381 91.05960 2.000000 3.000000 1.184230 0.155579 0.453404
## 1003 24.10871 1.700000 80.76141 2.000000 3.000000 2.879402 0.000000 0.322405
## 1004 28.83056 1.700000 78.00000 3.000000 3.000000 1.699971 1.727114 1.000000
## 1005 17.57009 1.700000 83.19903 2.097373 2.547086 1.538626 1.000000 0.761898
## 1006 19.02757 1.659877 77.27265 2.061461 2.812283 3.000000 0.362441 0.785190
## 1007 25.63245 1.836943 96.19266 1.317729 2.278652 2.000000 1.806740 1.939770
## 1008 22.94313 1.819614 93.08642 1.882235 1.240046 2.000000 0.000000 1.541493
## 1009 23.28555 1.717775 85.31264 2.951591 3.000000 2.971557 0.000000 0.947192
## 1010 23.00000 1.791867 90.00000 2.067817 3.000000 1.082084 0.000000 1.922364
## 1011 25.19291 1.700000 80.74966 2.545270 3.000000 2.269564 0.503122 1.000000
## 1012 34.38991 1.681080 83.56803 2.000000 1.660768 2.482294 0.891205 0.000000
## 1013 26.59589 1.660756 78.57479 2.000000 2.597608 2.000000 0.000000 0.434198
## 1014 55.24625 1.769269 80.49134 2.000000 3.000000 2.000000 1.000000 0.000000
## 1015 34.54356 1.765188 85.00000 2.694281 3.000000 2.653831 1.965820 0.891189
## 1016 21.80816 1.650000 80.00000 2.000000 3.000000 2.000000 0.826609 2.000000
## 1017 18.11828 1.654757 80.00000 2.821977 2.044035 1.954968 1.000000 0.854536
## 1018 42.18902 1.647768 79.16531 2.000000 3.000000 1.000000 0.000000 1.481890
## 1019 22.00000 1.691303 80.53900 2.000000 2.038373 2.000000 2.708250 1.506576
## 1020 28.77085 1.532897 65.03188 2.000000 1.000000 1.000000 0.262171 0.000000
## 1021 25.48338 1.565288 64.84863 2.000000 1.000000 1.000000 0.740633 0.000000
## 1022 21.67315 1.500000 63.65233 2.000000 1.474836 2.000000 0.274838 0.613902
## 1023 23.46954 1.507106 64.81411 2.252472 3.986652 2.000000 0.934286 0.890626
## 1024 23.00000 1.700740 81.32297 2.000000 2.720642 1.519700 0.279375 1.043435
## 1025 23.00000 1.715118 81.65078 2.000000 1.976744 1.628997 0.880584 1.127675
## 1026 38.46454 1.696423 78.96792 3.000000 3.000000 2.981604 0.000000 0.000000
## 1027 37.49618 1.653088 80.00000 2.033745 3.000000 1.517225 0.000000 1.517897
## 1028 33.69024 1.681842 77.42646 3.000000 2.679724 1.999737 1.747347 0.681773
## 1029 34.36969 1.652202 77.13322 2.595128 1.619796 1.642251 0.662831 0.999268
## 1030 31.42657 1.848683 99.00000 2.759286 2.592570 2.549617 1.427233 0.519395
## 1031 34.28825 1.835678 96.01851 2.000000 1.546665 3.000000 1.000000 0.000000
## 1032 18.86388 1.560029 71.72807 3.000000 3.339914 2.000000 1.000000 1.000000
## 1033 18.95114 1.621048 72.10586 3.000000 3.884861 2.000000 1.000000 1.000000
## 1034 19.67188 1.699474 78.00000 1.925064 2.358298 2.774043 0.000000 0.133566
## 1035 50.83256 1.745528 82.13073 2.000000 3.000000 1.774778 0.943266 0.000000
## 1036 17.97157 1.720379 85.00000 2.000000 3.000000 2.802498 1.000000 0.417580
## 1037 18.00000 1.758787 85.05056 2.846981 3.000000 2.877810 1.000000 0.429081
## 1038 18.70177 1.704908 81.38422 2.650629 1.000000 1.708083 1.876051 0.938791
## 1039 34.38968 1.691322 77.56160 3.000000 1.802305 2.000000 0.390877 0.000000
## 1040 17.17848 1.786290 95.27739 2.000000 3.000000 3.000000 1.072318 0.651904
## 1041 33.08160 1.705617 83.01697 2.000000 2.797600 2.991671 2.148738 0.000000
## 1042 33.27045 1.733439 84.75383 2.631565 2.627173 2.253422 2.690756 0.845774
## 1043 36.31029 1.701397 83.00000 2.000000 1.000000 2.000000 1.472172 0.000000
## 1044 20.00000 1.625236 74.43336 2.522399 1.032887 2.397653 2.358699 0.440087
## 1045 18.54944 1.545196 72.46786 3.000000 3.014808 2.000000 1.997529 1.000000
## 1046 34.24315 1.843172 92.69551 2.000000 2.271734 2.629043 1.000000 0.075823
## 1047 23.32012 1.705813 82.01196 2.784471 2.122545 2.984153 2.164472 0.203978
## 1048 19.70310 1.704141 78.79094 1.650505 3.000000 2.000000 1.732340 1.000000
## 1049 19.22326 1.706082 78.07353 1.961347 3.000000 2.000000 1.655488 1.000000
## 1050 29.69560 1.842943 93.79806 2.133955 2.902766 1.753464 1.729987 1.000000
## 1051 27.00000 1.880992 99.62378 2.684528 1.000000 1.056680 1.516147 0.084006
## 1052 21.02766 1.726774 82.85375 2.265973 2.687502 2.000000 2.217220 0.648522
## 1053 33.01526 1.731960 84.31561 2.000000 3.000000 2.205911 1.293396 0.000000
## 1054 18.00000 1.751278 86.96363 3.000000 3.000000 2.000000 1.271667 0.155278
## 1055 30.55310 1.780448 88.43195 2.000000 1.178708 1.791286 0.893362 0.276364
## 1056 33.00000 1.850000 97.92035 2.000000 3.000000 1.117464 1.000000 0.663649
## 1057 24.91199 1.785241 88.03748 1.306844 2.279546 2.000000 0.000000 0.739609
## 1058 24.44485 1.718845 86.31989 2.000000 2.677693 2.693978 0.000000 0.688013
## 1059 19.91125 1.530248 68.85097 2.258795 3.530090 1.172186 0.678943 1.000000
## 1060 34.20441 1.664927 80.38608 2.000000 3.000000 2.641642 0.285889 1.503010
## 1061 34.28168 1.673333 77.20569 2.689929 1.835543 1.718569 0.674348 0.707246
## 1062 23.38437 1.725587 82.48021 2.712747 2.853676 1.526313 1.000000 0.173665
## 1063 43.23840 1.733875 86.94538 2.353603 2.337035 1.830614 0.706287 0.000000
## 1064 45.00000 1.675953 79.66832 2.598051 3.000000 1.000000 0.000000 0.000000
## 1065 22.08739 1.786238 89.80249 1.718156 1.631184 2.000000 0.000000 0.306124
## 1066 21.37804 1.718534 80.00000 2.000000 3.000000 2.000000 2.721646 1.269982
## 1067 31.39828 1.919543 101.54459 2.000000 1.005391 2.001936 1.000000 0.000000
## 1068 31.48449 1.707613 82.58689 2.795086 3.250467 1.367876 0.022958 0.000000
## 1069 21.70916 1.658393 80.00000 2.000000 3.000000 2.000000 2.939733 1.692287
## 1070 30.71138 1.536819 65.91269 2.030256 2.948721 1.984323 0.986414 0.333673
## 1071 34.82144 1.805459 90.13868 2.000000 1.809930 2.174835 0.340915 0.020153
## 1072 20.84336 1.521008 67.08312 2.493448 3.000000 1.849997 0.954459 1.444532
## 1073 19.44364 1.744733 87.27989 2.442536 3.000000 2.825629 3.000000 0.000000
## 1074 20.49208 1.529223 65.14041 2.003951 3.000000 1.207978 1.916751 1.228995
## 1075 22.94435 1.799742 89.98168 1.341380 1.946710 2.000000 0.000000 0.975504
## 1076 23.00000 1.681314 80.03720 2.000000 2.979600 1.964435 0.189957 1.732160
## 1077 24.06894 1.706912 85.74373 2.000000 2.994198 2.747302 0.000000 0.799756
## 1078 23.72871 1.663509 80.00000 2.000000 3.000000 2.137550 0.000000 0.124977
## 1079 29.21602 1.752265 88.09606 2.000000 1.894384 2.000000 0.000000 0.000000
## 1080 24.75151 1.735343 83.33772 2.607335 3.000000 2.000000 0.451009 0.630866
## 1081 28.97779 1.700000 78.00000 3.000000 3.000000 1.507638 1.824340 1.000000
## 1082 17.44159 1.700000 83.41407 2.061384 2.579291 1.909253 1.000000 0.962468
## 1083 19.12615 1.633794 77.85853 2.696381 3.000000 2.472964 1.856119 1.000000
## 1084 24.12259 1.856759 95.88706 1.116068 2.449067 2.000000 0.926350 1.971170
## 1085 23.00000 1.774330 90.00000 2.116432 3.000000 1.002292 0.000000 1.066708
## 1086 28.82419 1.700000 78.00000 3.000000 3.000000 2.147074 1.416076 1.000000
## 1087 34.20461 1.719509 84.41652 2.031246 3.000000 2.803002 1.984480 0.418623
## 1088 28.16780 1.658202 78.00000 2.938031 1.532833 1.931242 0.525002 0.371941
## 1089 55.13788 1.657221 80.99321 2.000000 3.000000 2.000000 1.000000 0.000000
## 1090 34.97037 1.713348 84.72222 2.884212 3.000000 3.000000 2.000000 0.832400
## 1091 20.98683 1.677178 80.37958 2.000000 2.961706 2.000000 1.661556 1.114716
## 1092 38.37806 1.678050 77.22457 2.444599 3.000000 1.029798 0.000000 0.000000
## 1093 22.18881 1.717722 81.92991 2.000000 1.152521 1.723159 1.390160 1.094941
## 1094 21.08238 1.486484 60.11799 2.000000 1.104642 1.000000 0.000000 0.969097
## 1095 25.29320 1.503379 64.34246 2.000000 1.000000 1.639807 0.072117 0.000000
## 1096 23.00000 1.718981 81.66995 2.000000 1.729553 1.400247 0.887923 1.011983
## 1097 39.17003 1.688354 79.27890 3.000000 3.000000 2.994515 0.000000 0.000000
## 1098 34.04423 1.665807 77.09897 2.976975 1.346987 1.868349 0.702538 0.879333
## 1099 33.18213 1.838441 97.02925 2.000000 1.977221 3.000000 1.000000 0.000000
## 1100 19.82200 1.653431 75.09044 2.766036 2.443812 2.707927 0.702839 0.827439
## 1101 19.14971 1.699818 78.00000 1.096455 2.491315 2.450069 0.000000 0.726118
## 1102 46.49186 1.718097 88.60088 2.129969 3.000000 1.568035 0.870127 0.000000
## 1103 17.89478 1.731389 84.06488 2.019674 2.843319 2.832004 1.000000 0.608607
## 1104 18.88485 1.699667 79.67793 2.735297 2.157164 1.087166 0.110174 0.003695
## 1105 38.38418 1.698626 78.63731 3.000000 3.000000 2.503198 0.000000 0.000000
## 1106 22.67568 1.823765 96.94526 1.588782 2.601675 2.469469 1.736538 1.886855
## 1107 33.04912 1.708742 83.00164 2.000000 1.171027 2.405172 2.300282 0.000000
## 1108 37.20517 1.667469 80.99337 2.010540 2.776840 1.651548 0.000000 0.790967
## 1109 19.02742 1.588147 73.93927 3.000000 3.362758 2.000000 2.892922 1.000000
## 1110 37.49244 1.835024 92.36836 2.000000 1.672706 2.766674 1.000000 0.027093
## 1111 24.65760 1.708800 83.52011 2.689577 2.714115 2.279214 0.970661 0.828549
## 1112 18.01172 1.680991 79.75292 2.413156 2.521546 1.985312 0.007050 0.965464
## 1113 27.34974 1.835271 97.58826 2.923433 1.338033 1.944095 1.931829 1.000000
## 1114 18.00000 1.742819 86.56515 3.000000 3.000000 2.000000 2.040816 0.860321
## 1115 33.00928 1.741192 84.77335 2.000000 3.000000 2.035954 1.210736 0.000000
## 1116 18.00000 1.759721 86.08050 2.882522 3.000000 2.452986 1.000000 0.746651
## 1117 30.07937 1.810616 92.86025 2.000000 3.000000 1.622638 0.033745 0.105895
## 1118 25.03591 1.763101 88.53203 1.973499 1.081805 2.000000 0.000000 0.464022
## 1119 18.19832 1.543338 71.79998 3.000000 3.087119 2.000000 1.403872 1.000000
## 1120 35.45633 1.651812 79.43792 2.156065 2.909117 1.221281 0.503279 1.796136
## 1121 23.80679 1.732492 84.55780 2.992205 3.000000 2.413813 0.458237 0.688293
## 1122 39.39257 1.706349 85.72079 2.944287 1.466393 2.442775 0.675262 0.779334
## 1123 21.38426 1.780679 89.66741 1.780746 1.471053 2.000000 0.467562 0.568668
## 1124 22.73041 1.758687 89.67365 2.164062 2.983201 2.168904 0.752926 0.000000
## 1125 21.20563 1.704573 80.00000 2.000000 3.000000 2.000000 2.847761 1.413375
## 1126 21.33343 1.716545 80.00581 2.000000 2.783336 2.000000 2.536615 1.206535
## 1127 32.78710 1.903832 99.81244 2.000000 1.863012 2.196471 1.000000 0.000000
## 1128 32.61002 1.742538 83.39098 2.247704 3.053598 1.919629 0.408023 0.000000
## 1129 30.02260 1.747739 83.31416 2.011656 3.165837 1.844645 0.889963 0.395979
## 1130 21.12305 1.717037 80.00000 2.000000 3.000000 2.000000 2.270555 1.343044
## 1131 22.98985 1.650000 80.00000 2.000000 3.000000 2.000000 0.146919 2.000000
## 1132 24.32015 1.577921 65.29318 2.034140 2.741413 1.996384 1.276552 1.019452
## 1133 37.27530 1.746055 83.28223 2.746408 1.058123 2.265727 0.885633 0.673408
## 1134 34.09817 1.841151 91.79810 2.000000 2.997414 1.259454 0.935217 0.997600
## 1135 21.00128 1.517998 64.69625 2.123900 1.672958 2.000000 1.582428 1.313363
## 1136 21.95994 1.483284 62.89428 2.000000 1.680838 1.833635 0.281876 0.575848
## 1137 19.79527 1.758972 87.86143 2.332074 3.000000 2.999495 2.405963 0.441502
## 1138 19.09002 1.562434 70.44277 2.748243 3.070386 1.962322 1.145752 1.000000
## 1139 20.82045 1.547066 67.47328 2.303656 3.000000 1.163111 1.926381 1.119877
## 1140 22.08706 1.792435 89.99873 1.904732 2.608416 1.204175 0.000000 1.895312
## 1141 22.18576 1.784555 89.83669 1.979944 1.599464 2.000000 0.170480 0.819475
## 1142 22.98096 1.700216 80.47359 2.000000 2.815255 1.622214 0.463891 1.462664
## 1143 23.00000 1.672101 80.93973 2.000000 2.395785 1.400770 0.788659 1.544357
## 1144 24.19090 1.700000 84.84935 2.000000 3.000000 2.056053 0.000000 1.000000
## 1145 23.94003 1.721348 83.98671 2.407817 2.844138 1.983649 0.868721 0.089354
## 1146 26.59163 1.700000 78.00839 2.734314 3.000000 3.000000 0.897702 0.908271
## 1147 31.26463 1.803129 91.05222 2.000000 3.000000 1.199517 0.047738 0.163329
## 1148 23.62916 1.700020 80.42043 2.000000 3.000000 2.386904 0.926201 1.344030
## 1149 26.20813 1.700000 78.04134 2.784383 3.000000 2.165605 0.855973 0.839659
## 1150 17.68906 1.713599 83.28575 2.009952 2.716106 1.660614 1.000000 0.604730
## 1151 19.16097 1.662728 77.47320 2.008656 1.402771 3.000000 0.112383 0.328030
## 1152 25.45763 1.837399 95.95203 1.122127 2.865657 2.000000 1.287750 1.944177
## 1153 22.98800 1.808270 91.36329 1.963965 1.836226 1.855370 0.000000 1.667745
## 1154 23.60319 1.714508 85.13711 2.319776 2.884848 2.154898 0.325534 0.954216
## 1155 22.88256 1.793451 89.90926 1.899116 2.375026 1.398540 0.000000 1.365793
## 1156 23.58606 1.700499 81.10860 2.042762 2.977400 1.522426 0.501417 1.029135
## 1157 34.43267 1.694997 84.45142 2.129668 2.693646 2.606690 1.170823 0.290898
## 1158 25.47300 1.688911 78.43449 2.182401 2.832018 2.456939 0.038809 0.524015
## 1159 55.02249 1.673394 80.40031 2.000000 3.000000 2.000000 1.000000 0.000000
## 1160 34.64704 1.769499 85.00000 2.802696 3.000000 2.978465 1.974656 0.936925
## 1161 21.99733 1.650000 80.00000 2.000000 3.000000 2.000000 0.527341 2.000000
## 1162 18.18182 1.662669 79.86355 2.492758 2.270163 1.992586 1.452467 0.864583
## 1163 41.74333 1.678610 79.84925 2.733129 3.000000 1.302594 0.000000 1.103349
## 1164 21.47308 1.694423 80.31127 2.000000 2.646717 2.000000 2.627515 1.358812
## 1165 27.75719 1.505437 63.89207 2.000000 1.000000 1.278578 0.021120 0.000000
## 1166 25.11354 1.505387 63.71522 2.000000 1.193729 1.846441 0.546402 0.235711
## 1167 21.82165 1.491441 62.26991 2.000000 1.477581 1.995035 0.324676 0.517430
## 1168 20.67097 1.509408 64.85295 2.294067 3.209508 2.000000 1.103088 1.261043
## 1169 22.64979 1.685045 81.02212 2.000000 2.756622 1.606076 0.432973 1.749586
## 1170 23.15431 1.723072 82.33846 2.315932 2.658478 1.568476 0.949976 0.544899
## 1171 38.09739 1.696954 78.15604 3.000000 3.000000 2.166024 0.000000 0.000000
## 1172 37.64218 1.676095 79.07974 2.802128 3.000000 1.744628 0.000000 0.721167
## 1173 34.17679 1.681021 77.39218 2.796060 1.971472 1.921601 0.935217 0.704637
## 1174 34.23108 1.654067 79.69728 2.086898 1.818026 2.088929 0.305422 1.040787
## 1175 31.96540 1.840708 98.25942 2.333503 1.820779 2.559265 1.327193 0.481357
## 1176 33.18566 1.836007 97.41642 2.000000 1.724887 3.000000 1.000000 0.000000
## 1177 18.74119 1.556789 71.78818 3.000000 3.129155 2.000000 1.634134 1.000000
## 1178 19.95526 1.589100 72.71361 3.000000 3.856434 2.000000 1.324170 1.000000
## 1179 19.68489 1.700627 78.04821 1.653081 2.753418 2.192063 1.474937 0.518542
## 1180 47.70610 1.743935 84.72920 2.535315 3.000000 1.146595 0.313810 0.000000
## 1181 17.99701 1.742654 85.00000 2.000000 3.000000 2.976229 1.000000 0.121992
## 1182 17.97179 1.754441 85.00288 2.765769 3.000000 2.845134 1.000000 0.426830
## 1183 20.43272 1.719342 80.79081 2.215464 2.116195 1.809960 1.910577 0.971746
## 1184 33.95443 1.682253 77.43168 3.000000 2.049908 1.999882 1.637368 0.107240
## 1185 17.03906 1.799902 95.41967 2.000000 3.000000 3.000000 1.047290 0.933802
## 1186 33.07014 1.709428 83.01403 2.000000 1.044628 2.010510 2.805801 0.000000
## 1187 34.99383 1.752456 84.78376 2.631650 2.982120 2.778587 2.667739 0.905181
## 1188 35.71946 1.685947 83.32580 2.000000 1.009426 2.136398 1.060349 0.000000
## 1189 19.00573 1.599999 73.51387 2.942154 2.667711 2.184768 1.524405 0.805008
## 1190 18.85047 1.550053 72.95180 3.000000 3.000974 2.000000 2.274248 1.000000
## 1191 31.54075 1.828092 91.49572 2.000000 2.698883 2.035104 0.598438 0.017016
## 1192 23.33539 1.713380 82.08555 2.716909 2.598079 2.905450 1.600431 0.176892
## 1193 19.74963 1.680764 79.62146 1.837460 3.000000 2.000000 1.194519 1.212762
## 1194 19.56550 1.705584 78.02563 1.936479 2.837388 2.159987 1.475772 0.646514
## 1195 30.35775 1.841852 93.61425 2.045027 2.946063 1.307563 1.442485 0.934493
## 1196 27.00000 1.834986 99.08348 2.760607 1.000000 1.336378 1.898889 0.487375
## 1197 21.38034 1.724839 82.27635 2.094490 1.873484 2.000000 2.079709 0.880414
## 1198 33.15190 1.685127 83.98690 2.000000 2.473911 2.452789 0.932792 0.000000
## 1199 18.00000 1.750097 86.37214 2.907062 3.000000 2.740848 1.219827 0.037634
## 1200 32.24159 1.757961 87.90602 2.000000 1.795580 1.855054 1.083572 0.218574
## 1201 31.66281 1.848965 98.91226 2.399531 2.623079 2.535127 1.030752 0.606264
## 1202 24.34741 1.789193 89.39359 1.521604 2.174968 2.000000 0.000000 0.632467
## 1203 24.36212 1.716677 85.26134 2.000000 2.676148 2.083939 0.632164 0.993786
## 1204 19.46271 1.550122 69.93607 2.501683 3.394788 1.337378 0.932888 1.000000
## 1205 35.43206 1.663178 80.13517 2.000000 3.000000 1.992548 0.039207 1.528714
## 1206 33.86426 1.679299 77.35542 2.768020 2.137068 1.873591 0.966973 0.691944
## 1207 23.80718 1.729177 82.52724 2.742796 2.937607 1.994670 1.000000 0.023564
## 1208 39.58581 1.719153 86.46484 2.325623 1.313403 1.946090 0.604259 0.000000
## 1209 45.82127 1.687326 80.41400 2.076689 3.000000 1.026729 0.647798 0.000000
## 1210 25.92975 1.772449 105.00000 3.000000 3.000000 2.045069 1.725931 1.619596
## 1211 26.04274 1.837117 105.71222 3.000000 3.000000 2.509147 2.000000 1.564796
## 1212 30.55176 1.784377 102.87251 2.271306 3.000000 1.771198 2.000000 0.413752
## 1213 39.75957 1.792507 101.78010 2.333610 2.113575 2.504136 2.998981 1.000000
## 1214 31.38640 1.556579 78.23334 2.136830 2.092179 1.505381 0.000000 0.000000
## 1215 25.70629 1.585547 80.35126 2.000000 1.000000 2.000000 0.000000 0.000000
## 1216 43.60490 1.569234 81.82729 2.909853 1.000000 2.000000 1.308852 0.000000
## 1217 42.31607 1.583943 81.93640 2.490507 2.974204 1.846754 0.000000 0.000000
## 1218 22.65432 1.621233 82.00000 1.063449 1.000000 2.000000 0.000000 1.482016
## 1219 22.67994 1.608400 82.60398 2.699282 1.000000 2.598632 0.292093 2.000000
## 1220 24.07952 1.733439 97.91187 2.000000 3.000000 2.843675 1.309304 1.338655
## 1221 21.19615 1.650000 88.47236 2.427700 1.001633 3.000000 1.172641 1.000000
## 1222 22.59658 1.650052 87.27255 2.875990 1.291900 2.777712 0.432813 1.000000
## 1223 23.00000 1.644161 84.34041 2.177243 3.000000 2.715572 2.230109 0.070897
## 1224 37.35629 1.559499 77.26813 2.000000 3.000000 1.630528 0.000000 0.000000
## 1225 22.75465 1.734237 95.00000 2.000000 3.000000 2.287248 2.669179 1.237867
## 1226 23.25291 1.775815 97.81302 2.000000 3.000000 3.000000 3.000000 2.000000
## 1227 22.02544 1.640426 87.34416 3.000000 1.000000 3.000000 1.280924 1.777950
## 1228 18.08677 1.650000 82.13682 3.000000 3.000000 1.000000 1.029750 1.350099
## 1229 25.99439 1.753321 107.99881 3.000000 3.000000 1.776991 1.757724 0.000000
## 1230 40.82151 1.553026 77.74518 2.000000 3.000000 1.406115 0.000000 0.000000
## 1231 23.00000 1.706525 90.50006 2.000000 3.000000 1.530493 0.967627 1.000000
## 1232 37.95537 1.560648 80.00000 2.846452 1.139317 1.459511 1.718070 0.000000
## 1233 31.31559 1.673352 90.00000 2.190110 2.029858 2.348981 1.946907 0.000000
## 1234 22.66156 1.660324 94.18917 2.000000 3.000000 2.000000 0.000000 0.105936
## 1235 40.31779 1.786318 98.44731 2.000000 3.000000 2.680292 1.549693 0.522259
## 1236 23.36565 1.757691 95.36180 2.000000 3.000000 3.000000 3.000000 2.000000
## 1237 21.72127 1.712163 98.69997 2.000000 2.977543 2.205977 2.698874 2.000000
## 1238 35.38949 1.780000 100.84763 2.069267 1.476204 3.000000 2.052520 0.092736
## 1239 22.06146 1.600000 82.04032 1.362441 2.570380 2.166228 2.232851 1.281141
## 1240 23.00000 1.610820 82.53299 2.096630 2.879541 2.432967 1.887012 0.000000
## 1241 23.00000 1.665199 83.15115 2.928234 1.458507 2.777379 0.354541 1.707018
## 1242 40.95159 1.542122 80.00000 2.000000 1.105617 1.372811 1.629432 0.000000
## 1243 39.13563 1.507867 79.58958 2.000000 3.000000 1.000000 0.000000 0.000000
## 1244 26.27162 1.660955 90.00000 2.000000 3.000000 3.000000 0.669278 0.505266
## 1245 23.77923 1.553127 78.00000 2.000000 1.000000 2.000000 0.827502 0.000000
## 1246 20.58698 1.781952 102.91061 2.000000 3.000000 1.689793 1.464204 0.000000
## 1247 21.66948 1.750000 96.94025 2.000000 3.000000 2.771469 2.359339 1.206251
## 1248 23.00000 1.615854 80.61532 2.000000 1.000000 2.000000 0.026142 0.000000
## 1249 20.82596 1.793378 105.65504 2.000000 3.000000 1.155384 0.003938 0.526999
## 1250 18.17802 1.854780 114.77484 2.000000 1.854536 2.160169 1.000000 2.000000
## 1251 18.00000 1.685633 90.03267 2.496455 3.000000 1.850344 1.066101 0.732265
## 1252 18.26770 1.706343 93.34884 1.708250 3.000000 1.000000 0.899864 1.000000
## 1253 23.00000 1.791415 105.13807 2.262171 3.000000 2.034150 0.317363 0.508663
## 1254 23.00000 1.753716 106.49141 2.740633 3.000000 2.081005 0.650235 0.769060
## 1255 20.98590 1.780503 103.18953 2.000000 3.000000 1.608128 0.478134 0.000000
## 1256 21.50494 1.819867 106.03847 2.000000 3.000000 2.715252 0.000000 0.621605
## 1257 18.00000 1.791174 108.96060 2.000000 1.086870 2.279124 1.000000 1.609773
## 1258 18.00000 1.820930 108.74201 2.000000 1.255350 2.497065 1.000000 1.441605
## 1259 19.44266 1.627812 82.00000 1.081585 2.870661 1.117560 0.000000 1.616826
## 1260 22.86502 1.632118 82.00000 2.587789 1.482103 1.911664 0.000000 0.128681
## 1261 21.94858 1.773594 105.00079 2.252653 3.000000 2.962371 1.000000 0.000000
## 1262 21.21462 1.930416 118.56051 2.000000 3.000000 3.000000 0.732186 1.000000
## 1263 22.27786 1.947406 116.89311 2.000000 3.000000 3.000000 0.975187 1.000000
## 1264 37.83295 1.610867 80.00000 2.036613 1.816980 1.930590 1.851404 0.000000
## 1265 37.63177 1.513202 75.41065 2.000000 2.582591 1.535134 1.884520 0.000000
## 1266 17.67390 1.738465 97.18547 2.000000 3.000000 2.000000 0.000000 0.233314
## 1267 37.52455 1.567915 76.12978 2.000000 3.000000 2.102976 0.000000 0.000000
## 1268 43.51067 1.587546 76.12611 2.000000 3.000000 2.091934 0.000000 0.000000
## 1269 18.00000 1.820385 108.39500 2.000000 2.164839 2.094479 1.000000 0.676557
## 1270 18.00000 1.792239 108.24438 2.000000 2.141839 2.939847 1.000000 0.103056
## 1271 29.50629 1.826970 108.75150 2.000000 2.877583 2.358038 0.877295 1.817146
## 1272 18.00000 1.670058 86.24268 2.609123 3.000000 1.955053 1.186013 0.000000
## 1273 24.73331 1.639383 91.26709 1.036159 3.000000 1.000000 0.344013 0.329367
## 1274 29.00000 1.682916 89.99167 1.851262 3.000000 2.112670 0.388269 0.000000
## 1275 18.00000 1.609321 84.49316 2.000000 3.000000 1.051735 1.000000 0.000000
## 1276 21.09803 1.690437 96.36678 2.000000 2.958330 2.000000 0.000000 1.595306
## 1277 19.08959 1.700164 99.20470 2.000000 2.119826 2.000000 0.000000 1.882539
## 1278 18.31266 1.600740 82.24983 2.501236 3.000000 1.220331 0.245003 0.537202
## 1279 18.26008 1.801848 104.74191 2.000000 3.000000 3.000000 1.783858 0.000000
## 1280 26.00429 1.844751 105.02581 3.000000 3.000000 2.925029 2.000000 1.758865
## 1281 25.99475 1.811602 106.04214 3.000000 3.000000 2.858171 1.813318 0.680215
## 1282 36.72662 1.787521 100.62455 2.031185 2.992606 2.852254 2.001230 0.360370
## 1283 38.29726 1.789109 100.06627 2.014194 2.050121 2.184707 2.000561 0.853891
## 1284 30.16341 1.533364 78.03038 2.028225 1.923607 1.798917 0.000000 0.000000
## 1285 28.77004 1.580858 79.71349 2.000000 1.000000 2.000000 0.005405 0.000000
## 1286 42.33728 1.646390 86.63986 2.816460 2.273740 1.722063 0.000000 0.000000
## 1287 47.28337 1.643786 81.97874 2.037585 1.418985 1.827351 0.000000 0.000000
## 1288 22.51879 1.634342 82.41448 1.853314 1.320768 2.135552 0.248034 1.727828
## 1289 22.83631 1.604893 82.00000 1.008760 1.000000 2.000000 0.000000 0.585912
## 1290 23.00000 1.654961 94.79058 2.000000 3.000000 1.490613 0.654316 1.000000
## 1291 22.97553 1.701986 95.00000 2.000000 3.000000 2.021270 1.814869 1.066603
## 1292 22.72045 1.650000 89.13921 2.103335 2.964024 3.000000 0.632947 1.000000
## 1293 23.88757 1.657995 90.00000 2.000000 3.000000 3.000000 0.603638 0.969085
## 1294 23.00000 1.634688 82.62800 2.060922 2.933409 2.235282 0.380633 0.002600
## 1295 23.00000 1.628168 84.49798 2.058687 2.962004 2.010596 0.851059 0.630866
## 1296 38.14885 1.557808 79.66169 2.000000 3.000000 1.274774 0.000000 0.000000
## 1297 37.96543 1.560199 80.00000 2.533605 1.271624 1.893691 1.296535 0.000000
## 1298 22.77161 1.750384 95.32428 2.000000 3.000000 3.000000 3.000000 2.000000
## 1299 22.58237 1.753081 95.26909 2.000000 3.000000 3.000000 3.000000 2.000000
## 1300 21.00805 1.650000 88.12654 2.457547 1.000610 3.000000 1.361533 1.000000
## 1301 22.59103 1.650012 87.67615 2.983851 1.068443 2.854161 1.103209 1.000000
## 1302 16.12928 1.650000 85.58348 2.954996 3.000000 1.000000 2.091862 1.060530
## 1303 16.91384 1.634832 85.80381 2.061969 3.000000 1.229171 2.392047 1.256119
## 1304 29.43879 1.770126 108.60272 3.000000 3.000000 1.163264 1.866023 1.604608
## 1305 29.88130 1.758189 108.72189 3.000000 3.000000 1.271178 1.944728 0.000000
## 1306 43.59200 1.595165 77.35474 2.000000 3.000000 2.117346 0.000000 0.000000
## 1307 40.99318 1.567756 79.49363 2.000000 3.000000 2.952506 0.000000 0.000000
## 1308 22.93610 1.702825 93.63832 2.000000 3.000000 1.746197 0.455216 0.335158
## 1309 23.00000 1.735659 93.42920 2.000000 3.000000 1.249307 0.973465 1.000000
## 1310 37.59795 1.629010 80.00000 2.450784 2.952821 1.335192 0.180276 0.000000
## 1311 37.53207 1.615385 80.00000 2.972426 3.000000 1.636326 0.000000 0.000000
## 1312 31.63005 1.671705 90.00000 2.467002 1.851088 2.104054 1.991565 0.000000
## 1313 31.64108 1.676595 89.99381 2.934671 2.119682 2.041462 0.578074 0.000000
## 1314 21.87248 1.699998 95.56443 2.000000 2.970675 2.000000 0.000000 0.169294
## 1315 21.83489 1.722785 94.09418 2.000000 2.966803 2.000000 0.000000 1.281541
## 1316 36.02397 1.670667 90.57593 2.903545 1.508685 2.450069 1.454730 0.000000
## 1317 39.65656 1.789992 98.02177 2.043359 2.209314 2.785804 1.259613 0.669616
## 1318 24.18489 1.768834 97.44974 2.000000 3.000000 2.973729 2.491642 1.365950
## 1319 23.23730 1.761008 97.82934 2.000000 3.000000 2.988771 2.429923 1.978043
## 1320 35.32211 1.780000 102.26596 2.787589 1.114564 3.000000 2.710338 0.572185
## 1321 31.38798 1.810215 105.25435 2.397280 2.036794 2.659419 1.062011 1.771135
## 1322 23.00000 1.608469 82.95480 2.150054 2.988539 2.768325 2.085150 0.000000
## 1323 23.00000 1.630357 83.10110 2.977585 1.630506 2.839319 1.091474 0.889517
## 1324 22.67945 1.628260 82.96794 2.274491 1.000000 2.269500 0.946461 1.731070
## 1325 22.48089 1.605662 82.47038 1.557287 1.000000 2.371015 0.288032 2.000000
## 1326 41.40386 1.567973 81.05685 2.152264 2.977999 1.513199 0.000000 0.000000
## 1327 40.70277 1.548403 80.00000 2.000000 3.000000 1.326165 0.000000 0.000000
## 1328 29.38924 1.681855 90.00000 2.088410 2.644692 2.773236 1.252472 0.000000
## 1329 30.96742 1.688436 90.00000 2.180047 2.733077 2.779620 1.454129 0.000000
## 1330 23.47416 1.577115 78.00000 2.000000 1.000000 2.000000 0.876101 0.000000
## 1331 24.31761 1.586751 79.10903 2.000000 1.000000 2.000000 0.852446 0.000000
## 1332 17.05291 1.710616 99.86025 2.000000 3.000000 2.000000 0.067491 0.894105
## 1333 18.04892 1.721384 99.43061 2.000000 3.000000 2.000000 1.579431 0.839862
## 1334 22.87522 1.624367 82.00000 1.826885 1.000000 2.000000 0.000000 0.459274
## 1335 22.88472 1.622787 82.00000 1.754401 1.000000 2.000000 0.000000 0.301909
## 1336 18.72957 1.855433 112.87528 2.000000 2.427137 2.574073 1.000000 2.000000
## 1337 21.01112 1.856315 118.18380 2.000000 3.000000 3.000000 0.788585 1.220029
## 1338 18.60350 1.681719 90.67187 1.524428 3.000000 1.383831 0.130417 1.000000
## 1339 21.10606 1.722884 92.94925 1.164062 3.000000 1.157395 0.000000 0.320851
## 1340 23.00000 1.799406 106.52881 2.123159 3.000000 2.415343 0.295178 0.569852
## 1341 21.98085 1.819875 106.04852 2.000000 3.000000 2.745242 0.000000 0.808980
## 1342 21.01666 1.790172 105.04219 2.259679 3.000000 1.026143 0.268801 0.077818
## 1343 21.72738 1.783782 105.00028 2.044326 3.000000 2.358180 0.349371 0.000000
## 1344 18.00000 1.783906 109.20761 2.000000 1.867836 2.438398 1.000000 0.802305
## 1345 18.00000 1.844218 109.19553 2.000000 1.548407 2.191401 1.000000 1.676944
## 1346 19.43166 1.631662 82.00000 2.843456 2.937989 1.001995 0.000000 1.554404
## 1347 18.16632 1.649553 82.32395 2.864776 3.000000 1.876915 0.631565 0.186414
## 1348 22.35203 1.754711 105.00071 2.871137 3.000000 2.627569 1.000000 0.000000
## 1349 22.46935 1.762515 105.00010 2.282803 3.000000 2.104264 1.000000 0.000000
## 1350 19.52470 1.942725 121.65798 2.000000 3.000000 3.000000 1.000000 1.014808
## 1351 20.49148 1.975663 120.70293 2.000000 3.000000 3.000000 0.767013 1.000000
## 1352 39.21340 1.586301 80.00000 2.020502 1.237454 1.931420 1.967973 0.000000
## 1353 38.09875 1.598448 80.00000 2.020785 1.169173 1.972551 1.903338 0.000000
## 1354 19.03403 1.703098 98.29665 2.000000 2.391753 2.000000 0.000000 1.119877
## 1355 17.07365 1.706996 99.54470 2.000000 3.000000 2.000000 1.732090 0.048617
## 1356 38.54727 1.526472 75.15035 2.000000 3.000000 1.084442 0.000000 0.000000
## 1357 38.68379 1.501993 76.64294 2.000000 3.000000 1.000000 0.000000 0.000000
## 1358 18.00000 1.784402 108.41312 2.000000 2.475444 2.655795 1.000000 0.169879
## 1359 18.00000 1.792687 108.20455 2.000000 2.478794 2.967064 1.000000 0.434600
## 1360 29.62280 1.814052 109.41162 2.407817 2.070033 1.796257 1.234483 0.178708
## 1361 30.79626 1.789421 109.59945 2.214980 2.282392 1.179942 1.771754 0.537659
## 1362 18.00000 1.686904 90.00405 2.737149 3.000000 1.997195 1.352663 0.468483
## 1363 18.10709 1.703259 91.49968 1.899793 3.000000 1.439962 0.952900 0.838847
## 1364 31.33509 1.665798 89.73860 2.274164 1.049534 1.358172 1.482411 0.000000
## 1365 29.00000 1.666710 89.04815 1.897796 3.000000 1.193039 0.011519 0.000000
## 1366 18.01190 1.650000 84.21053 2.859160 3.000000 1.000000 1.020525 0.786066
## 1367 18.00000 1.649439 84.89774 2.000000 3.000000 1.039313 1.000000 0.000000
## 1368 21.07736 1.702002 97.97160 2.000000 1.663380 2.000000 0.000000 1.865851
## 1369 21.05202 1.693820 99.53097 2.000000 1.672751 2.000000 0.000000 1.946173
## 1370 18.07826 1.622999 82.40308 2.340405 3.000000 1.655245 1.006884 0.548539
## 1371 18.06358 1.633675 82.45958 2.921576 3.000000 1.003636 1.000227 0.905596
## 1372 20.41883 1.836669 105.25754 2.000000 3.000000 2.793505 2.219390 0.202902
## 1373 20.58098 1.798354 103.70542 2.000000 3.000000 2.401315 2.891986 0.000000
## 1374 26.03242 1.824432 105.13196 3.000000 3.000000 2.110611 1.890907 1.584830
## 1375 25.95536 1.830384 105.47931 3.000000 3.000000 2.480277 1.796779 1.596562
## 1376 26.01545 1.829907 105.43617 3.000000 3.000000 2.224914 1.781589 1.594050
## 1377 25.92074 1.823755 105.80016 2.927110 3.000000 2.151496 1.166064 1.509831
## 1378 29.63371 1.834842 105.19936 2.805533 3.000000 1.882847 2.000000 0.707780
## 1379 32.89564 1.783901 103.77137 2.902469 1.734762 2.600238 2.113992 0.584755
## 1380 38.74831 1.782067 103.58634 2.845961 1.928220 2.642273 2.999918 1.000000
## 1381 39.68585 1.781032 96.30385 2.252698 2.475228 2.923856 2.165429 0.616045
## 1382 33.22681 1.557943 77.64772 2.020910 2.093831 1.506518 0.000000 0.000000
## 1383 26.22007 1.560258 78.43590 2.108163 1.231915 1.808127 0.000000 0.000000
## 1384 23.09022 1.596586 80.72620 1.518966 1.000000 2.000000 0.000000 1.094046
## 1385 24.56563 1.620930 81.71823 2.260543 1.374791 1.947935 0.000000 0.078607
## 1386 42.58628 1.571417 81.91881 2.522183 1.326982 1.872673 1.048507 0.000000
## 1387 43.71939 1.584322 80.98650 2.186322 2.900915 2.471033 0.256113 0.000000
## 1388 43.37634 1.582523 81.91945 2.766320 1.317884 1.889341 0.990642 0.000000
## 1389 39.64895 1.572791 80.08652 2.071622 2.977909 1.468297 0.000000 0.000000
## 1390 22.69399 1.627908 82.00000 1.918251 1.355752 1.998108 0.000000 1.382906
## 1391 22.67624 1.620938 82.28319 1.967061 1.000000 2.548651 0.249264 1.516731
## 1392 22.80482 1.613119 82.63616 2.964419 1.000000 2.977516 0.742113 2.000000
## 1393 22.85712 1.626860 82.41019 2.640801 1.015488 2.022355 0.244749 0.289218
## 1394 23.09635 1.728183 97.95990 2.000000 2.986172 2.364208 2.492402 1.632506
## 1395 22.81542 1.732694 98.44113 2.000000 2.993623 2.326635 2.236586 1.529423
## 1396 21.02064 1.650000 88.12944 2.870152 1.001383 3.000000 1.322558 1.000000
## 1397 21.00146 1.650000 88.02694 2.482575 1.001542 3.000000 1.751656 1.000000
## 1398 22.87795 1.669130 86.00274 2.290095 2.590283 2.506296 0.312254 1.000000
## 1399 22.84762 1.669136 85.56839 2.074843 1.773916 2.428271 0.035091 1.000000
## 1400 23.00000 1.611058 84.19112 2.141280 2.989112 2.519841 2.111370 0.013483
## 1401 23.00000 1.649736 84.13471 2.334474 1.496776 2.776724 0.782416 0.167728
## 1402 39.12929 1.532643 77.55034 2.000000 3.000000 1.186996 0.000000 0.000000
## 1403 37.44104 1.524293 76.20276 2.000000 2.994046 1.603549 1.335857 0.000000
## 1404 22.96937 1.701634 95.00000 2.000000 3.000000 2.133469 1.030199 1.082838
## 1405 22.73533 1.723921 94.74389 2.000000 3.000000 2.183149 1.932386 0.212767
## 1406 23.32471 1.769484 96.07846 2.000000 3.000000 3.000000 3.000000 2.000000
## 1407 23.66814 1.777416 97.84241 2.000000 3.000000 3.000000 3.000000 2.000000
## 1408 21.89547 1.644560 88.11914 2.693859 1.000283 3.000000 1.201403 1.612432
## 1409 21.39280 1.641149 88.07918 2.607747 1.000414 3.000000 1.269169 1.460564
## 1410 18.17808 1.642892 82.14441 2.668890 3.000000 1.172593 0.886448 1.252677
## 1411 18.90751 1.650000 82.01831 3.000000 3.000000 1.000000 0.215187 1.195929
## 1412 26.01193 1.777251 106.45237 3.000000 3.000000 1.911379 1.911096 1.032392
## 1413 25.69674 1.814696 107.55963 2.921225 3.000000 2.869439 0.181753 0.133523
## 1414 40.46631 1.559005 77.60148 2.000000 3.000000 1.572371 0.000000 0.000000
## 1415 38.44515 1.556028 77.68423 2.000000 3.000000 1.440629 0.000000 0.000000
## 1416 24.47306 1.653751 91.20475 1.492834 3.000000 1.005367 0.922739 0.733221
## 1417 23.47918 1.680171 91.06805 1.220024 3.000000 1.046254 0.520989 0.615990
## 1418 38.39746 1.552648 80.00000 2.667676 1.135278 1.399629 1.648883 0.000000
## 1419 37.97448 1.560215 80.00000 2.569075 2.463113 1.567366 0.359134 0.000000
## 1420 31.78352 1.672959 90.00000 2.949242 1.782109 2.210997 1.992719 0.000000
## 1421 29.68131 1.680058 89.99435 2.104772 2.376374 2.218691 1.521840 0.000000
## 1422 21.58774 1.664752 94.25655 2.000000 2.976098 2.000000 0.000000 1.393220
## 1423 21.74611 1.668553 94.45439 2.000000 2.968098 2.000000 0.000000 1.292476
## 1424 39.56900 1.785286 100.43162 2.871768 1.792695 2.691322 2.545707 0.903903
## 1425 36.67933 1.780725 98.79017 2.540949 1.116401 2.929123 2.787319 0.732881
## 1426 22.92701 1.751046 95.28590 2.000000 3.000000 2.530301 2.891180 1.287117
## 1427 23.32934 1.751365 95.29043 2.000000 3.000000 3.000000 3.000000 2.000000
## 1428 22.12633 1.717262 98.57916 2.000000 2.984523 2.263551 2.819661 2.000000
## 1429 21.67916 1.741393 98.18250 2.000000 2.978103 2.668261 2.462269 1.402414
## 1430 36.67388 1.792100 101.28576 2.222282 1.578751 2.791604 2.352091 0.317846
## 1431 37.93604 1.785957 99.19929 2.045160 1.874532 2.856521 2.005286 0.105408
## 1432 22.22681 1.609068 83.78531 2.094184 2.735706 2.257922 2.230547 0.195339
## 1433 22.53893 1.603963 82.01264 1.123672 1.014916 2.042078 1.846666 1.426103
## 1434 22.30741 1.605495 82.52858 2.049112 2.622055 2.280555 2.052896 0.896185
## 1435 22.36288 1.607182 82.36844 1.880534 2.806566 2.313245 2.146778 0.196084
## 1436 22.89974 1.661715 82.59579 1.203754 1.355354 2.765593 0.128342 1.659476
## 1437 22.99717 1.655742 82.46376 2.736910 1.478334 2.677409 0.065264 0.406990
## 1438 38.89507 1.549257 80.00000 2.736628 1.130751 1.385175 1.666965 0.000000
## 1439 40.78953 1.549748 80.00000 2.000000 1.099151 1.687611 1.874662 0.000000
## 1440 40.65416 1.529060 79.76092 2.000000 3.000000 1.000000 0.000000 0.000000
## 1441 38.54294 1.517248 79.84322 2.000000 3.000000 1.095134 0.000000 0.000000
## 1442 25.95383 1.657310 90.00000 2.000000 3.000000 3.000000 0.413643 0.920858
## 1443 26.82696 1.673287 90.00000 2.000000 3.000000 3.000000 0.884935 0.122280
## 1444 23.80390 1.581527 78.08957 2.000000 1.000000 2.000000 0.057758 0.000000
## 1445 23.65244 1.562724 80.53570 2.000000 1.000000 2.000000 0.389717 0.000000
## 1446 20.67711 1.781251 102.95093 2.000000 3.000000 1.618189 0.571648 0.000000
## 1447 21.79739 1.775584 103.60590 2.121909 3.000000 2.500556 1.207580 0.000000
## 1448 22.71938 1.746645 96.87550 2.000000 3.000000 2.714091 2.641020 1.224737
## 1449 22.17710 1.741353 96.73801 2.000000 3.000000 2.697661 2.614909 1.229474
## 1450 23.09991 1.571812 78.99717 2.000000 1.000000 2.000000 0.402614 0.000000
## 1451 24.17851 1.589027 80.55307 2.000000 1.000000 2.000000 0.011477 0.000000
## 1452 20.92481 1.803245 105.68609 2.000000 3.000000 2.290368 0.001086 0.544128
## 1453 20.97597 1.792646 105.61914 2.000000 3.000000 1.025275 0.002030 0.175587
## 1454 21.85630 1.871990 115.62755 2.000000 2.358455 2.515765 0.982320 1.157466
## 1455 18.14075 1.859056 111.23519 2.000000 1.706551 2.039514 1.000000 2.000000
## 1456 18.00000 1.692242 90.01950 2.642744 3.000000 1.904054 1.645654 0.363549
## 1457 18.00000 1.683000 90.92421 2.387426 3.000000 1.779620 0.743005 0.920162
## 1458 20.20636 1.738397 93.89068 1.996638 3.000000 1.033199 0.584793 0.518297
## 1459 18.15288 1.694969 92.50812 2.107854 3.000000 1.383894 1.030526 0.831412
## 1460 22.33622 1.785718 105.05569 2.253707 3.000000 2.524432 0.582160 0.175694
## 1461 23.00000 1.742500 105.02867 2.393837 3.000000 2.014990 0.978815 0.413220
## 1462 22.08806 1.803132 106.32957 2.348745 3.000000 2.096751 0.544564 0.676880
## 1463 23.00000 1.774644 105.96689 2.312825 3.000000 2.073497 0.614466 0.579541
## 1464 20.99307 1.782269 104.97003 2.000000 3.000000 1.234943 0.008368 0.000000
## 1465 20.65475 1.780791 102.92122 2.000000 3.000000 1.613829 1.251665 0.000000
## 1466 21.62455 1.790151 106.32069 2.490776 3.000000 2.654517 0.112454 0.756339
## 1467 21.68264 1.818641 105.49698 2.078082 3.000000 2.895614 0.062750 0.261793
## 1468 18.00000 1.806827 108.82940 2.000000 1.248840 2.416213 1.000000 1.546738
## 1469 18.00000 1.811189 108.80096 2.000000 1.250548 2.121176 1.000000 0.741069
## 1470 18.00000 1.811738 108.89732 2.000000 1.202179 2.362930 1.000000 1.475740
## 1471 18.00000 1.799779 108.93457 2.000000 1.194815 2.434832 1.000000 1.541455
## 1472 19.37421 1.632605 82.00000 2.805512 2.880817 1.001307 0.000000 1.376597
## 1473 19.27569 1.623377 82.85132 1.276858 2.918124 1.403784 0.552511 1.560402
## 1474 22.95685 1.618686 81.28158 2.396265 1.073421 1.979833 0.022598 0.061282
## 1475 22.82968 1.616085 82.58295 2.663866 1.416309 2.379275 0.256323 0.598244
## 1476 22.20078 1.769328 105.00058 2.685484 3.000000 2.649459 1.000000 0.000000
## 1477 21.68856 1.807029 105.69636 2.055209 3.000000 2.885852 0.903369 0.144510
## 1478 20.80319 1.882533 117.46852 2.000000 2.181620 2.325091 0.891444 1.223661
## 1479 19.51532 1.879144 112.93298 2.000000 2.152733 2.533690 0.917563 1.285838
## 1480 21.96222 1.931263 118.20313 2.000000 3.000000 3.000000 0.743593 1.000000
## 1481 20.53409 1.861358 115.39792 2.000000 3.000000 3.000000 0.987591 1.914531
## 1482 39.29266 1.567131 80.00000 2.025479 1.046144 1.941224 1.983265 0.000000
## 1483 37.87297 1.565366 80.00000 2.002564 1.974233 1.935398 1.649299 0.000000
## 1484 37.61338 1.516007 77.03305 2.000000 2.880794 1.618370 0.120165 0.000000
## 1485 37.47168 1.549812 76.08252 2.000000 2.765213 1.551266 1.350001 0.000000
## 1486 18.61120 1.714143 96.56881 2.000000 2.967089 2.000000 0.000000 0.467048
## 1487 17.41263 1.723191 97.35037 2.000000 3.000000 2.000000 0.000000 0.931721
## 1488 39.12631 1.562889 76.65949 2.000000 3.000000 1.440526 0.000000 0.000000
## 1489 37.06360 1.502609 75.27961 2.000000 3.000000 1.759803 0.000000 0.000000
## 1490 41.31830 1.544937 77.05395 2.000000 3.000000 2.090413 0.000000 0.000000
## 1491 43.72608 1.592316 77.00103 2.000000 3.000000 2.806922 0.000000 0.000000
## 1492 18.00000 1.787733 108.01921 2.000000 2.379850 2.616138 1.000000 0.652485
## 1493 18.00000 1.782722 108.04431 2.000000 2.655265 2.297896 1.000000 0.552665
## 1494 18.00000 1.797523 108.31646 2.000000 1.941307 2.708168 1.000000 1.425852
## 1495 18.00000 1.803527 108.25104 2.000000 1.709546 2.530157 1.000000 0.645400
## 1496 29.40983 1.801224 108.15619 2.385502 2.883984 2.140544 1.144876 1.767468
## 1497 28.42153 1.829239 107.10819 2.465575 2.935381 2.480555 1.001830 1.670313
## 1498 18.00000 1.692913 89.93889 2.818502 3.000000 1.991251 1.492967 0.000000
## 1499 18.00000 1.668555 85.60747 2.081238 3.000000 1.183630 1.171770 0.000000
## 1500 23.24670 1.652971 93.31028 1.368978 3.000000 1.953152 0.104707 0.221830
## 1501 24.48103 1.661277 90.74496 1.712848 3.000000 1.162153 0.458981 0.885532
## 1502 29.00000 1.641784 89.42495 1.330700 3.000000 1.880967 0.322013 0.000000
## 1503 27.96877 1.673767 89.99503 1.961069 3.000000 2.652327 0.569310 0.319008
## 1504 18.02474 1.617192 83.12181 2.976509 3.000000 1.022705 1.025690 0.313016
## 1505 18.10682 1.602129 82.41267 2.319648 3.000000 1.107164 0.692123 0.304020
## 1506 21.37968 1.701413 96.71073 2.000000 2.961192 2.623344 0.981686 1.355370
## 1507 21.35324 1.709731 95.03218 2.000000 2.973476 2.000000 0.000000 1.331527
## 1508 20.33882 1.698829 98.57275 2.000000 2.392811 2.000000 0.000000 1.809310
## 1509 20.72064 1.705304 99.87372 2.000000 1.293342 2.000000 0.000000 1.917679
## 1510 19.04536 1.612910 82.19340 1.261288 2.930044 1.166655 0.133398 0.951740
## 1511 18.94596 1.605469 82.03900 2.765330 3.000000 1.048584 0.192559 0.720411
## 1512 18.88061 1.804160 104.40682 2.000000 3.000000 3.000000 2.240500 0.000000
## 1513 19.85052 1.785062 104.18731 2.000000 3.000000 2.151570 1.605983 0.000000
## 1514 30.20095 1.755926 112.28988 2.317734 3.000000 2.152736 0.000000 1.108145
## 1515 25.31459 1.787802 115.12766 1.588114 3.000000 2.115967 1.541072 0.000000
## 1516 37.18679 1.704877 107.94747 2.549782 3.985442 1.000000 1.976582 0.000000
## 1517 32.70765 1.695347 102.81070 2.795086 2.129909 1.000000 1.989316 0.000000
## 1518 27.56243 1.908608 128.82812 2.206276 3.000000 1.813082 1.949840 0.000000
## 1519 30.42160 1.819296 122.13792 2.000000 3.000000 1.984323 0.793262 0.000000
## 1520 26.94514 1.773259 118.15435 2.183540 3.000000 2.277937 0.681830 0.000000
## 1521 34.13945 1.774647 120.15197 2.962415 3.000000 2.172649 1.097905 0.000000
## 1522 26.22544 1.773664 116.16033 2.442536 3.000000 2.174371 0.000000 1.928972
## 1523 28.36315 1.793476 112.72500 1.991240 3.000000 2.000000 0.000000 0.292956
## 1524 27.99147 1.825590 120.86039 3.000000 3.000000 3.000000 0.691369 1.415536
## 1525 25.49875 1.885543 121.25308 2.408561 3.000000 2.851904 1.320065 0.000000
## 1526 30.60523 1.750000 120.00000 2.758394 3.000000 2.174248 1.079524 1.358163
## 1527 31.45741 1.874070 128.86744 2.956297 3.000000 1.275100 0.901924 1.875023
## 1528 24.82929 1.755967 112.25616 1.369529 3.000000 2.000000 1.596576 0.002600
## 1529 24.73942 1.757069 117.29823 1.392665 3.000000 2.000000 1.097983 0.630866
## 1530 41.00000 1.750000 116.59435 2.000000 2.831771 1.725226 0.356288 0.000000
## 1531 27.83173 1.704028 101.63431 2.630401 1.000000 1.000000 0.245354 0.315261
## 1532 23.26006 1.849003 121.41474 3.000000 2.595126 2.054072 0.835271 0.000000
## 1533 22.70577 1.841989 122.02495 3.000000 2.527510 1.645338 1.025438 0.000000
## 1534 24.04104 1.613491 98.49077 3.000000 2.120936 1.000000 1.543386 0.890213
## 1535 20.01391 1.647821 106.50995 2.869778 1.468948 1.656082 0.000000 1.444033
## 1536 30.02019 1.758340 112.01050 1.868212 3.000000 2.023328 0.000000 0.613992
## 1537 25.15462 1.758398 112.08902 1.108663 3.000000 2.000000 1.230219 0.001716
## 1538 30.87072 1.670774 101.62619 2.907744 3.990925 1.000000 1.999750 0.000000
## 1539 28.71299 1.665585 98.66176 2.958010 2.834253 1.000000 1.999886 0.000000
## 1540 30.71051 1.914186 129.85253 2.197261 3.000000 1.111840 0.906843 0.976473
## 1541 29.82748 1.899588 124.26925 2.048962 3.000000 2.822871 1.066169 0.000000
## 1542 31.86893 1.750000 118.10290 2.139196 3.000000 2.048430 0.368026 0.360986
## 1543 36.54288 1.750000 119.43465 2.729890 3.000000 2.030084 0.592607 0.754417
## 1544 21.55636 1.773664 116.16033 2.000000 3.000000 2.000000 1.399183 1.000000
## 1545 23.96365 1.792998 116.10262 1.994679 3.000000 2.000000 0.966617 0.739006
## 1546 24.14530 1.825590 120.86039 2.403421 3.000000 2.490613 2.000000 0.707768
## 1547 25.29840 1.827279 120.99607 3.000000 3.000000 3.000000 1.110215 0.396352
## 1548 31.75539 1.775416 121.20467 2.758394 3.000000 2.161303 0.428173 0.716327
## 1549 30.62865 1.766975 118.36338 2.964319 3.000000 2.377257 0.614959 1.875023
## 1550 23.45456 1.754218 117.38474 1.617093 3.000000 2.000000 1.818052 0.631825
## 1551 23.43223 1.754996 119.08756 1.631144 3.000000 2.000000 1.593183 0.863740
## 1552 40.50021 1.748103 108.30811 2.317459 3.734323 1.000000 1.628637 0.000000
## 1553 34.57671 1.733250 103.66912 2.501224 2.049565 1.000000 1.746583 0.000000
## 1554 22.27697 1.849950 121.78648 3.000000 2.272214 1.555534 0.348839 0.000000
## 1555 21.96379 1.849601 122.33343 3.000000 2.218285 1.340117 0.428259 0.000000
## 1556 24.00168 1.606066 99.96173 3.000000 1.418833 1.000000 1.191020 1.384186
## 1557 20.02776 1.611434 103.17552 2.983042 1.109956 1.430444 0.000000 1.690901
## 1558 28.70446 1.762887 113.90198 2.323351 3.000000 2.165048 0.000000 1.493716
## 1559 26.77411 1.755938 112.28768 1.428289 3.000000 2.117733 0.485322 0.696948
## 1560 25.53941 1.787052 115.42828 1.992889 3.000000 2.141271 1.121038 0.000000
## 1561 25.30021 1.765258 114.33002 1.562804 3.000000 2.075493 1.553734 0.000436
## 1562 31.19446 1.726279 110.71471 1.794825 3.914454 1.972016 0.668963 0.000000
## 1563 40.79406 1.735851 109.88933 2.305349 3.169089 1.021610 0.908981 0.000000
## 1564 33.55336 1.699793 103.84167 2.576449 2.419656 1.000000 1.982379 0.000000
## 1565 30.30420 1.703202 103.03440 2.754645 2.175432 1.541733 0.358709 1.073900
## 1566 30.95805 1.906821 128.85668 2.633855 3.000000 1.619305 1.847802 0.424612
## 1567 29.42969 1.910987 129.93567 2.200588 3.000000 1.295697 1.058378 0.000000
## 1568 30.52085 1.784049 120.64418 2.499108 3.000000 2.040952 0.838739 0.489854
## 1569 30.61044 1.783914 120.54959 2.056870 3.000000 2.358088 0.093418 1.759954
## 1570 26.74066 1.863883 120.20260 2.247795 3.000000 2.816015 0.712726 0.000000
## 1571 26.68038 1.812259 118.27766 2.239634 3.000000 2.684264 0.979306 0.000000
## 1572 37.05619 1.750150 118.20656 2.092830 3.000000 2.077704 0.598655 0.000000
## 1573 28.82528 1.815347 120.39976 2.967300 3.000000 2.530035 1.045107 0.947866
## 1574 25.88375 1.767077 114.13315 2.225731 3.000000 2.154326 1.266866 0.390178
## 1575 25.48652 1.762461 115.53162 2.178308 3.000000 2.165804 1.420675 1.875683
## 1576 29.88302 1.779049 112.43851 2.065752 3.000000 2.078297 0.000000 0.677354
## 1577 26.95764 1.780731 112.95792 2.263245 3.000000 2.092509 0.000000 1.836853
## 1578 26.49093 1.872517 120.89840 2.443538 3.000000 2.939492 1.208142 0.738935
## 1579 27.55880 1.801224 119.05038 2.744994 3.000000 2.478838 0.684487 0.677909
## 1580 22.90888 1.876898 121.27783 2.630137 2.806298 1.970508 1.304291 0.000000
## 1581 24.20162 1.775580 120.58942 2.113843 3.000000 2.316069 1.804157 0.357314
## 1582 31.68977 1.765690 120.08294 2.821727 3.000000 2.173279 1.096556 0.232858
## 1583 30.24260 1.759772 118.38236 2.312528 3.000000 2.208068 1.076720 1.035711
## 1584 31.34684 1.823545 126.46094 2.938801 3.000000 1.478994 0.946763 1.360463
## 1585 30.57734 1.868923 125.06426 2.050619 3.000000 1.515183 0.849811 0.261901
## 1586 25.12459 1.771510 113.20712 1.457758 3.000000 2.020249 1.556709 0.001330
## 1587 25.50903 1.772190 114.09766 2.193310 3.000000 2.089983 1.360994 0.857438
## 1588 25.47866 1.858265 117.57457 2.028571 3.000000 2.530428 1.312570 0.066805
## 1589 25.10051 1.830596 118.42416 1.455602 3.000000 2.363307 1.144683 0.101026
## 1590 38.52365 1.765836 118.53325 2.177896 2.987652 1.745095 0.656548 0.000000
## 1591 38.71216 1.770278 117.29188 2.252382 2.842848 1.879381 0.919388 0.000000
## 1592 25.71752 1.673491 103.70618 2.668949 1.134321 1.279443 0.112430 1.135503
## 1593 32.25962 1.703346 102.68624 2.723953 1.924168 1.000000 1.622055 0.069367
## 1594 23.47007 1.842906 121.14253 3.000000 2.701689 2.738485 0.992253 0.000000
## 1595 24.40881 1.779547 118.74004 2.736298 2.992903 2.045561 0.854957 0.428452
## 1596 24.44301 1.873368 121.82962 2.722161 2.658837 2.375707 1.299469 0.000000
## 1597 22.90634 1.755902 120.02116 2.971574 2.807420 1.962646 1.583832 0.504816
## 1598 24.00749 1.617655 100.94136 2.871016 1.834472 1.016585 0.236168 0.974939
## 1599 30.68670 1.644517 100.00442 2.964050 2.123138 1.000000 1.699181 0.620465
## 1600 20.18445 1.701284 104.57825 2.653721 1.265463 1.368457 0.218356 0.768071
## 1601 25.44721 1.658910 104.54879 2.859097 1.340361 1.530508 0.174475 1.261705
## 1602 30.00203 1.759324 112.00038 1.572036 3.000000 2.003563 0.000000 0.340196
## 1603 30.18830 1.758382 112.10074 1.387489 3.000000 2.017712 0.000000 0.731257
## 1604 24.24403 1.622297 99.98254 2.941929 3.989492 1.014135 1.958694 0.687342
## 1605 24.52188 1.623278 97.58296 2.973569 2.650088 1.003063 1.981154 0.157007
## 1606 29.72196 1.918859 129.99162 2.041376 3.000000 1.120213 1.055450 0.000000
## 1607 29.90658 1.913252 129.23222 2.024720 3.000000 1.800335 1.196368 0.000000
## 1608 37.08474 1.750000 118.07381 2.133964 3.000000 2.008361 0.202029 0.200516
## 1609 39.08886 1.750000 119.02910 2.702457 3.000000 2.005194 0.325313 0.419055
## 1610 22.65857 1.784994 113.71452 1.760038 3.000000 2.003531 1.089061 0.072264
## 1611 22.88910 1.792533 116.15777 1.996646 3.000000 2.000000 1.600536 0.739684
## 1612 24.63474 1.829757 120.98051 2.644094 3.000000 2.740525 2.000000 0.500936
## 1613 24.92036 1.796415 120.98845 2.475892 3.000000 2.949356 1.866839 0.100048
## 1614 31.78384 1.750000 120.00000 2.941627 3.000000 2.318134 0.582686 1.588046
## 1615 31.62796 1.762389 118.54873 2.998441 3.000000 2.462916 0.554646 1.992190
## 1616 22.97619 1.825718 121.23691 2.397284 2.892920 1.983973 1.859667 0.002600
## 1617 22.97736 1.839699 120.43155 2.382705 2.938902 1.999278 1.686229 0.630866
## 1618 40.97301 1.749405 109.90878 2.176317 2.986637 1.015672 0.941410 0.000000
## 1619 41.00000 1.750000 115.80698 2.000000 2.701521 1.142644 0.514225 0.000000
## 1620 21.72151 1.849998 122.11968 3.000000 2.014671 1.292786 0.145687 0.000000
## 1621 21.54455 1.849980 122.60991 3.000000 1.971659 1.179254 0.178856 0.000000
## 1622 24.00031 1.607939 100.61824 2.877743 1.311797 1.000463 0.182249 1.431200
## 1623 24.04090 1.603226 99.60553 3.000000 1.262831 1.000000 0.883171 1.382995
## 1624 29.50915 1.770663 112.47112 2.303041 3.000000 2.065817 0.000000 0.725222
## 1625 29.24627 1.758038 112.39531 2.323003 3.000000 2.155558 0.000000 1.251554
## 1626 25.34140 1.786997 115.02536 1.999530 3.000000 2.111908 1.453042 0.849503
## 1627 25.31416 1.771837 114.90609 1.585183 3.000000 2.101841 1.543961 0.000073
## 1628 40.36624 1.722396 109.34902 2.281963 3.770379 1.000000 1.330519 0.000000
## 1629 33.74959 1.701387 107.02541 2.561638 2.877470 1.000000 1.980401 0.000000
## 1630 32.86733 1.697421 103.01762 2.600217 2.175153 1.000000 1.985536 0.000000
## 1631 30.40320 1.696365 102.81598 2.791660 2.132290 1.254589 0.652736 1.040713
## 1632 29.68749 1.909198 129.67913 2.088680 3.000000 1.520215 1.857351 0.000000
## 1633 28.99281 1.909105 129.87486 2.206119 3.000000 1.483856 1.113169 0.000000
## 1634 30.47525 1.801368 121.09426 2.328469 3.000000 2.001208 0.800487 0.176678
## 1635 30.35052 1.860292 123.72135 2.002784 3.000000 2.292906 1.034031 0.000000
## 1636 26.68435 1.819535 118.33269 1.975675 3.000000 2.357969 0.704236 0.010721
## 1637 26.60748 1.793174 118.16508 2.002076 3.000000 2.338373 0.897562 0.081156
## 1638 33.17415 1.750150 118.29958 2.218599 3.000000 2.104337 0.766007 0.262118
## 1639 32.29016 1.754956 120.09881 2.967300 3.000000 2.530035 0.955317 1.339232
## 1640 26.05011 1.773115 115.08932 2.392179 3.000000 2.164670 1.079934 1.073026
## 1641 25.84628 1.772731 115.82817 2.381164 3.000000 2.170225 1.211048 1.899330
## 1642 29.62009 1.787933 112.53637 2.008245 3.000000 2.040137 0.000000 0.474216
## 1643 27.43906 1.785277 112.74080 2.155182 3.000000 2.049079 0.000000 1.749920
## 1644 28.49340 1.817572 120.81580 2.969233 3.000000 2.807984 0.982134 1.191998
## 1645 27.47424 1.843420 120.42041 2.765063 3.000000 2.867206 0.706777 0.677909
## 1646 25.03627 1.874519 121.24497 2.630137 3.000000 2.960088 1.356468 0.000000
## 1647 24.82540 1.796332 120.90159 2.195964 3.000000 2.514872 1.664722 0.127673
## 1648 30.49395 1.756221 119.11712 2.619987 3.000000 2.194746 1.076926 1.090995
## 1649 30.60755 1.757132 118.56557 2.918113 3.000000 2.240463 1.076248 1.480875
## 1650 31.19432 1.889104 129.15735 2.889485 3.000000 1.279771 0.941424 0.008343
## 1651 31.36347 1.869323 127.50741 2.939727 3.000000 1.344122 0.923428 1.432336
## 1652 25.02725 1.757154 112.20081 1.264234 3.000000 2.000000 1.333435 0.002168
## 1653 25.05857 1.764484 113.23435 1.517912 3.000000 2.038958 1.590255 0.001640
## 1654 24.41755 1.774775 117.39898 2.233720 2.993634 2.028368 0.863158 0.449886
## 1655 24.58220 1.769933 117.70870 1.475906 2.999346 2.019430 1.046878 0.460866
## 1656 40.10614 1.760175 117.65105 2.032883 2.976211 1.726109 0.477855 0.000000
## 1657 40.17419 1.763029 116.97450 2.046651 2.842035 1.732072 0.584272 0.000000
## 1658 27.18687 1.679515 102.87280 2.667229 1.097490 1.225958 0.206954 1.003011
## 1659 30.42437 1.699354 100.17687 2.819934 1.918630 1.000000 1.393020 0.553311
## 1660 23.14140 1.849307 121.65873 3.000000 2.510135 1.693362 0.769709 0.000000
## 1661 24.17864 1.867410 121.68431 2.954417 2.657720 2.104696 0.870056 0.000000
## 1662 22.83210 1.867140 121.83588 2.826251 2.604998 1.842173 1.284798 0.000000
## 1663 23.08362 1.848553 121.42112 3.000000 2.567567 2.011023 0.916478 0.000000
## 1664 24.07997 1.619810 98.54302 2.958410 2.434347 1.000000 1.930033 0.754023
## 1665 26.94779 1.647807 99.59222 2.935157 1.845858 1.000000 1.089891 0.715993
## 1666 20.10103 1.619128 104.30371 2.870895 1.627555 1.375728 0.210181 1.163117
## 1667 22.78940 1.641870 104.27006 2.869833 1.569176 1.533682 0.167943 1.368262
## 1668 28.40433 1.787379 112.17373 1.878251 3.000000 2.022933 0.000000 0.325445
## 1669 30.00336 1.758355 112.00710 1.750809 3.000000 2.002871 0.000000 0.114457
## 1670 25.13612 1.764140 113.08972 1.168856 3.000000 2.013205 1.246223 0.001590
## 1671 25.13947 1.767186 112.22603 1.443674 3.000000 2.002194 1.386151 0.001337
## 1672 31.74382 1.677820 102.02206 2.826036 2.371658 1.000000 1.996487 0.000000
## 1673 30.79626 1.668478 100.54398 2.955300 2.378211 1.000000 1.738267 0.394533
## 1674 28.39311 1.685462 99.54012 2.774562 2.301129 1.000000 1.621733 0.138314
## 1675 27.93982 1.694642 99.70933 2.772027 2.454432 1.000000 0.858554 0.051268
## 1676 31.03409 1.886109 129.34947 2.499626 3.000000 1.125338 0.945220 1.022505
## 1677 30.68435 1.915000 129.96643 2.108638 3.000000 1.014876 0.987521 0.047473
## 1678 30.10822 1.841908 124.07072 2.467548 3.000000 2.660290 0.994422 0.310394
## 1679 31.34750 1.868127 123.17221 2.585942 3.000000 2.302506 0.597863 0.111925
## 1680 31.76180 1.751688 119.20531 2.149610 3.000000 2.133876 0.393452 0.345887
## 1681 30.97693 1.755333 118.23778 2.938616 3.000000 2.060390 0.371508 1.333559
## 1682 37.58863 1.754217 117.89720 2.535154 2.915921 1.892400 0.693732 0.067410
## 1683 37.99791 1.760710 118.66833 2.611222 2.992083 1.796376 0.641954 0.202810
## 1684 21.65480 1.755938 116.31196 1.800122 3.000000 2.000000 1.689525 0.764452
## 1685 22.82975 1.765137 116.66991 1.482722 3.000000 2.000000 1.112504 0.690353
## 1686 25.01517 1.788239 115.38252 1.735664 3.000000 2.041536 1.392406 0.391740
## 1687 23.81280 1.767121 116.16435 1.655684 3.000000 2.000000 0.976425 0.690082
## 1688 23.97568 1.840039 120.97549 2.598207 2.849347 2.006167 1.520010 0.295685
## 1689 24.14904 1.824901 120.80572 2.225149 3.000000 2.357978 1.943743 0.682128
## 1690 25.06294 1.828391 120.99827 3.000000 3.000000 3.000000 1.685369 0.264969
## 1691 25.14007 1.829529 120.99658 3.000000 3.000000 3.000000 1.467863 0.343635
## 1692 30.72280 1.779325 120.75166 2.519592 3.000000 2.229145 0.350717 1.140348
## 1693 30.91643 1.781139 120.79453 2.111887 3.000000 2.357373 0.425621 1.416353
## 1694 31.01030 1.764166 119.37302 2.970983 3.000000 2.828861 0.454944 1.915818
## 1695 30.60546 1.754796 118.80594 2.907542 3.000000 2.284494 0.647632 1.668318
## 1696 24.62205 1.756509 117.36872 1.451337 3.000000 2.000000 1.384607 0.631217
## 1697 23.74583 1.756772 117.32652 1.537505 3.000000 2.000000 1.631912 0.631422
## 1698 23.32784 1.754439 119.44121 1.893428 3.000000 2.000000 1.917383 0.936480
## 1699 23.41114 1.755142 119.19292 2.007845 2.954446 1.968796 1.587406 0.838947
## 1700 39.82559 1.706741 108.01260 2.487781 3.755976 1.000000 1.860765 0.000000
## 1701 36.83976 1.742850 106.42104 2.541785 2.902639 1.000000 1.668961 0.000000
## 1702 33.78930 1.681100 102.52311 2.813775 2.372705 1.000000 1.979355 0.000000
## 1703 34.16200 1.705682 103.06777 2.562687 2.100918 1.458545 1.167856 0.412329
## 1704 22.58004 1.849507 121.56094 3.000000 2.272801 1.560064 0.796770 0.000000
## 1705 22.85172 1.853373 121.73784 2.922511 2.692889 1.809531 0.478595 0.000000
## 1706 23.25493 1.847530 122.06261 3.000000 2.280545 1.591597 0.932783 0.000000
## 1707 22.34320 1.870340 121.45823 2.836055 2.675411 1.711666 0.937320 0.000000
## 1708 24.00627 1.607787 100.78343 2.880759 1.487674 1.013780 1.001090 1.098380
## 1709 24.00120 1.603091 100.20941 3.000000 1.020750 1.000000 0.233056 1.707421
## 1710 20.15666 1.620109 103.39335 2.766441 1.240424 1.413218 0.165269 0.862587
## 1711 23.36031 1.610647 100.64226 2.997524 1.154318 1.238057 1.129300 1.665621
## 1712 28.98624 1.758618 113.50155 2.320201 3.000000 2.164784 0.000000 1.465479
## 1713 29.71317 1.763259 113.21581 2.181057 3.000000 2.085540 0.000000 1.439004
## 1714 27.39412 1.764138 112.32321 1.924632 3.000000 2.006595 0.176800 0.511694
## 1715 24.91225 1.755960 112.27757 1.397468 3.000000 2.018970 0.665439 0.062167
## 1716 25.52675 1.783381 115.34718 2.191429 3.000000 2.102709 1.325340 0.380979
## 1717 25.52313 1.786532 114.53468 2.100177 3.000000 2.099687 1.281165 0.247332
## 1718 25.82235 1.766626 114.18710 2.075321 3.000000 2.144838 1.501754 0.276319
## 1719 25.87941 1.765464 114.14438 1.626369 3.000000 2.109697 1.352973 0.076693
## 1720 30.36136 1.758530 111.63546 1.263216 3.219347 1.981782 0.482625 0.000000
## 1721 30.45117 1.758539 111.95041 1.067909 3.656401 1.984590 0.054238 0.000000
## 1722 40.56451 1.748015 109.75874 2.310751 3.220181 1.006643 1.158040 0.000000
## 1723 40.50172 1.744974 111.16968 2.294259 2.850948 1.870290 0.917014 0.000000
## 1724 30.31578 1.701566 103.74353 2.576490 2.187145 1.381070 1.928275 0.413663
## 1725 33.29317 1.696412 103.25035 2.679664 2.415522 1.000000 1.987296 0.000000
## 1726 30.63894 1.680489 102.00455 2.938687 2.138375 1.251715 1.181811 0.778375
## 1727 29.79110 1.703317 102.59217 2.654792 1.077331 1.345407 0.327418 0.386861
## 1728 31.20567 1.877732 127.16138 2.731368 3.000000 1.486824 1.485978 1.150439
## 1729 30.89922 1.909639 129.01318 2.222590 3.000000 1.591909 1.392026 0.917727
## 1730 29.66922 1.909188 129.19449 2.432355 3.000000 1.336526 1.638120 0.090341
## 1731 30.59563 1.910672 129.23271 2.497548 3.000000 1.362583 1.144076 0.173232
## 1732 30.55496 1.779136 120.60094 2.671238 3.000000 2.145368 0.882709 0.593917
## 1733 31.57139 1.767485 120.15805 2.576910 3.000000 2.080187 1.042680 0.376683
## 1734 30.57794 1.783953 120.61356 2.341999 3.000000 2.299878 0.565242 0.921991
## 1735 30.71773 1.767140 120.34440 2.117121 3.000000 2.193008 0.992829 1.556052
## 1736 26.73448 1.816197 119.62276 2.247037 3.000000 2.718408 0.763595 0.000000
## 1737 26.69932 1.839941 119.95665 2.244654 3.000000 2.795752 0.839481 0.000000
## 1738 25.65909 1.848420 117.63171 2.128574 3.000000 2.531984 1.003294 0.026575
## 1739 26.34816 1.830317 117.75701 2.068834 3.000000 2.543841 1.217993 0.038253
## 1740 37.63810 1.750085 118.11418 2.073224 3.000000 2.024035 0.131371 0.000000
## 1741 37.76536 1.763582 117.86159 2.145114 2.888193 2.038128 0.852344 0.000000
## 1742 28.25520 1.816547 120.69912 2.997951 3.000000 2.715856 0.739881 0.972054
## 1743 27.93143 1.805445 119.48461 2.911312 3.000000 2.501808 0.946760 0.785701
## 1744 25.49285 1.770124 114.16392 2.159033 3.000000 2.116399 1.331526 0.052942
## 1745 25.55051 1.772740 114.25428 2.175276 3.000000 2.128176 1.306476 0.079334
## 1746 25.54245 1.763215 115.10813 2.219650 3.000000 2.165408 1.315045 0.688985
## 1747 25.75831 1.766547 115.45845 2.203962 3.000000 2.156870 1.289421 1.220767
## 1748 29.98149 1.773181 112.34872 1.947495 3.000000 2.042073 0.000000 0.618087
## 1749 29.89147 1.760030 112.40919 2.262292 3.000000 2.115354 0.000000 0.847587
## 1750 26.77868 1.780089 113.15464 2.219186 3.000000 2.092326 0.545919 1.742880
## 1751 28.37796 1.766946 113.23554 2.314175 3.000000 2.151809 0.000000 1.578517
## 1752 26.19932 1.885119 121.06505 2.423291 3.000000 2.902682 1.243567 0.555591
## 1753 27.26629 1.828276 120.87229 2.637202 3.000000 2.966647 1.159598 0.758897
## 1754 27.63503 1.806227 120.42357 2.974006 3.000000 2.565828 0.690269 1.339691
## 1755 26.89989 1.812919 119.84145 2.347942 3.000000 2.730663 0.689371 0.188693
## 1756 22.75900 1.859717 121.28453 2.654076 2.574108 1.784710 1.170537 0.000000
## 1757 22.77100 1.865160 121.52737 2.739000 2.740492 1.824561 1.094839 0.000000
## 1758 23.82668 1.783609 120.92154 2.591292 2.956422 2.310830 1.485240 0.281815
## 1759 24.18627 1.794827 120.91970 2.611847 2.749334 2.364849 1.141708 0.063005
## 1760 30.94537 1.759647 120.00939 2.766612 3.000000 2.173417 1.089344 1.198439
## 1761 31.49070 1.773521 120.20971 2.777165 3.000000 2.106861 0.925941 0.291600
## 1762 31.56724 1.753327 118.26569 2.232836 3.000000 2.146398 0.886817 0.477870
## 1763 30.44408 1.761068 118.37063 2.571274 3.000000 2.224164 1.018158 1.152899
## 1764 31.19926 1.848845 125.07786 2.496190 3.000000 1.662117 0.992371 0.217632
## 1765 31.19022 1.842812 125.97393 2.151335 3.000000 1.491169 0.883542 0.527766
## 1766 30.57535 1.825449 124.95278 2.016950 3.000000 1.834120 0.797209 0.185499
## 1767 30.70256 1.861980 126.41841 2.927187 3.000000 1.508796 0.902776 1.015467
## 1768 25.05788 1.763987 113.06967 1.412566 3.000000 2.002495 1.592795 0.001867
## 1769 25.15129 1.761519 112.83519 1.289315 3.000000 2.007348 1.376217 0.001518
## 1770 25.13709 1.772045 114.06794 1.624366 3.000000 2.081719 1.538922 0.356868
## 1771 25.32920 1.771817 114.00483 1.528331 3.000000 2.079353 1.522429 0.228598
## 1772 25.66668 1.798580 117.93329 2.037042 3.000000 2.436990 1.016254 0.020044
## 1773 25.01277 1.788586 117.84935 2.191108 2.993856 2.444917 1.055854 0.145284
## 1774 25.04794 1.803207 118.33297 1.431346 3.000000 2.098959 1.110868 0.196952
## 1775 25.42646 1.836592 118.37760 1.841990 3.000000 2.503244 1.226019 0.078207
## 1776 37.20708 1.762921 118.40174 2.136830 2.993084 1.885926 0.615298 0.000000
## 1777 38.10894 1.752863 119.20146 2.499388 2.989791 1.959777 0.608100 0.646760
## 1778 38.64444 1.768235 117.79227 2.230742 2.920373 1.831187 0.756277 0.000000
## 1779 38.11299 1.766888 118.13490 2.240757 2.911568 1.895876 0.822186 0.000000
## 1780 24.82539 1.603501 101.03826 2.996186 1.134042 1.270166 0.073065 1.551934
## 1781 26.62434 1.690262 103.18092 2.649406 1.120102 1.153286 0.216908 0.619012
## 1782 33.72245 1.712905 103.27609 2.525884 2.040582 1.000000 1.670360 0.023959
## 1783 32.51647 1.695735 102.78486 2.736647 2.015675 1.000000 1.977918 0.056351
## 1784 23.88194 1.829971 121.04172 2.684335 2.711238 2.732331 1.156024 0.442456
## 1785 23.31964 1.846290 121.24804 3.000000 2.695396 2.628816 0.975384 0.000000
## 1786 23.91239 1.774983 119.08180 2.425503 2.996834 2.017602 1.580263 0.531769
## 1787 24.98300 1.789680 118.43617 1.469384 2.996444 2.067741 1.082236 0.150544
## 1788 24.51144 1.852664 121.31026 2.906269 2.894142 2.435489 1.266739 0.362160
## 1789 24.05331 1.872561 121.47108 2.808027 2.683061 2.640483 1.280191 0.000000
## 1790 22.90689 1.819550 120.77544 2.636719 2.806341 1.967591 1.525384 0.315595
## 1791 23.14764 1.815514 120.33766 2.996717 2.791366 2.626309 1.194898 0.034897
## 1792 24.00189 1.614075 100.24530 2.880483 1.703299 1.006378 1.076729 1.058007
## 1793 24.00240 1.609418 100.07837 2.885693 1.685134 1.011849 0.503105 1.217929
## 1794 30.71516 1.650189 101.14128 2.913452 2.269799 1.000000 1.889937 0.378818
## 1795 30.64243 1.653876 102.58389 2.919526 2.142328 1.175714 0.958555 0.636289
## 1796 20.06843 1.657132 105.58049 2.724121 1.437959 1.590418 0.029603 1.122118
## 1797 20.91437 1.644751 101.06799 2.801992 1.343117 1.128942 0.233987 0.819980
## 1798 25.51205 1.660761 104.32146 2.748971 1.213431 1.448875 0.128548 1.239038
## 1799 26.84481 1.691510 102.59518 2.680375 1.089048 1.366238 0.181324 1.041677
## 1800 25.91924 1.611462 102.09322 3.000000 3.000000 1.023328 0.050930 1.000000
## 1801 26.00000 1.584782 105.05560 3.000000 3.000000 1.197667 0.000000 0.534769
## 1802 18.23354 1.792378 137.85974 3.000000 3.000000 2.838893 1.990317 0.735868
## 1803 18.14770 1.802257 149.93585 3.000000 3.000000 2.181811 1.995582 0.939665
## 1804 26.00000 1.656320 111.93301 3.000000 3.000000 2.774014 0.000000 0.138418
## 1805 26.00000 1.600762 105.44826 3.000000 3.000000 1.031354 0.000000 0.374650
## 1806 25.90228 1.678658 104.95483 3.000000 3.000000 1.666160 0.210351 0.734210
## 1807 25.54087 1.678201 109.90047 3.000000 3.000000 1.471664 0.143955 0.444532
## 1808 22.39251 1.655630 121.20517 3.000000 3.000000 1.347559 0.462951 0.317940
## 1809 21.30540 1.694952 133.76473 3.000000 3.000000 1.338241 1.926280 0.886135
## 1810 26.00000 1.622771 109.95971 3.000000 3.000000 2.679137 0.000000 0.479348
## 1811 26.00000 1.583889 110.54538 3.000000 3.000000 2.578292 0.000000 0.492394
## 1812 21.33459 1.729045 131.52927 3.000000 3.000000 1.302193 1.742453 0.942320
## 1813 22.97865 1.664622 114.46542 3.000000 3.000000 2.408442 0.194056 0.803141
## 1814 21.01245 1.747773 127.90284 3.000000 3.000000 1.705218 0.390937 0.998646
## 1815 21.05606 1.730113 152.09436 3.000000 3.000000 2.374958 0.750111 0.671458
## 1816 18.77100 1.746652 133.80013 3.000000 3.000000 2.869234 1.465931 0.627886
## 1817 24.26594 1.719365 114.51154 3.000000 3.000000 2.987406 0.389260 0.526776
## 1818 26.00000 1.632377 111.94666 3.000000 3.000000 2.737091 0.000000 0.037078
## 1819 26.00000 1.642572 111.86817 3.000000 3.000000 2.623489 0.000000 0.138563
## 1820 25.96701 1.654875 104.75871 3.000000 3.000000 2.612758 0.246290 0.802136
## 1821 26.00000 1.627567 107.48266 3.000000 3.000000 2.687378 0.000000 0.410651
## 1822 20.59005 1.736276 130.92714 3.000000 3.000000 1.852692 1.463610 0.962336
## 1823 24.49737 1.737056 132.52701 3.000000 3.000000 2.865590 0.973864 0.583450
## 1824 25.99189 1.580968 102.00338 3.000000 3.000000 1.003563 0.008127 1.000000
## 1825 25.90843 1.607128 103.02686 3.000000 3.000000 1.077253 0.162083 0.824607
## 1826 18.17788 1.821566 142.10247 3.000000 3.000000 2.714949 1.999773 0.813784
## 1827 18.11250 1.827730 152.72054 3.000000 3.000000 2.154949 1.999897 0.957463
## 1828 26.00000 1.656504 111.99305 3.000000 3.000000 2.893117 0.000000 0.019310
## 1829 26.00000 1.637725 111.20896 3.000000 3.000000 2.709140 0.000000 0.110518
## 1830 25.90228 1.669701 104.58578 3.000000 3.000000 1.570188 0.210351 0.881848
## 1831 25.54087 1.668709 104.75496 3.000000 3.000000 1.412049 0.143955 0.753077
## 1832 20.52099 1.668642 124.70478 3.000000 3.000000 1.156350 0.786828 0.366385
## 1833 20.87115 1.690614 129.76914 3.000000 3.000000 1.154698 1.718360 0.959218
## 1834 26.00000 1.622418 110.67634 3.000000 3.000000 2.691584 0.000000 0.425473
## 1835 26.00000 1.643332 110.82470 3.000000 3.000000 2.709654 0.000000 0.251150
## 1836 21.76883 1.733383 135.52486 3.000000 3.000000 1.485736 1.950374 0.869238
## 1837 20.89149 1.748313 133.57379 3.000000 3.000000 2.874336 1.624981 0.825609
## 1838 20.94194 1.812963 138.73062 3.000000 3.000000 2.641489 0.481555 0.735201
## 1839 20.98902 1.807340 155.87209 3.000000 3.000000 2.417122 0.952725 0.573958
## 1840 18.36748 1.745644 133.66559 3.000000 3.000000 2.900857 1.508897 0.625371
## 1841 21.05111 1.753266 133.85243 3.000000 3.000000 2.953110 1.445148 0.673210
## 1842 26.00000 1.632193 111.88661 3.000000 3.000000 2.617988 0.000000 0.156187
## 1843 26.00000 1.641098 111.81834 3.000000 3.000000 2.550570 0.000000 0.204820
## 1844 25.99865 1.640741 104.80854 3.000000 3.000000 2.653531 0.190061 0.692343
## 1845 26.00000 1.618573 104.92864 3.000000 3.000000 1.698767 0.000000 0.543960
## 1846 22.84636 1.757442 133.36509 3.000000 3.000000 2.848370 1.206059 0.766668
## 1847 19.88565 1.763343 133.95267 3.000000 3.000000 2.835622 1.419473 0.816986
## 1848 25.93038 1.610086 102.38745 3.000000 3.000000 1.050564 0.026033 0.539074
## 1849 25.89782 1.664463 102.78197 3.000000 3.000000 1.068493 0.112122 1.000000
## 1850 26.00000 1.602025 104.89935 3.000000 3.000000 2.613928 0.000000 0.553093
## 1851 25.96879 1.632896 104.98892 3.000000 3.000000 1.239833 0.162279 0.619235
## 1852 18.33502 1.771043 137.04496 3.000000 3.000000 2.861533 1.704640 0.655571
## 1853 21.70075 1.789555 137.76779 3.000000 3.000000 2.832659 1.505775 0.923005
## 1854 18.22254 1.801746 141.16627 3.000000 3.000000 2.418488 1.995070 0.893514
## 1855 20.37560 1.787195 151.97586 3.000000 3.000000 2.304716 0.826660 0.914492
## 1856 26.00000 1.644141 111.94254 3.000000 3.000000 2.763005 0.000000 0.101867
## 1857 26.00000 1.643355 111.60055 3.000000 3.000000 2.652616 0.000000 0.250502
## 1858 26.00000 1.623707 105.03746 3.000000 3.000000 2.553198 0.000000 0.393838
## 1859 26.00000 1.610636 105.42353 3.000000 3.000000 2.180566 0.000000 0.519905
## 1860 25.94383 1.629491 104.83907 3.000000 3.000000 2.209790 0.114698 0.604422
## 1861 25.29197 1.684768 104.82117 3.000000 3.000000 1.444379 0.224482 0.912187
## 1862 25.65323 1.664940 110.92217 3.000000 3.000000 1.604075 0.029728 0.200122
## 1863 25.78386 1.655646 110.21734 3.000000 3.000000 1.528258 0.015860 0.436068
## 1864 19.17614 1.666194 124.80587 3.000000 3.000000 1.228838 0.792553 0.639561
## 1865 21.20742 1.707508 121.86433 3.000000 3.000000 1.615548 1.376534 0.926052
## 1866 21.63306 1.754174 133.78395 3.000000 3.000000 1.945950 1.493018 0.906611
## 1867 21.00960 1.714193 131.86673 3.000000 3.000000 1.709556 1.592494 0.925843
## 1868 26.00000 1.624390 110.00864 3.000000 3.000000 2.507461 0.000000 0.368472
## 1869 26.00000 1.638836 110.97048 3.000000 3.000000 2.644135 0.000000 0.357581
## 1870 26.00000 1.621245 111.26733 3.000000 3.000000 2.605685 0.000000 0.199227
## 1871 25.95451 1.623514 109.98014 3.000000 3.000000 2.217348 0.001015 0.481031
## 1872 21.00197 1.736215 132.14555 3.000000 3.000000 1.657541 1.672639 0.629285
## 1873 21.77225 1.732951 132.90488 3.000000 3.000000 1.817899 1.577824 0.930836
## 1874 23.76197 1.691350 114.48070 3.000000 3.000000 2.509535 0.334264 0.668172
## 1875 24.44965 1.635062 113.27739 3.000000 3.000000 2.578038 0.165422 0.463196
## 1876 18.37820 1.746061 128.26140 3.000000 3.000000 2.501638 1.546179 0.664880
## 1877 19.72572 1.746529 129.36377 3.000000 3.000000 2.250711 0.642350 0.685129
## 1878 21.34402 1.746516 144.30226 3.000000 3.000000 2.366510 1.247505 0.723366
## 1879 21.32210 1.751118 149.29111 3.000000 3.000000 2.309409 1.682910 0.705580
## 1880 19.26293 1.741014 132.57927 3.000000 3.000000 2.436261 1.464674 0.870920
## 1881 21.56681 1.748533 133.94608 3.000000 3.000000 2.833566 1.413239 0.862724
## 1882 24.47524 1.694726 112.77661 3.000000 3.000000 2.724099 0.336795 0.153462
## 1883 25.61246 1.674515 112.87966 3.000000 3.000000 2.989389 0.360090 0.169016
## 1884 26.00000 1.631332 111.82996 3.000000 3.000000 2.559750 0.000000 0.237307
## 1885 26.00000 1.641918 111.86899 3.000000 3.000000 2.635454 0.000000 0.088309
## 1886 26.00000 1.640125 111.53949 3.000000 3.000000 2.625537 0.000000 0.162494
## 1887 26.00000 1.649178 111.91436 3.000000 3.000000 2.884077 0.000000 0.096576
## 1888 25.96773 1.603404 105.03191 3.000000 3.000000 1.919473 0.027101 0.546137
## 1889 25.98994 1.644199 105.03607 3.000000 3.000000 2.310076 0.071150 0.733085
## 1890 26.00000 1.628909 106.87593 3.000000 3.000000 2.686824 0.000000 0.540812
## 1891 25.61723 1.628019 108.26592 3.000000 3.000000 1.621300 0.090917 0.438216
## 1892 21.03091 1.718180 133.46676 3.000000 3.000000 1.517215 1.486289 0.937492
## 1893 20.95108 1.708581 131.27485 3.000000 3.000000 1.796956 1.684582 0.887388
## 1894 22.98022 1.724983 132.94066 3.000000 3.000000 2.085553 1.271651 0.587932
## 1895 23.42604 1.739991 133.48548 3.000000 3.000000 2.837797 1.343875 0.803156
## 1896 25.99919 1.568543 102.00012 3.000000 3.000000 1.000544 0.001297 1.000000
## 1897 25.93476 1.579893 102.13465 3.000000 3.000000 1.005864 0.020060 0.695838
## 1898 20.32772 1.782714 154.61845 3.000000 3.000000 2.319559 1.970730 0.768375
## 1899 19.47219 1.793824 160.93535 3.000000 3.000000 2.069257 1.986646 0.947091
## 1900 26.00000 1.659557 111.99910 3.000000 3.000000 2.956548 0.000000 0.010056
## 1901 26.00000 1.657820 111.95611 3.000000 3.000000 2.777557 0.000000 0.051858
## 1902 25.81645 1.684082 104.59237 3.000000 3.000000 1.295436 0.282063 0.929356
## 1903 25.49896 1.683950 104.84682 3.000000 3.000000 1.241378 0.259427 0.852362
## 1904 19.13750 1.716521 127.64232 3.000000 3.000000 1.313834 0.912334 0.707494
## 1905 20.19073 1.680762 125.41855 3.000000 3.000000 1.124366 0.877067 0.552006
## 1906 26.00000 1.623303 110.81746 3.000000 3.000000 2.673754 0.000000 0.339290
## 1907 26.00000 1.631856 110.80434 3.000000 3.000000 2.704850 0.000000 0.243338
## 1908 21.84065 1.747479 136.51665 3.000000 3.000000 1.607531 1.963379 0.858392
## 1909 20.87167 1.782453 137.85262 3.000000 3.000000 2.748909 1.989171 0.832515
## 1910 21.50172 1.809871 152.39474 3.000000 3.000000 2.351207 0.246831 0.913360
## 1911 21.52129 1.803677 160.63941 3.000000 3.000000 2.404049 0.427905 0.639894
## 1912 18.31459 1.745602 133.55469 3.000000 3.000000 2.923792 1.536555 0.625350
## 1913 19.52975 1.751038 133.84303 3.000000 3.000000 2.955075 1.460460 0.655558
## 1914 26.00000 1.631547 111.58862 3.000000 3.000000 2.554007 0.000000 0.252635
## 1915 26.00000 1.635905 111.57108 3.000000 3.000000 2.511399 0.000000 0.258472
## 1916 26.00000 1.616975 104.84622 3.000000 3.000000 2.653563 0.000000 0.554150
## 1917 26.00000 1.627880 104.92057 3.000000 3.000000 2.588107 0.000000 0.465607
## 1918 21.76815 1.764160 133.88863 3.000000 3.000000 2.325020 1.441791 0.918468
## 1919 21.23842 1.763847 133.93787 3.000000 3.000000 2.836791 1.467820 0.890527
## 1920 25.93038 1.608808 102.08396 3.000000 3.000000 1.019684 0.026033 1.000000
## 1921 25.91957 1.610488 102.17495 3.000000 3.000000 1.032834 0.045250 0.922749
## 1922 25.91852 1.621231 104.98679 3.000000 3.000000 1.653049 0.139159 0.711331
## 1923 25.56566 1.642392 104.98808 3.000000 3.000000 1.204055 0.094851 0.603736
## 1924 18.74491 1.801983 138.03453 3.000000 3.000000 2.691591 1.168368 0.735372
## 1925 21.70470 1.787614 137.85825 3.000000 3.000000 2.531456 1.980738 0.835771
## 1926 20.08997 1.801478 151.41729 3.000000 3.000000 2.226081 1.881761 0.933964
## 1927 18.12074 1.807576 152.56767 3.000000 3.000000 2.164718 1.999631 0.941336
## 1928 26.00000 1.650125 111.93967 3.000000 3.000000 2.770732 0.000000 0.125235
## 1929 26.00000 1.652674 111.91916 3.000000 3.000000 2.814517 0.000000 0.101598
## 1930 25.98618 1.663632 105.12211 3.000000 3.000000 1.626467 0.010183 0.412806
## 1931 25.98211 1.627818 105.42863 3.000000 3.000000 1.480750 0.098043 0.663492
## 1932 25.74863 1.668770 104.77414 3.000000 3.000000 1.526416 0.180158 0.747909
## 1933 25.95977 1.642098 104.96676 3.000000 3.000000 1.482002 0.204108 0.657221
## 1934 25.65323 1.657570 109.93123 3.000000 3.000000 1.610472 0.029728 0.472343
## 1935 25.78386 1.643111 109.91001 3.000000 3.000000 1.530992 0.015860 0.445495
## 1936 21.41243 1.675562 121.63918 3.000000 3.000000 1.484938 0.742250 0.604692
## 1937 22.77789 1.661415 120.74821 3.000000 3.000000 1.910390 0.217455 0.775820
## 1938 21.14016 1.713133 133.73589 3.000000 3.000000 1.411365 1.564618 0.910683
## 1939 21.41350 1.719900 133.88603 3.000000 3.000000 2.417520 1.556155 0.873936
## 1940 26.00000 1.622701 109.98269 3.000000 3.000000 2.688229 0.000000 0.451377
## 1941 26.00000 1.622468 110.40085 3.000000 3.000000 2.695094 0.000000 0.413474
## 1942 26.00000 1.618867 110.77739 3.000000 3.000000 2.618198 0.000000 0.380695
## 1943 26.00000 1.600905 110.07495 3.000000 3.000000 2.555189 0.000000 0.462973
## 1944 21.39137 1.730636 131.90259 3.000000 3.000000 1.419136 1.700889 0.930888
## 1945 21.05198 1.729719 131.87756 3.000000 3.000000 1.422483 1.708971 0.673009
## 1946 23.45530 1.677672 114.47048 3.000000 3.000000 2.426094 0.294763 0.737226
## 1947 23.69484 1.637524 113.90506 3.000000 3.000000 2.495961 0.189831 0.652289
## 1948 20.60122 1.738717 128.11416 3.000000 3.000000 1.797041 1.427413 0.966181
## 1949 20.81158 1.741193 128.76384 3.000000 3.000000 1.768111 0.616503 0.968151
## 1950 19.99357 1.792833 152.43563 3.000000 3.000000 2.365188 1.256115 0.760091
## 1951 20.07445 1.810427 152.21714 3.000000 3.000000 2.299156 1.699056 0.729722
## 1952 18.90404 1.743589 133.28133 3.000000 3.000000 2.684819 1.465250 0.804491
## 1953 19.78323 1.747962 133.93653 3.000000 3.000000 2.841740 1.429256 0.775378
## 1954 24.29121 1.711460 113.37285 3.000000 3.000000 2.796894 0.382189 0.167790
## 1955 25.31153 1.685482 113.45122 3.000000 3.000000 2.987718 0.387074 0.283804
## 1956 26.00000 1.639251 111.92700 3.000000 3.000000 2.675567 0.000000 0.081929
## 1957 26.00000 1.654784 111.93315 3.000000 3.000000 2.770125 0.000000 0.088236
## 1958 26.00000 1.641209 111.85649 3.000000 3.000000 2.621877 0.000000 0.153669
## 1959 26.00000 1.643167 111.89423 3.000000 3.000000 2.720050 0.000000 0.127443
## 1960 25.96650 1.630730 104.79055 3.000000 3.000000 2.436097 0.129178 0.683736
## 1961 25.95090 1.649867 104.79103 3.000000 3.000000 2.535629 0.152713 0.770200
## 1962 26.00000 1.613574 107.01226 3.000000 3.000000 2.678779 0.000000 0.508848
## 1963 26.00000 1.627532 106.69053 3.000000 3.000000 2.569713 0.000000 0.396972
## 1964 20.84861 1.726606 131.76807 3.000000 3.000000 1.759352 1.469928 0.950438
## 1965 20.80179 1.721476 131.04227 3.000000 3.000000 1.837184 1.525165 0.926443
## 1966 23.71264 1.742901 132.80710 3.000000 3.000000 2.856795 1.046463 0.586163
## 1967 24.06387 1.737313 133.16660 3.000000 3.000000 2.846259 1.295759 0.723154
## 1968 25.95774 1.624140 102.23345 3.000000 3.000000 1.067716 0.030541 1.000000
## 1969 25.90935 1.644078 102.27777 3.000000 3.000000 1.029241 0.075776 1.000000
## 1970 25.95500 1.592529 102.87455 3.000000 3.000000 1.074412 0.006265 0.845633
## 1971 25.90883 1.607734 102.30577 3.000000 3.000000 1.030501 0.065820 0.991473
## 1972 19.29700 1.817271 141.91780 3.000000 3.000000 2.699675 1.520818 0.763990
## 1973 18.30177 1.808765 140.29202 3.000000 3.000000 2.830247 1.783138 0.789064
## 1974 19.87267 1.817231 152.37191 3.000000 3.000000 2.305521 1.956278 0.923760
## 1975 18.13782 1.819728 151.27853 3.000000 3.000000 2.155926 1.999836 0.946030
## 1976 26.00000 1.656465 111.94997 3.000000 3.000000 2.784303 0.000000 0.127775
## 1977 26.00000 1.648143 111.95011 3.000000 3.000000 2.786417 0.000000 0.079673
## 1978 26.00000 1.622703 111.21619 3.000000 3.000000 2.707201 0.000000 0.167272
## 1979 26.00000 1.640606 111.03688 3.000000 3.000000 2.709428 0.000000 0.228486
## 1980 25.42724 1.683502 104.75964 3.000000 3.000000 1.525127 0.220825 0.896105
## 1981 25.79519 1.669039 104.59393 3.000000 3.000000 1.554925 0.209586 0.823069
## 1982 25.49359 1.673665 104.70471 3.000000 3.000000 1.170515 0.264831 0.896842
## 1983 25.52434 1.668931 104.76832 3.000000 3.000000 1.436616 0.167086 0.764717
## 1984 20.90879 1.700996 126.49024 3.000000 3.000000 1.242832 0.530925 0.575969
## 1985 20.78175 1.734092 125.11763 3.000000 3.000000 1.542490 0.627700 0.450479
## 1986 21.28910 1.708291 130.98634 3.000000 3.000000 1.205548 1.723934 0.952352
## 1987 21.21073 1.716497 130.87113 3.000000 3.000000 1.301657 1.718543 0.947884
## 1988 26.00000 1.624950 111.00492 3.000000 3.000000 2.704315 0.000000 0.322666
## 1989 26.00000 1.594776 110.64093 3.000000 3.000000 2.639816 0.000000 0.452236
## 1990 26.00000 1.626503 110.81876 3.000000 3.000000 2.708927 0.000000 0.278962
## 1991 26.00000 1.624576 110.80312 3.000000 3.000000 2.704827 0.000000 0.269577
## 1992 21.65691 1.729099 134.84266 3.000000 3.000000 1.395400 1.931173 0.878258
## 1993 21.76073 1.735810 135.34668 3.000000 3.000000 2.611654 1.618512 0.868788
## 1994 21.02899 1.748524 133.87884 3.000000 3.000000 2.868167 1.483720 0.835090
## 1995 21.28224 1.748951 133.66258 3.000000 3.000000 2.247979 1.609938 0.849236
## 1996 20.38805 1.777971 137.78503 3.000000 3.000000 2.702789 1.606109 0.731213
## 1997 21.02221 1.739950 135.69338 3.000000 3.000000 1.663213 1.094035 0.786665
## 1998 20.10224 1.816868 153.95995 3.000000 3.000000 2.414739 1.917014 0.927982
## 1999 21.29197 1.800200 155.24267 3.000000 3.000000 2.351193 1.051889 0.686491
## 2000 20.53100 1.746470 133.64471 3.000000 3.000000 2.896088 1.612741 0.773190
## 2001 18.97697 1.759091 133.90361 3.000000 3.000000 2.862408 1.456933 0.742423
## 2002 20.92496 1.752531 133.61871 3.000000 3.000000 2.887659 1.480919 0.779641
## 2003 21.28253 1.761773 133.90347 3.000000 3.000000 2.893062 1.408177 0.807457
## 2004 26.00000 1.633195 111.88375 3.000000 3.000000 2.619517 0.000000 0.140368
## 2005 26.00000 1.633945 111.93070 3.000000 3.000000 2.682804 0.000000 0.151710
## 2006 26.00000 1.641601 111.83092 3.000000 3.000000 2.552388 0.000000 0.196288
## 2007 26.00000 1.641132 111.84171 3.000000 3.000000 2.617401 0.000000 0.200379
## 2008 25.99917 1.638218 104.81002 3.000000 3.000000 2.654636 0.069238 0.629578
## 2009 25.99994 1.627483 104.88199 3.000000 3.000000 2.569364 0.159255 0.419446
## 2010 26.00000 1.610225 104.93638 3.000000 3.000000 1.322004 0.000000 0.539876
## 2011 26.00000 1.617390 105.01390 3.000000 3.000000 1.292479 0.000000 0.541309
## 2012 23.36504 1.744319 133.45249 3.000000 3.000000 2.839069 1.231031 0.792496
## 2013 23.42173 1.755467 133.47861 3.000000 3.000000 2.843782 1.302507 0.773807
## 2014 18.82678 1.746416 133.74701 3.000000 3.000000 2.858389 1.444382 0.713823
## 2015 18.94093 1.746411 133.67666 3.000000 3.000000 2.864933 1.501647 0.786846
## 2016 25.92168 1.611452 102.36315 3.000000 3.000000 1.031701 0.034650 0.912345
## 2017 25.94015 1.596813 102.32044 3.000000 3.000000 1.000536 0.005939 0.566353
## 2018 25.99964 1.610126 102.68691 3.000000 3.000000 1.020313 0.108386 1.000000
## 2019 25.90783 1.623113 102.55569 3.000000 3.000000 1.063422 0.051097 0.543118
## 2020 25.99119 1.618348 104.94582 3.000000 3.000000 2.451260 0.043689 0.670402
## 2021 25.99315 1.609401 104.85493 3.000000 3.000000 2.613504 0.067985 0.778632
## 2022 25.98867 1.621671 105.31397 3.000000 3.000000 1.042989 0.097114 0.429540
## 2023 25.97621 1.614484 104.99940 3.000000 3.000000 1.237557 0.083675 0.543761
## 2024 18.74359 1.789143 138.20287 3.000000 3.000000 2.833770 0.806422 0.672513
## 2025 20.32377 1.774207 138.14316 3.000000 3.000000 2.816052 1.571865 0.688058
## 2026 21.39405 1.792933 137.83241 3.000000 3.000000 2.682909 1.318743 0.900497
## 2027 21.83832 1.758959 137.79299 3.000000 3.000000 2.640539 1.879818 0.885993
## 2028 18.20634 1.807406 141.79943 3.000000 3.000000 2.472903 1.998047 0.840911
## 2029 18.53283 1.750910 142.54518 3.000000 3.000000 2.372058 1.324805 0.870795
## 2030 20.43848 1.805803 153.14949 3.000000 3.000000 2.387991 0.850715 0.656491
## 2031 20.79627 1.796538 152.47367 3.000000 3.000000 2.322003 0.886602 0.843283
## 2032 26.00000 1.634894 111.94632 3.000000 3.000000 2.737353 0.000000 0.076094
## 2033 26.00000 1.639524 111.94559 3.000000 3.000000 2.739351 0.000000 0.064769
## 2034 26.00000 1.643017 111.72024 3.000000 3.000000 2.632498 0.000000 0.140792
## 2035 26.00000 1.641849 111.68269 3.000000 3.000000 2.632253 0.000000 0.244205
## 2036 26.00000 1.621167 104.94770 3.000000 3.000000 2.577210 0.000000 0.402075
## 2037 25.99290 1.638075 105.03652 3.000000 3.000000 2.419153 0.019404 0.597626
## 2038 26.00000 1.609370 105.40731 3.000000 3.000000 2.609052 0.000000 0.548590
## 2039 26.00000 1.608283 105.35969 3.000000 3.000000 2.476002 0.000000 0.546345
## 2040 25.95174 1.629442 104.83535 3.000000 3.000000 2.225139 0.035928 0.565315
## 2041 25.98226 1.629225 104.83843 3.000000 3.000000 2.556068 0.016820 0.582840
## 2042 25.47065 1.680218 104.80728 3.000000 3.000000 1.423073 0.197993 0.763359
## 2043 25.28943 1.686033 104.77216 3.000000 3.000000 1.299194 0.234303 0.946888
## 2044 25.69607 1.662978 110.93051 3.000000 3.000000 1.679489 0.017804 0.215230
## 2045 25.56187 1.675185 110.62172 3.000000 3.000000 1.495830 0.109327 0.384129
## 2046 25.83402 1.624560 110.10589 3.000000 3.000000 1.817860 0.011161 0.447224
## 2047 25.89555 1.626179 110.07402 3.000000 3.000000 1.967707 0.014370 0.434073
## 2048 19.03556 1.682594 127.42746 3.000000 3.000000 1.441289 1.425712 0.662277
## 2049 18.63429 1.669354 126.08830 3.000000 3.000000 1.144539 0.922014 0.899673
## 2050 20.70088 1.688380 121.88980 3.000000 3.000000 1.353167 1.093679 0.534553
## 2051 20.74144 1.694439 122.81303 3.000000 3.000000 1.409444 0.933595 0.840393
## 2052 21.69589 1.755476 133.87050 3.000000 3.000000 1.959287 1.433151 0.911335
## 2053 21.63598 1.748106 133.25903 3.000000 3.000000 1.931163 1.562213 0.926565
## 2054 21.23266 1.719913 131.56748 3.000000 3.000000 1.651462 1.655993 0.939982
## 2055 21.00830 1.723587 131.92971 3.000000 3.000000 1.683448 1.645532 0.858059
## 2056 25.96295 1.623812 109.99674 3.000000 3.000000 2.395387 0.000272 0.461532
## 2057 26.00000 1.624099 109.97840 3.000000 3.000000 2.523793 0.000000 0.383953
## 2058 26.00000 1.632983 111.15781 3.000000 3.000000 2.638896 0.000000 0.224559
## 2059 26.00000 1.640745 110.91965 3.000000 3.000000 2.666178 0.000000 0.276907
## 2060 26.00000 1.629727 111.27565 3.000000 3.000000 2.495851 0.000000 0.218645
## 2061 26.00000 1.624134 111.53121 3.000000 3.000000 2.609188 0.000000 0.174030
## 2062 25.96479 1.623938 109.98426 3.000000 3.000000 2.471721 0.000096 0.433463
## 2063 25.99495 1.593321 110.16817 3.000000 3.000000 2.447306 0.000454 0.486558
## 2064 20.95274 1.730333 132.11649 3.000000 3.000000 1.674061 1.683497 0.780199
## 2065 20.97817 1.721057 132.05479 3.000000 3.000000 1.678791 1.682490 0.818871
## 2066 21.67447 1.719780 132.26256 3.000000 3.000000 1.777805 1.584716 0.927341
## 2067 21.56895 1.699315 133.10761 3.000000 3.000000 1.733306 1.773304 0.921136
## 2068 23.64794 1.681394 114.47946 3.000000 3.000000 2.435978 0.232742 0.692608
## 2069 24.19637 1.697421 114.48239 3.000000 3.000000 2.909675 0.360908 0.573887
## 2070 24.28483 1.650726 113.77420 3.000000 3.000000 2.751370 0.324913 0.516764
## 2071 24.69311 1.667383 112.98255 3.000000 3.000000 2.887909 0.312923 0.210997
## 2072 18.86226 1.746277 128.70576 3.000000 3.000000 2.411582 0.985287 0.675076
## 2073 18.42348 1.735461 126.79817 3.000000 3.000000 2.386390 1.544632 0.900067
## 2074 20.39408 1.747714 128.14811 3.000000 3.000000 2.232601 0.554323 0.836151
## 2075 20.21701 1.715820 129.46654 3.000000 3.000000 1.755907 1.488090 0.857718
## 2076 21.33018 1.747987 147.29619 3.000000 3.000000 2.336349 1.416400 0.711724
## 2077 19.52894 1.817917 142.55916 3.000000 3.000000 2.562002 1.976427 0.740331
## 2078 19.36434 1.808350 150.51648 3.000000 3.000000 2.305574 1.734424 0.863043
## 2079 21.13153 1.739457 150.37757 3.000000 3.000000 2.319912 1.582675 0.680746
## 2080 19.01287 1.742062 133.77992 3.000000 3.000000 2.701960 1.465909 0.813235
## 2081 18.46909 1.741925 133.01710 3.000000 3.000000 2.474518 1.560261 0.662489
## 2082 21.57211 1.751067 133.84506 3.000000 3.000000 2.748569 1.427037 0.902825
## 2083 21.68012 1.749118 133.95509 3.000000 3.000000 2.827773 1.412357 0.901071
## 2084 24.46976 1.663341 113.07719 3.000000 3.000000 2.632224 0.300964 0.269560
## 2085 25.12791 1.668537 112.55546 3.000000 3.000000 2.868679 0.115369 0.028583
## 2086 25.98637 1.668951 112.24970 3.000000 3.000000 2.930137 0.043101 0.138629
## 2087 25.95198 1.661712 112.09862 3.000000 3.000000 2.961899 0.259424 0.080128
## 2088 26.00000 1.633442 111.82182 3.000000 3.000000 2.550672 0.000000 0.224655
## 2089 26.00000 1.633020 111.86319 3.000000 3.000000 2.584305 0.000000 0.232108
## 2090 26.00000 1.633887 111.87813 3.000000 3.000000 2.621976 0.000000 0.123861
## 2091 26.00000 1.643421 111.93998 3.000000 3.000000 2.722276 0.000000 0.091711
## 2092 26.00000 1.640535 111.55597 3.000000 3.000000 2.634342 0.000000 0.178301
## 2093 26.00000 1.626483 111.35706 3.000000 3.000000 2.619390 0.000000 0.171034
## 2094 26.00000 1.645990 111.92249 3.000000 3.000000 2.786780 0.000000 0.097760
## 2095 26.00000 1.643892 111.88453 3.000000 3.000000 2.768141 0.000000 0.094213
## 2096 25.97731 1.617817 104.95078 3.000000 3.000000 1.716590 0.001272 0.545993
## 2097 25.95501 1.626449 104.87960 3.000000 3.000000 2.094901 0.070890 0.599441
## 2098 25.99672 1.626580 105.03720 3.000000 3.000000 2.347322 0.008013 0.503896
## 2099 25.99235 1.606474 104.95429 3.000000 3.000000 2.331123 0.063383 0.561661
## 2100 25.97445 1.628855 108.09001 3.000000 3.000000 1.757105 0.085119 0.465444
## 2101 25.77756 1.628205 107.37870 3.000000 3.000000 2.506631 0.025787 0.484165
## 2102 25.72200 1.628470 107.21895 3.000000 3.000000 2.487070 0.067329 0.455823
## 2103 25.76563 1.627839 108.10736 3.000000 3.000000 2.320068 0.045246 0.413106
## 2104 21.01685 1.724268 133.03352 3.000000 3.000000 1.650612 1.537639 0.912457
## 2105 21.68237 1.732383 133.04394 3.000000 3.000000 1.610768 1.510398 0.931455
## 2106 21.28597 1.726920 131.33579 3.000000 3.000000 1.796267 1.728332 0.897924
## 2107 20.97684 1.710730 131.40853 3.000000 3.000000 1.728139 1.676269 0.906247
## 2108 21.98294 1.748584 133.74294 3.000000 3.000000 2.005130 1.341390 0.599270
## 2109 22.52404 1.752206 133.68935 3.000000 3.000000 2.054193 1.414209 0.646288
## 2110 24.36194 1.739450 133.34664 3.000000 3.000000 2.852339 1.139107 0.586035
## 2111 23.66471 1.738836 133.47264 3.000000 3.000000 2.863513 1.026452 0.714137datos_obesidad <- scale(datos_obesidad)Una representación gráfica permite comprobar que si el set de datos dado contiene grupos reales. Al haber más de dos variables es necesario reducir la dimensionalidad mediante un Principal Component Analysis.
#Cargamos ggpubr
library(ggpubr)## Warning: package 'ggpubr' was built under R version 4.3.2datos_obesidad <- prcomp(datos_obesidad)
p1 <- fviz_pca_ind(X = datos_obesidad, habillage = obesidad$NObeyesdad,
geom = "point", title = "PCA - datos_obesidad",
pallete = "jco") +
theme_bw() + theme(legend.position = "bottom")
ggarrange(p1, common.legend = TRUE)
Método Elbow
En el contexto de clustering por partición, como el algoritmo K-means, las observaciones se agrupan para minimizar la varianza total intra-cluster. El método Elbow calcula esta varianza en función del número de clusters y selecciona el valor óptimo donde agregar más clusters ya no aporta mejoras sustanciales.
datos <- scale(dbs)
fviz_nbclust(x = datos, FUNcluster = kmeans, method = "wss", k.max = 15) +
labs(title = "Número óptimo de clusters")
Se tiene una mejoría mínima de 5 a 7 clusters.
5. Conclusiones
El análisis a la base de datos dada arroja indica que no se evidencia una diferencia sustancial entre fumadores y no fumadores en términos de peso. Respecto a la edad de los fumadores, se destaca una concentración mayor entre los 20 y 30 años, aunque esta información no proporciona detalles adicionales significativos. Respecto al consumo de calorías, se identifica una correlación intermedia; las personas con historial familiar de sobrepeso tienden a no estar tan conscientes de su ingesta calórica. Estos hallazgos resaltan la complejidad de las interacciones entre diversas variables y sugieren áreas que podrían beneficiarse de investigaciones más detalladas.