Unsupervised Learning in Action: Discovering Patterns Without Labels
Autor: DATAMANZ
Octubre 2024
Section 1 - Hawks
The exercises will be based on the Hawks dataset from the R package Stat2Data.
Students and faculty at Cornell College in Mount Vernon, Iowa, collected data over many years at the Lake MacBride Hawk Watch, near Iowa City, Iowa. The dataset analyzed here is a subset of the original dataset, including only species with more than 10 observations. The data were collected from random samples of three different hawk species: Red-tailed Hawk, Sharp-shinned Hawk, and Cooper’s Hawk.
We selected this dataset due to its similarity to the penguins dataset and its potential for applying unsupervised data mining algorithms.
if (!require('Stat2Data')) install.packages('Stat2Data')
library(Stat2Data)
data("Hawks")
summary(Hawks)## Month Day Year CaptureTime ReleaseTime
## Min. : 8.000 Min. : 1.00 Min. :1992 11:35 : 14 :842
## 1st Qu.: 9.000 1st Qu.: 9.00 1st Qu.:1995 13:30 : 14 11:00 : 2
## Median :10.000 Median :16.00 Median :1999 11:45 : 13 11:35 : 2
## Mean : 9.843 Mean :15.74 Mean :1998 12:10 : 13 12:05 : 2
## 3rd Qu.:10.000 3rd Qu.:23.00 3rd Qu.:2001 14:00 : 13 12:50 : 2
## Max. :11.000 Max. :31.00 Max. :2003 13:05 : 12 13:32 : 2
## (Other):829 (Other): 56
## BandNumber Species Age Sex Wing Weight
## : 2 CH: 70 A:224 :576 Min. : 37.2 Min. : 56.0
## 1142-09240: 1 RT:577 I:684 F:174 1st Qu.:202.0 1st Qu.: 185.0
## 1142-09241: 1 SS:261 M:158 Median :370.0 Median : 970.0
## 1142-09242: 1 Mean :315.6 Mean : 772.1
## 1142-18229: 1 3rd Qu.:390.0 3rd Qu.:1120.0
## 1142-19209: 1 Max. :480.0 Max. :2030.0
## (Other) :901 NA's :1 NA's :10
## Culmen Hallux Tail StandardTail
## Min. : 8.6 Min. : 9.50 Min. :119.0 Min. :115.0
## 1st Qu.:12.8 1st Qu.: 15.10 1st Qu.:160.0 1st Qu.:162.0
## Median :25.5 Median : 29.40 Median :214.0 Median :215.0
## Mean :21.8 Mean : 26.41 Mean :198.8 Mean :199.2
## 3rd Qu.:27.3 3rd Qu.: 31.40 3rd Qu.:225.0 3rd Qu.:226.0
## Max. :39.2 Max. :341.40 Max. :288.0 Max. :335.0
## NA's :7 NA's :6 NA's :337
## Tarsus WingPitFat KeelFat Crop
## Min. :24.70 Min. :0.0000 Min. :0.000 Min. :0.0000
## 1st Qu.:55.60 1st Qu.:0.0000 1st Qu.:2.000 1st Qu.:0.0000
## Median :79.30 Median :1.0000 Median :2.000 Median :0.0000
## Mean :71.95 Mean :0.7922 Mean :2.184 Mean :0.2345
## 3rd Qu.:87.00 3rd Qu.:1.0000 3rd Qu.:3.000 3rd Qu.:0.2500
## Max. :94.00 Max. :3.0000 Max. :4.000 Max. :5.0000
## NA's :833 NA's :831 NA's :341 NA's :343Data Cleaning
Present the dataset, including the column names and their meanings, as well as the distributions of their values.
We start by loading the necessary libraries for our analysis.
if (!require('cluster')) install.packages('cluster')## Cargando paquete requerido: clusterlibrary(cluster)
if (!require('Stat2Data')) install.packages('Stat2Data')
library(Stat2Data)
if (!require('Stat2Data')) install.packages('Stat2Data')
if (!require('dplyr')) install.packages('dplyr')## Cargando paquete requerido: dplyr##
## Adjuntando el paquete: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(dplyr)
if (!require('ggplot2')) install.packages("ggplot2")## Cargando paquete requerido: ggplot2library(ggplot2)
if (!require('factoextra')) install.packages("factoextra")## Cargando paquete requerido: factoextra## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBalibrary(factoextra)
if (!require('NbClust')) install.packages("NbClust")## Cargando paquete requerido: NbClustlibrary(NbClust)
if (!require('dbscan')) install.packages('dbscan')## Cargando paquete requerido: dbscan##
## Adjuntando el paquete: 'dbscan'## The following object is masked from 'package:stats':
##
## as.dendrogramlibrary(dbscan)
if (!require('tidyr')) install.packages('tidyr')## Cargando paquete requerido: tidyrlibrary(tidyr)We perform a comprehensive summary to examine all variables in the dataset, including their quartiles.
This initial analysis is an essential preliminary step that is highly beneficial when working with datasets. By conducting this review, we can gain an overview of the data distribution, identify potential anomalies, and better understand the dataset’s underlying structure.
This allows us to make informed decisions in the subsequent steps.
data("Hawks")
summary(Hawks)## Month Day Year CaptureTime ReleaseTime
## Min. : 8.000 Min. : 1.00 Min. :1992 11:35 : 14 :842
## 1st Qu.: 9.000 1st Qu.: 9.00 1st Qu.:1995 13:30 : 14 11:00 : 2
## Median :10.000 Median :16.00 Median :1999 11:45 : 13 11:35 : 2
## Mean : 9.843 Mean :15.74 Mean :1998 12:10 : 13 12:05 : 2
## 3rd Qu.:10.000 3rd Qu.:23.00 3rd Qu.:2001 14:00 : 13 12:50 : 2
## Max. :11.000 Max. :31.00 Max. :2003 13:05 : 12 13:32 : 2
## (Other):829 (Other): 56
## BandNumber Species Age Sex Wing Weight
## : 2 CH: 70 A:224 :576 Min. : 37.2 Min. : 56.0
## 1142-09240: 1 RT:577 I:684 F:174 1st Qu.:202.0 1st Qu.: 185.0
## 1142-09241: 1 SS:261 M:158 Median :370.0 Median : 970.0
## 1142-09242: 1 Mean :315.6 Mean : 772.1
## 1142-18229: 1 3rd Qu.:390.0 3rd Qu.:1120.0
## 1142-19209: 1 Max. :480.0 Max. :2030.0
## (Other) :901 NA's :1 NA's :10
## Culmen Hallux Tail StandardTail
## Min. : 8.6 Min. : 9.50 Min. :119.0 Min. :115.0
## 1st Qu.:12.8 1st Qu.: 15.10 1st Qu.:160.0 1st Qu.:162.0
## Median :25.5 Median : 29.40 Median :214.0 Median :215.0
## Mean :21.8 Mean : 26.41 Mean :198.8 Mean :199.2
## 3rd Qu.:27.3 3rd Qu.: 31.40 3rd Qu.:225.0 3rd Qu.:226.0
## Max. :39.2 Max. :341.40 Max. :288.0 Max. :335.0
## NA's :7 NA's :6 NA's :337
## Tarsus WingPitFat KeelFat Crop
## Min. :24.70 Min. :0.0000 Min. :0.000 Min. :0.0000
## 1st Qu.:55.60 1st Qu.:0.0000 1st Qu.:2.000 1st Qu.:0.0000
## Median :79.30 Median :1.0000 Median :2.000 Median :0.0000
## Mean :71.95 Mean :0.7922 Mean :2.184 Mean :0.2345
## 3rd Qu.:87.00 3rd Qu.:1.0000 3rd Qu.:3.000 3rd Qu.:0.2500
## Max. :94.00 Max. :3.0000 Max. :4.000 Max. :5.0000
## NA's :833 NA's :831 NA's :341 NA's :343We observe that we will be working with measurements of various characteristics of hawks that have been captured and released.
In our dataset, we have several numerical variables, such as wing length and weight.
To better understand the structure of our dataset, we use the str function.
str(Hawks)## 'data.frame': 908 obs. of 19 variables:
## $ Month : int 9 9 9 9 9 9 9 9 9 9 ...
## $ Day : int 19 22 23 23 27 28 28 29 29 30 ...
## $ Year : int 1992 1992 1992 1992 1992 1992 1992 1992 1992 1992 ...
## $ CaptureTime : Factor w/ 308 levels " ","1:15","1:31",..: 181 25 138 42 62 71 181 88 261 192 ...
## $ ReleaseTime : Factor w/ 60 levels ""," ","10:20",..: 1 2 2 2 2 2 2 2 2 2 ...
## $ BandNumber : Factor w/ 907 levels " ","1142-09240",..: 856 857 858 809 437 280 859 860 861 281 ...
## $ Species : Factor w/ 3 levels "CH","RT","SS": 2 2 2 1 3 2 2 2 2 2 ...
## $ Age : Factor w/ 2 levels "A","I": 2 2 2 2 2 2 2 1 1 2 ...
## $ Sex : Factor w/ 3 levels "","F","M": 1 1 1 2 2 1 1 1 1 1 ...
## $ Wing : num 385 376 381 265 205 412 370 375 412 405 ...
## $ Weight : int 920 930 990 470 170 1090 960 855 1210 1120 ...
## $ Culmen : num 25.7 NA 26.7 18.7 12.5 28.5 25.3 27.2 29.3 26 ...
## $ Hallux : num 30.1 NA 31.3 23.5 14.3 32.2 30.1 30 31.3 30.2 ...
## $ Tail : int 219 221 235 220 157 230 212 243 210 238 ...
## $ StandardTail: int NA NA NA NA NA NA NA NA NA NA ...
## $ Tarsus : num NA NA NA NA NA NA NA NA NA NA ...
## $ WingPitFat : int NA NA NA NA NA NA NA NA NA NA ...
## $ KeelFat : num NA NA NA NA NA NA NA NA NA NA ...
## $ Crop : num NA NA NA NA NA NA NA NA NA NA ...For our analysis, we use the dataset documentation
available at
https://rdrr.io/rforge/Stat2Data/man/Hawks.html.
This source provides detailed and specific information about the attributes present in the dataset.
Variable Descriptions:
- Month: Capture month code, where 8 =
September and 12 = December.
- Day: Day of the month when the hawk was
captured.
- Year: Capture year, ranging from 1992 to
2003.
- CaptureTime: Time of capture in HH
format.
- ReleaseTime: Time of release in HH
format.
- BandNumber: ID band code assigned
to the bird.
- Species: Bird species:
- CH = Cooper’s Hawk
- RT = Red-tailed Hawk
- SS = Sharp-shinned Hawk
- CH = Cooper’s Hawk
- Age: Age of the bird:
- A = Adult
- I = Immature
- A = Adult
- Sex: Sex of the bird:
- F = Female
- M = Male
- Missing values indicate unknown sex.
- F = Female
- Wing: Primary wing feather length
(mm), measured from tip to wrist.
- Weight: Body weight (grams).
- Culmen: Upper bill length (mm),
measured from tip to the fleshy part.
- Hallux: Killing talon length
(mm).
- Tail: Tail length measurement (mm)
(MacBride Raptor Center method).
- StandardTail: Standard tail length
measurement (mm).
- Tarsus: Basic foot bone length
(mm).
- WingPitFat: Amount of fat in the wing
pit.
- KeelFat: Amount of fat on the
breastbone (measured by touch).
- Crop: Food content in the crop, coded 1 = full to 0 = empty.
Now, we continue preparing the dataset by searching for missing values.
missing_values <- colSums(is.na(Hawks))
print(missing_values)## Month Day Year CaptureTime ReleaseTime BandNumber
## 0 0 0 0 0 0
## Species Age Sex Wing Weight Culmen
## 0 0 0 1 10 7
## Hallux Tail StandardTail Tarsus WingPitFat KeelFat
## 6 0 337 833 831 341
## Crop
## 343We begin cleaning the dataset.
Since we observe a high percentage of missing values
in certain variables and considering that our dataset contains
918 records, the best option is to remove the
following attributes:
StandardTail, Tarsus, WingPitFat, KeelFat, and
Crop.
Afterward, we check for missing values again.
limpio_hawks <- Hawks[, !(names(Hawks) %in% c("StandardTail", "Tarsus", "WingPitFat", "KeelFat", "Crop"))]
missing_values2 <- colSums(is.na(limpio_hawks))
print(missing_values2)## Month Day Year CaptureTime ReleaseTime BandNumber
## 0 0 0 0 0 0
## Species Age Sex Wing Weight Culmen
## 0 0 0 1 10 7
## Hallux Tail
## 6 0The number of missing values has significantly decreased.
Currently, the missing values are:
- Wing: 1 missing value
- Weight: 10 missing values
- Culmen: 7 missing values
- Hallux: 6 missing values
Following the methodology, we will attempt to impute these values to obtain a fully clean dataset.
We will start with the Wing variable, using mean values based on age and species.
We chose this attribute first since it only has one missing value, making it easier to apply the same method to the other variables.
First, we calculate the mean values based on species and age.
mean_wing <- Hawks %>%
group_by(Species, Age) %>%
summarise(mean_wing = mean(Wing, na.rm = TRUE), .groups = 'drop')
print(mean_wing)## # A tibble: 6 × 3
## Species Age mean_wing
## <fct> <fct> <dbl>
## 1 CH A 242.
## 2 CH I 246.
## 3 RT A 386.
## 4 RT I 383.
## 5 SS A 186.
## 6 SS I 185.We identify the row corresponding to the NA value in the Wing attribute that we need to replace.
Since we know it belongs to an adult Cooper’s Hawk, and based on the previously calculated means, we determine that the average weight is 242.
na_wing_row <- Hawks[is.na(Hawks$Wing), ]
print(na_wing_row)## Month Day Year CaptureTime ReleaseTime BandNumber Species Age Sex Wing
## 263 10 15 1995 14:20 CH A NA
## Weight Culmen Hallux Tail StandardTail Tarsus WingPitFat KeelFat Crop
## 263 480 17.7 32.1 198 NA NA NA NA NAWe impute the value 242.4839 to the missing value in the Wing attribute.
Hawks <- Hawks %>%
mutate(Wing = ifelse(is.na(Wing), 242.4839, Wing))Now, we merge the imputed values back into the original dataset to ensure data consistency.
We apply this imputation process to all variables with missing values.
mean_values <- Hawks %>%
group_by(Species, Age) %>%
summarise(
mean_wing = mean(Wing, na.rm = TRUE),
mean_weight = mean(Weight, na.rm = TRUE),
mean_culmen = mean(Culmen, na.rm = TRUE),
mean_hallux = mean(Hallux, na.rm = TRUE),
.groups = 'drop'
)
print("Medias calculadas por especie y edad:")## [1] "Medias calculadas por especie y edad:"print(mean_values)## # A tibble: 6 × 6
## Species Age mean_wing mean_weight mean_culmen mean_hallux
## <fct> <fct> <dbl> <dbl> <dbl> <dbl>
## 1 CH A 242. 450. 18.0 23.9
## 2 CH I 246. 395. 17.2 21.9
## 3 RT A 386. 1161. 27.5 31.1
## 4 RT I 383. 1076. 26.8 32.2
## 5 SS A 186. 150. 11.7 16.9
## 6 SS I 185. 147. 11.4 14.2With the mean values calculated for all attributes of our missing variables, we impute them just as we initially did with Wing, but now for the other three variables.
As a result, we no longer have missing data (except in the original variables, which we will remove in the next step).
Hawks <- Hawks %>%
left_join(mean_values, by = c("Species", "Age")) %>%
mutate(
Wing = ifelse(is.na(Wing), mean_wing, Wing),
Weight = ifelse(is.na(Weight), mean_weight, Weight),
Culmen = ifelse(is.na(Culmen), mean_culmen, Culmen),
Hallux = ifelse(is.na(Hallux), mean_hallux, Hallux)
) %>%
select(-mean_wing, -mean_weight, -mean_culmen, -mean_hallux)
missing_values_after_imputation <- colSums(is.na(Hawks))
print("Valores faltantes después de la imputación:")## [1] "Valores faltantes después de la imputación:"print(missing_values_after_imputation)## Month Day Year CaptureTime ReleaseTime BandNumber
## 0 0 0 0 0 0
## Species Age Sex Wing Weight Culmen
## 0 0 0 0 0 0
## Hallux Tail StandardTail Tarsus WingPitFat KeelFat
## 0 0 337 833 831 341
## Crop
## 343We obtain our clean dataset, with no missing values, all imputations applied, and unnecessary variables removed.
hawks_limpio2 <- Hawks[, !(names(Hawks) %in% c("StandardTail", "Tarsus", "WingPitFat", "KeelFat", "Crop"))]
missing_values3 <- colSums(is.na(hawks_limpio2))
print(missing_values3)## Month Day Year CaptureTime ReleaseTime BandNumber
## 0 0 0 0 0 0
## Species Age Sex Wing Weight Culmen
## 0 0 0 0 0 0
## Hallux Tail
## 0 0We perform a new summary of our clean dataset and reanalyze the variables to conduct an initial exploratory analysis.
summary(hawks_limpio2)## Month Day Year CaptureTime ReleaseTime
## Min. : 8.000 Min. : 1.00 Min. :1992 11:35 : 14 :842
## 1st Qu.: 9.000 1st Qu.: 9.00 1st Qu.:1995 13:30 : 14 11:00 : 2
## Median :10.000 Median :16.00 Median :1999 11:45 : 13 11:35 : 2
## Mean : 9.843 Mean :15.74 Mean :1998 12:10 : 13 12:05 : 2
## 3rd Qu.:10.000 3rd Qu.:23.00 3rd Qu.:2001 14:00 : 13 12:50 : 2
## Max. :11.000 Max. :31.00 Max. :2003 13:05 : 12 13:32 : 2
## (Other):829 (Other): 56
## BandNumber Species Age Sex Wing Weight
## : 2 CH: 70 A:224 :576 Min. : 37.2 Min. : 56.0
## 1142-09240: 1 RT:577 I:684 F:174 1st Qu.:202.0 1st Qu.: 185.0
## 1142-09241: 1 SS:261 M:158 Median :370.0 Median : 970.0
## 1142-09242: 1 Mean :315.6 Mean : 770.5
## 1142-18229: 1 3rd Qu.:390.0 3rd Qu.:1120.0
## 1142-19209: 1 Max. :480.0 Max. :2030.0
## (Other) :901
## Culmen Hallux Tail
## Min. : 8.60 Min. : 9.50 Min. :119.0
## 1st Qu.:12.78 1st Qu.: 15.07 1st Qu.:160.0
## Median :25.50 Median : 29.40 Median :214.0
## Mean :21.79 Mean : 26.39 Mean :198.8
## 3rd Qu.:27.30 3rd Qu.: 31.40 3rd Qu.:225.0
## Max. :39.20 Max. :341.40 Max. :288.0
## At first glance, we can determine that the Weight variable shows a significant difference between the minimum and maximum values.
We calculate the standard deviation of the Weight variable to determine if there are outliers.
detect_outliers_sd <- function(data, column) {
mean_value <- mean(data[[column]], na.rm = TRUE)
sd_value <- sd(data[[column]], na.rm = TRUE)
lower_bound <- mean_value - 3 * sd_value
upper_bound <- mean_value + 3 * sd_value
outliers <- data %>% filter(data[[column]] < lower_bound | data[[column]] > upper_bound)
return(list(outliers = outliers, lower_bound = lower_bound, upper_bound = upper_bound))
}
result <- detect_outliers_sd(hawks_limpio2, "Weight")
outliers_weight_sd <- result$outliers
lower_bound <- result$lower_bound
upper_bound <- result$upper_bound
print("Outliers in the 'Weight' column using standard deviation:")## [1] "Outliers in the 'Weight' column using standard deviation:"print(outliers_weight_sd)## [1] Month Day Year CaptureTime ReleaseTime BandNumber
## [7] Species Age Sex Wing Weight Culmen
## [13] Hallux Tail
## <0 rows> (o 0- extensión row.names)plot(hawks_limpio2$Weight,
main = "Weight Scatter Plot",
ylab = "Weight",
xlab = "Index",
pch = ifelse(hawks_limpio2$Weight < lower_bound | hawks_limpio2$Weight > upper_bound, 19, 1),
col = ifelse(hawks_limpio2$Weight < lower_bound | hawks_limpio2$Weight > upper_bound, "red", "black"))
abline(h = c(lower_bound, upper_bound), col = "blue", lwd = 2, lty = 2)
We perform a second outlier analysis on foot
size measurements, as the summary statistics
indicate a significant difference between the
minimum and maximum values.
This time, we observe 7 outliers.
detect_outliers_sd <- function(data, column) {
mean_value <- mean(data[[column]], na.rm = TRUE)
sd_value <- sd(data[[column]], na.rm = TRUE)
lower_bound <- mean_value - 3 * sd_value
upper_bound <- mean_value + 3 * sd_value
outliers <- data %>% filter(data[[column]] < lower_bound | data[[column]] > upper_bound)
outlier_count <- nrow(outliers)
return(list(outliers = outliers, lower_bound = lower_bound, upper_bound = upper_bound, count = outlier_count))
}
result_hallux <- detect_outliers_sd(hawks_limpio2, "Hallux")
outliers_hallux_sd <- result_hallux$outliers
lower_bound_hallux <- result_hallux$lower_bound
upper_bound_hallux <- result_hallux$upper_bound
outlier_count_hallux_sd <- result_hallux$count
print("Outliers in the 'Hallux' column using standard deviation:")## [1] "Outliers in the 'Hallux' column using standard deviation:"print(outliers_hallux_sd)## Month Day Year CaptureTime ReleaseTime BandNumber Species Age Sex Wing Weight
## 1 9 13 1993 14:25 173-19904 SS I M 193 100
## 2 9 15 1994 13:35 1387-79108 RT I 410 1210
## 3 9 19 1994 12:58 1207-64604 RT I 418 1180
## 4 9 20 1994 14:00 2003-58437 SS A F 198 188
## 5 11 2 1994 12:20 1207-64619 RT I 401 1405
## 6 10 20 2000 12:38 1142-09241 SS A M 170 110
## 7 9 9 2001 11:51 1142-19244 SS I M 164 95
## Culmen Hallux Tail
## 1 9.3 101.0 144
## 2 27.5 308.0 227
## 3 30.1 341.4 235
## 4 12.2 143.0 150
## 5 29.1 82.8 235
## 6 11.4 121.0 135
## 7 11.4 130.0 136print(paste("Number of detected outliers:", outlier_count_hallux_sd))## [1] "Number of detected outliers: 7"plot(hawks_limpio2$Hallux,
main = "Hallux Scatter Plot",
ylab = "Hallux",
xlab = "Índex",
pch = ifelse(hawks_limpio2$Hallux < lower_bound_hallux | hawks_limpio2$Hallux > upper_bound_hallux, 19, 1),
col = ifelse(hawks_limpio2$Hallux < lower_bound_hallux | hawks_limpio2$Hallux > upper_bound_hallux, "red", "black"))
abline(h = c(lower_bound_hallux, upper_bound_hallux), col = "blue", lwd = 2, lty = 2)
Finally, to confirm our hypothesis, we perform the
outlier analysis on the entire cleaned dataset.
We verify that only those 7 Hallux values are identified as outliers.
detect_outliers_sd <- function(data, column) {
mean_value <- mean(data[[column]], na.rm = TRUE)
sd_value <- sd(data[[column]], na.rm = TRUE)
lower_bound <- mean_value - 3 * sd_value
upper_bound <- mean_value + 3 * sd_value
outliers <- data %>% filter(data[[column]] < lower_bound | data[[column]] > upper_bound)
outlier_count <- nrow(outliers)
return(list(outliers = outliers, lower_bound = lower_bound, upper_bound = upper_bound, count = outlier_count))
}
numeric_columns <- sapply(hawks_limpio2, is.numeric)
outlier_results <- list()
for (column_name in names(hawks_limpio2)[numeric_columns]) {
result <- detect_outliers_sd(hawks_limpio2, column_name)
outlier_results[[column_name]] <- result
}
for (column_name in names(outlier_results)) {
cat(paste("Outliers in the column:", column_name, "\n"))
print(outlier_results[[column_name]]$outliers)
cat(paste("Number of detected outliers:", outlier_results[[column_name]]$count, "\n\n"))
plot(hawks_limpio2[[column_name]],
main = paste("Scatter Plot of", column_name),
ylab = column_name,
xlab = "Index",
pch = ifelse(hawks_limpio2[[column_name]] < result$lower_bound | hawks_limpio2[[column_name]] > result$upper_bound, 19, 1),
col = ifelse(hawks_limpio2[[column_name]] < result$lower_bound | hawks_limpio2[[column_name]] > result$upper_bound, "red", "black"))
abline(h = c(result$lower_bound, result$upper_bound), col = "blue", lwd = 2, lty = 2)
}## Outliers in the column: Month
## [1] Month Day Year CaptureTime ReleaseTime BandNumber
## [7] Species Age Sex Wing Weight Culmen
## [13] Hallux Tail
## <0 rows> (o 0- extensión row.names)
## Number of detected outliers: 0
## Outliers in the column: Day
## [1] Month Day Year CaptureTime ReleaseTime BandNumber
## [7] Species Age Sex Wing Weight Culmen
## [13] Hallux Tail
## <0 rows> (o 0- extensión row.names)
## Number of detected outliers: 0
## Outliers in the column: Year
## [1] Month Day Year CaptureTime ReleaseTime BandNumber
## [7] Species Age Sex Wing Weight Culmen
## [13] Hallux Tail
## <0 rows> (o 0- extensión row.names)
## Number of detected outliers: 0
## Outliers in the column: Wing
## [1] Month Day Year CaptureTime ReleaseTime BandNumber
## [7] Species Age Sex Wing Weight Culmen
## [13] Hallux Tail
## <0 rows> (o 0- extensión row.names)
## Number of detected outliers: 0
## Outliers in the column: Weight
## [1] Month Day Year CaptureTime ReleaseTime BandNumber
## [7] Species Age Sex Wing Weight Culmen
## [13] Hallux Tail
## <0 rows> (o 0- extensión row.names)
## Number of detected outliers: 0
## Outliers in the column: Culmen
## [1] Month Day Year CaptureTime ReleaseTime BandNumber
## [7] Species Age Sex Wing Weight Culmen
## [13] Hallux Tail
## <0 rows> (o 0- extensión row.names)
## Number of detected outliers: 0
## Outliers in the column: Hallux
## Month Day Year CaptureTime ReleaseTime BandNumber Species Age Sex Wing Weight
## 1 9 13 1993 14:25 173-19904 SS I M 193 100
## 2 9 15 1994 13:35 1387-79108 RT I 410 1210
## 3 9 19 1994 12:58 1207-64604 RT I 418 1180
## 4 9 20 1994 14:00 2003-58437 SS A F 198 188
## 5 11 2 1994 12:20 1207-64619 RT I 401 1405
## 6 10 20 2000 12:38 1142-09241 SS A M 170 110
## 7 9 9 2001 11:51 1142-19244 SS I M 164 95
## Culmen Hallux Tail
## 1 9.3 101.0 144
## 2 27.5 308.0 227
## 3 30.1 341.4 235
## 4 12.2 143.0 150
## 5 29.1 82.8 235
## 6 11.4 121.0 135
## 7 11.4 130.0 136
## Number of detected outliers: 7
## Outliers in the column: Tail
## [1] Month Day Year CaptureTime ReleaseTime BandNumber
## [7] Species Age Sex Wing Weight Culmen
## [13] Hallux Tail
## <0 rows> (o 0- extensión row.names)
## Number of detected outliers: 0
Outlier attributes are identified in the same way as we did for missing values detection, but now focusing on outliers.
all_outliers <- data.frame()
for (column_name in names(hawks_limpio2)[numeric_columns]) {
result <- outlier_results[[column_name]]
if (result$count > 0) {
cat(paste("Outliers in the column:", column_name, "\n"))
print(result$outliers)
all_outliers <- bind_rows(all_outliers, result$outliers)
}
}## Outliers in the column: Hallux
## Month Day Year CaptureTime ReleaseTime BandNumber Species Age Sex Wing Weight
## 1 9 13 1993 14:25 173-19904 SS I M 193 100
## 2 9 15 1994 13:35 1387-79108 RT I 410 1210
## 3 9 19 1994 12:58 1207-64604 RT I 418 1180
## 4 9 20 1994 14:00 2003-58437 SS A F 198 188
## 5 11 2 1994 12:20 1207-64619 RT I 401 1405
## 6 10 20 2000 12:38 1142-09241 SS A M 170 110
## 7 9 9 2001 11:51 1142-19244 SS I M 164 95
## Culmen Hallux Tail
## 1 9.3 101.0 144
## 2 27.5 308.0 227
## 3 30.1 341.4 235
## 4 12.2 143.0 150
## 5 29.1 82.8 235
## 6 11.4 121.0 135
## 7 11.4 130.0 136cat("Complete rows of detected outliers:\n")## Complete rows of detected outliers:print(all_outliers)## Month Day Year CaptureTime ReleaseTime BandNumber Species Age Sex Wing Weight
## 1 9 13 1993 14:25 173-19904 SS I M 193 100
## 2 9 15 1994 13:35 1387-79108 RT I 410 1210
## 3 9 19 1994 12:58 1207-64604 RT I 418 1180
## 4 9 20 1994 14:00 2003-58437 SS A F 198 188
## 5 11 2 1994 12:20 1207-64619 RT I 401 1405
## 6 10 20 2000 12:38 1142-09241 SS A M 170 110
## 7 9 9 2001 11:51 1142-19244 SS I M 164 95
## Culmen Hallux Tail
## 1 9.3 101.0 144
## 2 27.5 308.0 227
## 3 30.1 341.4 235
## 4 12.2 143.0 150
## 5 29.1 82.8 235
## 6 11.4 121.0 135
## 7 11.4 130.0 136An attempt was made to remove the outlier rows, but it was unsuccessful
To address this, an internet search was conducted,
leading to a study that performs outlier imputation
->
https://rpubs.com/Kamaranis/unsupervised_methods.
We applied the method from this study to our dataset, and it worked correctly.
media_hallux_especie_edad <- hawks_limpio2 %>%
group_by(Species, Age) %>%
summarise(media_hallux = mean(Hallux, na.rm = TRUE), .groups = 'drop')
all_outliers <- data.frame()
for (column_name in names(hawks_limpio2)[numeric_columns]) {
result <- outlier_results[[column_name]]
if (result$count > 0) {
cat(paste("Outliers in the column:", column_name, "\n"))
print(result$outliers)
all_outliers <- bind_rows(all_outliers, result$outliers)
}
}## Outliers in the column: Hallux
## Month Day Year CaptureTime ReleaseTime BandNumber Species Age Sex Wing Weight
## 1 9 13 1993 14:25 173-19904 SS I M 193 100
## 2 9 15 1994 13:35 1387-79108 RT I 410 1210
## 3 9 19 1994 12:58 1207-64604 RT I 418 1180
## 4 9 20 1994 14:00 2003-58437 SS A F 198 188
## 5 11 2 1994 12:20 1207-64619 RT I 401 1405
## 6 10 20 2000 12:38 1142-09241 SS A M 170 110
## 7 9 9 2001 11:51 1142-19244 SS I M 164 95
## Culmen Hallux Tail
## 1 9.3 101.0 144
## 2 27.5 308.0 227
## 3 30.1 341.4 235
## 4 12.2 143.0 150
## 5 29.1 82.8 235
## 6 11.4 121.0 135
## 7 11.4 130.0 136cat("Complete rows of detected outliers:\n")## Complete rows of detected outliers:print(all_outliers)## Month Day Year CaptureTime ReleaseTime BandNumber Species Age Sex Wing Weight
## 1 9 13 1993 14:25 173-19904 SS I M 193 100
## 2 9 15 1994 13:35 1387-79108 RT I 410 1210
## 3 9 19 1994 12:58 1207-64604 RT I 418 1180
## 4 9 20 1994 14:00 2003-58437 SS A F 198 188
## 5 11 2 1994 12:20 1207-64619 RT I 401 1405
## 6 10 20 2000 12:38 1142-09241 SS A M 170 110
## 7 9 9 2001 11:51 1142-19244 SS I M 164 95
## Culmen Hallux Tail
## 1 9.3 101.0 144
## 2 27.5 308.0 227
## 3 30.1 341.4 235
## 4 12.2 143.0 150
## 5 29.1 82.8 235
## 6 11.4 121.0 135
## 7 11.4 130.0 136hallux_upper_limit <- 55.9
for (i in 1:nrow(hawks_limpio2)) {
if (hawks_limpio2$Hallux[i] > hallux_upper_limit) {
mean_hallux <- media_hallux_especie_edad$media_hallux[
media_hallux_especie_edad$Species == hawks_limpio2$Species[i] &
media_hallux_especie_edad$Age == hawks_limpio2$Age[i]
]
hawks_limpio2$Hallux[i] <- mean_hallux
}
}
remaining_outliers_hallux <- detect_outliers_sd(hawks_limpio2, "Hallux")
cat("Remaining outliers in Hallux after imputation:\n")## Remaining outliers in Hallux after imputation:print(remaining_outliers_hallux$outliers) ## Month Day Year CaptureTime ReleaseTime BandNumber Species Age Sex Wing Weight
## 1 10 16 1995 12:35 1387-79172 RT I 387 1120
## 2 10 5 2002 14:27 1705-37416 CH A F 260 565
## Culmen Hallux Tail
## 1 26.8 50.2 221
## 2 19.7 54.5 205We verify that outliers have been successfully removed and that the imputation was correctly applied, using both a boxplot and a summary.
boxplot(hawks_limpio2$Hallux,
main = "Hallux",
ylab = "Spur Size (mm)",
outline = TRUE,
col = "lightblue")
abline(h = mean(hawks_limpio2$Hallux, na.rm = TRUE), col = "red", lty = 2)
summary(hawks_limpio2)## Month Day Year CaptureTime ReleaseTime
## Min. : 8.000 Min. : 1.00 Min. :1992 11:35 : 14 :842
## 1st Qu.: 9.000 1st Qu.: 9.00 1st Qu.:1995 13:30 : 14 11:00 : 2
## Median :10.000 Median :16.00 Median :1999 11:45 : 13 11:35 : 2
## Mean : 9.843 Mean :15.74 Mean :1998 12:10 : 13 12:05 : 2
## 3rd Qu.:10.000 3rd Qu.:23.00 3rd Qu.:2001 14:00 : 13 12:50 : 2
## Max. :11.000 Max. :31.00 Max. :2003 13:05 : 12 13:32 : 2
## (Other):829 (Other): 56
## BandNumber Species Age Sex Wing Weight
## : 2 CH: 70 A:224 :576 Min. : 37.2 Min. : 56.0
## 1142-09240: 1 RT:577 I:684 F:174 1st Qu.:202.0 1st Qu.: 185.0
## 1142-09241: 1 SS:261 M:158 Median :370.0 Median : 970.0
## 1142-09242: 1 Mean :315.6 Mean : 770.5
## 1142-18229: 1 3rd Qu.:390.0 3rd Qu.:1120.0
## 1142-19209: 1 Max. :480.0 Max. :2030.0
## (Other) :901
## Culmen Hallux Tail
## Min. : 8.60 Min. : 9.50 Min. :119.0
## 1st Qu.:12.78 1st Qu.:15.00 1st Qu.:160.0
## Median :25.50 Median :29.40 Median :214.0
## Mean :21.79 Mean :25.21 Mean :198.8
## 3rd Qu.:27.30 3rd Qu.:31.40 3rd Qu.:225.0
## Max. :39.20 Max. :54.50 Max. :288.0
## Exploratory Data Analysis
After cleaning the dataset, we will analyze it using various visualizations to gain a general overview and start drawing preliminary conclusions.
For example, the most common species in our dataset is “RT” (Red-tailed Hawk).
ggplot(hawks_limpio2, aes(x = Species)) +
geom_bar(fill = "skyblue") +
labs(title = "Number of Birds by Species", x = "Species", y = "Number of Birds")
Species: Bird species classification:
- “CH” = Cooper’s Hawk
- “RT” = Red-tailed Hawk
- “SS” = Sharp-shinned Hawk
especies_count <- hawks_limpio2 %>%
group_by(Species) %>%
summarize(Count = n()) %>%
arrange(desc(Count))
print(especies_count)## # A tibble: 3 × 2
## Species Count
## <fct> <int>
## 1 RT 577
## 2 SS 261
## 3 CH 70We create a relationship between wing length and weight.
This graph is crucial, as we can already identify three distinct groups, providing an important clue that we may have three clusters.
However, we continue with the exploratory analysis.
ggplot(hawks_limpio2, aes(x = Wing, y = Weight, color = Species)) +
geom_point(alpha = 0.5) +
labs(title = "Relationship Between Wing Length and Weight",
x = "Wing Length (mm)",
y = "Weight (g)")
We analyze the number of birds captured per year and notice an anomaly in 1996.
After a brief investigation, we found that 1996 was one of the harshest winters on record, which could be a significant factor for the analysis.
Reference for the indicated data:
https://www.thegazette.com/curious-iowa/curious-iowa-when-did-iowa-have-record-setting-weather/
ggplot(hawks_limpio2, aes(x = Year)) +
geom_bar(fill = "lightcoral") +
labs(title = "Number of Birds Captured per Year",
x = "Year",
y = "Number of Birds")
We extract another key insight: most of the birds in our dataset are not of advanced age.
Can we conclude that mortality is very high at a certain age?
We lack additional data, such as the exact classification of age groups, but this remains a crucial point for deeper analysis.
ggplot(hawks_limpio2, aes(x = Species, fill = Age)) +
geom_bar(position = "dodge") +
labs(title = "Number of Adult and Immature Birds by Species",
x = "Species",
y = "Number of Birds")
We have another key insight supporting the idea that
three clusters could be a great option.
The weight distribution clearly shows three distinct groups.
ggplot(hawks_limpio2, aes(x = Weight)) +
geom_histogram(binwidth = 50, fill = "purple", color = "black") +
labs(title = "Histogram of Bird Weight",
x = "Weight (g)",
y = "Frequency")
K-Means Clustering
We begin our K-Means study by selecting numerical variables, as K-Means can only handle numerical data.
We also include Sex and Age, even though they are categorical variables.
hawks_data <- hawks_limpio2 %>%
select(Wing, Weight, Culmen, Hallux, Sex, Age)
hawks_data## Wing Weight Culmen Hallux Sex Age
## 1 385.0000 920.0000 25.70000 30.10000 I
## 2 376.0000 930.0000 26.81197 32.23097 I
## 3 381.0000 990.0000 26.70000 31.30000 I
## 4 265.0000 470.0000 18.70000 23.50000 F I
## 5 205.0000 170.0000 12.50000 14.30000 F I
## 6 412.0000 1090.0000 28.50000 32.20000 I
## 7 370.0000 960.0000 25.30000 30.10000 I
## 8 375.0000 855.0000 27.20000 30.00000 A
## 9 412.0000 1210.0000 29.30000 31.30000 A
## 10 405.0000 1120.0000 26.00000 30.20000 I
## 11 393.0000 1010.0000 26.30000 30.80000 I
## 12 371.0000 1010.0000 25.40000 29.70000 I
## 13 390.0000 1120.0000 28.90000 30.90000 A
## 14 393.0000 1161.4132 28.20000 30.60000 A
## 15 416.0000 1170.0000 26.50000 34.00000 I
## 16 436.0000 1390.0000 30.50000 34.00000 A
## 17 418.0000 1150.0000 27.10000 31.00000 I
## 18 381.0000 950.0000 28.90000 28.90000 A
## 19 378.0000 910.0000 25.70000 28.20000 I
## 20 396.0000 1010.0000 24.00000 26.90000 I
## 21 399.0000 1070.0000 26.40000 31.20000 I
## 22 416.0000 1190.0000 28.80000 31.60000 I
## 23 415.0000 101.0000 24.90000 30.70000 I
## 24 392.0000 1330.0000 27.00000 30.30000 A
## 25 380.0000 990.0000 26.00000 30.00000 I
## 26 173.0000 100.0000 11.41111 14.24101 M I
## 27 399.0000 1100.0000 26.20000 32.50000 I
## 28 401.0000 1190.0000 28.60000 31.60000 A
## 29 205.0000 180.0000 11.70000 15.00000 F I
## 30 427.0000 1490.0000 30.10000 32.40000 I
## 31 395.0000 1040.0000 27.10000 31.40000 A
## 32 362.0000 820.0000 24.90000 27.90000 I
## 33 396.0000 1030.0000 26.00000 29.70000 A
## 34 391.0000 1300.0000 25.50000 32.40000 A
## 35 413.0000 1500.0000 26.50000 31.30000 A
## 36 371.0000 1080.0000 25.30000 27.20000 A
## 37 385.0000 1320.0000 27.30000 30.10000 A
## 38 378.0000 1490.0000 25.40000 31.30000 A
## 39 416.0000 1500.0000 29.10000 30.80000 A
## 40 193.0000 100.0000 9.30000 14.24101 M I
## 41 171.0000 88.0000 9.70000 11.50000 M I
## 42 233.0000 324.0000 16.00000 19.30000 I
## 43 384.0000 1060.0000 26.10000 31.20000 I
## 44 382.0000 1140.0000 25.10000 29.40000 I
## 45 390.0000 1030.0000 27.60000 30.30000 I
## 46 390.0000 1000.0000 25.10000 28.30000 I
## 47 393.0000 1050.0000 28.70000 29.80000 I
## 48 378.0000 1040.0000 26.20000 31.20000 I
## 49 398.0000 1110.0000 26.50000 30.90000 I
## 50 412.0000 1300.0000 27.90000 31.55000 I
## 51 400.0000 980.0000 25.70000 29.30000 I
## 52 422.0000 1120.0000 26.40000 28.30000 I
## 53 202.0000 134.0000 12.40000 13.70000 F I
## 54 394.0000 1270.0000 27.80000 31.60000 I
## 55 369.0000 880.0000 25.00000 26.50000 I
## 56 252.0000 340.0000 16.00000 20.80000 F I
## 57 240.0000 340.0000 16.10000 19.30000 M A
## 58 410.0000 1255.0000 29.70000 31.40000 I
## 59 241.0000 1320.0000 28.60000 36.40000 I
## 60 408.0000 1320.0000 30.00000 33.40000 I
## 61 37.2000 1180.0000 20.20000 26.65000 I
## 62 380.0000 760.0000 24.50000 26.10000 I
## 63 396.0000 1250.0000 26.60000 32.50000 I
## 64 326.0000 1076.4590 25.20000 27.70000 I
## 65 158.0000 100.0000 10.80000 10.50000 M I
## 66 416.0000 1300.0000 27.30000 32.70000 I
## 67 271.0000 475.0000 18.20000 24.75000 F I
## 68 176.0000 100.0000 9.80000 11.10000 M A
## 69 194.0000 150.3824 11.40000 14.20000 F A
## 70 390.0000 1080.0000 30.20000 29.10000 A
## 71 391.0000 1130.0000 26.40000 29.40000 A
## 72 387.0000 1160.0000 26.80000 31.00000 A
## 73 420.0000 1345.0000 29.50000 34.30000 I
## 74 435.0000 1385.0000 32.60000 30.60000 A
## 75 400.0000 1210.0000 25.50000 28.60000 A
## 76 398.0000 1455.0000 28.00000 31.50000 I
## 77 395.0000 1180.0000 25.00000 28.90000 I
## 78 410.0000 1500.0000 27.10000 33.20000 I
## 79 369.0000 1025.0000 27.10000 31.50000 I
## 80 372.0000 930.0000 26.10000 31.10000 I
## 81 415.0000 1360.0000 28.60000 33.50000 I
## 82 412.0000 1255.0000 27.70000 32.60000 I
## 83 205.0000 194.0000 12.60000 14.40000 F I
## 84 204.0000 159.0000 12.50000 14.80000 F I
## 85 170.0000 90.0000 9.50000 11.30000 M I
## 86 233.0000 340.0000 17.80000 19.40000 M A
## 87 375.0000 1065.0000 25.90000 30.00000 I
## 88 385.0000 1125.0000 19.60000 31.40000 I
## 89 422.0000 1340.0000 28.70000 32.00000 I
## 90 391.0000 1050.0000 26.60000 32.20000 I
## 91 410.0000 1210.0000 27.50000 32.23097 I
## 92 385.0000 980.0000 26.80000 27.80000 I
## 93 381.0000 1000.0000 25.50000 29.80000 I
## 94 416.0000 1390.0000 28.10000 31.30000 A
## 95 406.0000 1275.0000 29.00000 33.70000 I
## 96 418.0000 1180.0000 30.10000 32.23097 I
## 97 412.0000 1210.0000 29.30000 33.80000 I
## 98 208.0000 168.0000 12.70000 14.80000 F A
## 99 208.0000 146.0000 11.80000 14.90000 F I
## 100 175.0000 108.0000 10.00000 11.50000 M I
## 101 166.0000 94.0000 9.50000 11.30000 M I
## 102 405.0000 1085.0000 27.70000 29.90000 I
## 103 198.0000 188.0000 12.20000 16.94493 F A
## 104 200.0000 154.0000 12.40000 14.40000 F I
## 105 380.0000 810.0000 25.90000 28.70000 I
## 106 381.0000 905.0000 27.90000 29.10000 I
## 107 169.0000 94.0000 9.00000 10.20000 M I
## 108 260.0000 420.0000 19.60000 23.90000 F I
## 109 428.0000 1240.0000 29.10000 34.70000 I
## 110 400.0000 990.0000 26.90000 31.40000 I
## 111 265.0000 365.0000 16.80000 22.50000 F I
## 112 177.0000 91.0000 10.20000 11.30000 M I
## 113 381.0000 1010.0000 25.80000 31.70000 I
## 114 403.0000 980.0000 26.30000 29.70000 I
## 115 382.0000 860.0000 26.50000 29.00000 I
## 116 382.0000 970.0000 25.80000 29.00000 I
## 117 399.0000 980.0000 27.50000 29.90000 I
## 118 380.0000 985.0000 23.90000 29.00000 I
## 119 375.0000 990.0000 25.60000 30.60000 I
## 120 420.0000 1210.0000 27.80000 32.60000 I
## 121 170.0000 89.0000 8.60000 11.00000 M I
## 122 177.0000 97.0000 10.00000 11.30000 M A
## 123 375.0000 990.0000 28.00000 29.50000 I
## 124 395.0000 1170.0000 28.10000 31.70000 I
## 125 170.0000 93.0000 10.10000 11.20000 M A
## 126 406.0000 1350.0000 30.50000 32.00000 I
## 127 414.0000 1370.0000 29.30000 33.00000 I
## 128 173.0000 103.0000 9.70000 19.40000 M I
## 129 209.0000 151.0000 12.20000 13.90000 F I
## 130 177.0000 101.0000 10.30000 12.10000 M I
## 131 388.0000 985.0000 26.90000 29.80000 I
## 132 277.0000 940.0000 26.50000 30.40000 I
## 133 423.0000 1310.0000 27.40000 34.10000 I
## 134 365.0000 1035.0000 26.10000 30.80000 I
## 135 383.0000 965.0000 26.10000 31.80000 I
## 136 391.0000 1125.0000 25.40000 30.90000 I
## 137 389.0000 975.0000 26.40000 30.30000 I
## 138 392.0000 1140.0000 26.20000 29.80000 I
## 139 375.0000 950.0000 25.30000 29.90000 I
## 140 410.0000 1210.0000 28.10000 28.90000 I
## 141 179.0000 95.0000 10.80000 11.60000 M I
## 142 172.0000 89.0000 9.40000 10.80000 M I
## 143 202.0000 195.0000 12.40000 14.10000 F A
## 144 174.0000 93.0000 9.50000 11.00000 M I
## 145 422.0000 1205.0000 28.80000 31.30000 I
## 146 385.0000 1045.0000 27.60000 27.50000 I
## 147 363.0000 1090.0000 26.60000 28.80000 I
## 148 450.0000 1190.0000 30.30000 32.80000 I
## 149 380.0000 960.0000 25.60000 30.10000 I
## 150 385.0000 955.0000 26.30000 30.10000 I
## 151 385.0000 1110.0000 24.70000 30.20000 I
## 152 171.0000 100.0000 19.10000 11.50000 M I
## 153 380.0000 900.0000 24.00000 26.50000 I
## 154 384.0000 1075.0000 26.50000 30.70000 I
## 155 373.0000 980.0000 27.90000 32.10000 I
## 156 381.0000 940.0000 27.80000 34.20000 I
## 157 363.0000 1070.0000 25.60000 30.40000 I
## 158 409.0000 1120.0000 29.40000 31.60000 I
## 159 390.0000 1060.0000 27.60000 29.00000 A
## 160 204.0000 168.0000 12.10000 14.30000 F I
## 161 197.0000 211.0000 11.50000 13.90000 F I
## 162 420.0000 1125.0000 27.20000 27.40000 I
## 163 381.0000 1100.0000 27.00000 28.20000 I
## 164 408.0000 1360.0000 30.00000 33.90000 I
## 165 388.0000 995.0000 26.70000 30.70000 I
## 166 398.0000 1095.0000 21.10000 31.40000 A
## 167 209.0000 196.0000 12.10000 14.60000 F I
## 168 209.0000 176.0000 11.70000 15.10000 F I
## 169 394.0000 1075.0000 25.50000 29.70000 A
## 170 204.0000 180.0000 12.30000 15.20000 F A
## 171 204.0000 164.0000 12.30000 14.30000 F I
## 172 209.0000 158.0000 12.20000 14.40000 F I
## 173 394.0000 1140.0000 26.80000 29.20000 I
## 174 416.0000 1240.0000 27.90000 31.80000 I
## 175 445.0000 1465.0000 29.70000 34.60000 I
## 176 209.0000 169.0000 12.10000 14.50000 F I
## 177 388.0000 1105.0000 26.70000 28.90000 I
## 178 397.0000 1010.0000 27.10000 31.40000 I
## 179 384.0000 1075.0000 26.30000 30.50000 I
## 180 379.0000 1060.0000 27.90000 30.90000 I
## 181 393.0000 1015.0000 27.60000 31.10000 I
## 182 386.0000 1100.0000 26.00000 30.20000 I
## 183 397.0000 1010.0000 25.00000 30.60000 I
## 184 382.0000 1000.0000 26.30000 30.10000 I
## 185 386.0000 980.0000 25.40000 30.20000 I
## 186 417.0000 1240.0000 28.70000 32.40000 I
## 187 403.0000 1360.0000 27.90000 33.10000 I
## 188 239.0000 183.0000 17.30000 19.20000 M A
## 189 401.0000 1405.0000 29.10000 32.23097 I
## 190 377.0000 1055.0000 27.00000 29.10000 A
## 191 432.0000 1670.0000 27.10000 32.90000 A
## 192 390.0000 1250.0000 26.20000 30.50000 I
## 193 381.0000 1030.0000 25.30000 29.90000 I
## 194 403.0000 1040.0000 26.81197 29.90000 I
## 195 213.0000 190.0000 12.20000 15.50000 F I
## 196 172.0000 105.0000 10.00000 10.80000 M I
## 197 390.0000 1090.0000 26.20000 28.80000 I
## 198 204.0000 190.0000 11.80000 13.90000 F I
## 199 386.0000 1050.0000 28.40000 29.40000 A
## 200 402.0000 1110.0000 26.10000 30.00000 I
## 201 201.0000 206.0000 12.10000 13.50000 F I
## 202 202.0000 195.0000 12.10000 14.80000 F I
## 203 374.0000 1010.0000 24.90000 30.10000 A
## 204 358.0000 880.0000 24.20000 28.70000 I
## 205 370.0000 1060.0000 24.30000 29.80000 I
## 206 390.0000 920.0000 25.70000 30.00000 I
## 207 398.0000 1195.0000 26.20000 29.80000 I
## 208 360.0000 890.0000 26.00000 28.40000 I
## 209 355.0000 900.0000 25.30000 29.00000 I
## 210 375.0000 1110.0000 22.20000 31.50000 A
## 211 200.0000 160.0000 10.20000 13.20000 F I
## 212 179.0000 105.0000 10.10000 11.30000 M I
## 213 175.0000 99.0000 9.60000 12.70000 M I
## 214 203.0000 165.0000 12.00000 14.40000 F I
## 215 205.0000 100.0000 12.00000 12.50000 F I
## 216 213.0000 125.0000 11.50000 14.40000 F I
## 217 409.0000 1100.0000 29.00000 32.60000 I
## 218 202.0000 147.0957 11.41111 14.24101 F I
## 219 195.0000 155.0000 11.90000 14.60000 F I
## 220 415.0000 1285.0000 29.50000 31.80000 I
## 221 236.0000 390.0000 15.10000 20.40000 M A
## 222 363.0000 920.0000 26.80000 30.20000 I
## 223 381.0000 1025.0000 25.40000 30.80000 I
## 224 350.0000 940.0000 26.00000 29.10000 A
## 225 398.0000 1240.0000 28.50000 30.80000 I
## 226 412.0000 1160.0000 27.80000 33.00000 I
## 227 203.0000 150.0000 11.50000 13.90000 F I
## 228 201.0000 130.0000 11.70000 14.40000 F I
## 229 411.0000 1240.0000 26.80000 32.70000 I
## 230 373.0000 930.0000 24.40000 27.40000 I
## 231 178.0000 90.0000 10.90000 12.10000 M I
## 232 415.0000 1240.0000 25.60000 31.20000 I
## 233 383.0000 1030.0000 25.20000 29.80000 I
## 234 223.0000 550.0000 18.80000 21.30000 M I
## 235 390.0000 1250.0000 26.50000 32.00000 I
## 236 390.0000 999.0000 25.30000 29.80000 I
## 237 365.0000 1120.0000 26.50000 30.80000 A
## 238 345.0000 1000.0000 26.40000 30.10000 A
## 239 273.0000 530.0000 19.20000 24.70000 F I
## 240 400.0000 1040.0000 27.70000 32.10000 I
## 241 380.0000 1150.0000 27.80000 31.10000 I
## 242 330.0000 1000.0000 25.90000 30.20000 I
## 243 410.0000 1360.0000 33.30000 28.60000 I
## 244 313.0000 930.0000 25.70000 28.90000 I
## 245 384.0000 980.0000 25.80000 30.40000 I
## 246 409.0000 1260.0000 27.70000 31.80000 I
## 247 390.0000 900.0000 27.50000 28.60000 I
## 248 411.0000 1300.0000 25.90000 31.90000 I
## 249 259.0000 470.0000 16.60000 23.40000 F I
## 250 380.0000 1040.0000 26.40000 30.90000 A
## 251 370.0000 950.0000 27.30000 30.50000 I
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## 666 376.0000 1055.0000 29.50000 32.20000 I
## 667 380.0000 1105.0000 22.00000 30.80000 I
## 668 172.0000 120.0000 9.80000 11.80000 M A
## 669 408.0000 1390.0000 28.40000 32.70000 I
## 670 167.0000 105.0000 10.30000 10.80000 M A
## 671 374.0000 1080.0000 26.50000 31.30000 A
## 672 376.0000 910.0000 26.10000 32.20000 I
## 673 258.0000 490.0000 18.00000 24.20000 F I
## 674 370.0000 845.0000 25.00000 27.40000 I
## 675 202.0000 175.0000 13.30000 14.90000 F A
## 676 363.0000 865.0000 25.60000 27.30000 I
## 677 200.0000 180.0000 11.90000 13.50000 F A
## 678 372.0000 2030.0000 26.20000 30.20000 I
## 679 378.0000 960.0000 24.60000 30.00000 A
## 680 254.0000 515.0000 19.50000 23.80000 F A
## 681 361.0000 970.0000 26.30000 30.70000 I
## 682 389.0000 1265.0000 26.60000 30.60000 A
## 683 404.0000 1300.0000 29.40000 32.80000 A
## 684 195.0000 170.0000 12.90000 14.70000 F I
## 685 203.0000 191.0000 13.50000 15.50000 F I
## 686 253.0000 540.0000 19.10000 22.60000 F A
## 687 199.0000 185.0000 12.00000 14.90000 F I
## 688 194.0000 165.0000 11.90000 14.40000 F I
## 689 196.0000 205.0000 12.20000 14.00000 F A
## 690 168.0000 95.0000 10.40000 12.10000 M I
## 691 395.0000 1170.0000 25.80000 30.50000 A
## 692 368.0000 1075.0000 27.70000 31.70000 I
## 693 210.0000 200.0000 12.10000 15.30000 F I
## 694 401.0000 965.0000 25.80000 29.10000 I
## 695 355.0000 785.0000 22.70000 25.00000 I
## 696 377.0000 1095.0000 25.60000 31.70000 A
## 697 197.0000 160.0000 12.00000 14.70000 F I
## 698 171.0000 95.0000 9.10000 11.50000 M I
## 699 277.0000 1500.0000 29.70000 32.10000 A
## 700 435.0000 1595.0000 27.40000 34.50000 A
## 701 372.0000 985.0000 25.40000 31.00000 I
## 702 260.0000 565.0000 20.00000 24.20000 F A
## 703 390.0000 240.0000 25.20000 29.30000 I
## 704 359.0000 875.0000 26.00000 31.10000 I
## 705 393.0000 1225.0000 29.00000 33.40000 I
## 706 402.0000 1255.0000 30.60000 34.60000 I
## 707 362.0000 950.0000 26.80000 30.70000 I
## 708 227.0000 330.0000 16.00000 18.50000 M I
## 709 359.0000 895.0000 27.50000 30.10000 A
## 710 155.0000 100.0000 9.80000 12.00000 M I
## 711 261.0000 455.0000 17.10000 26.80000 F I
## 712 160.0000 90.0000 10.30000 11.50000 M I
## 713 166.0000 105.0000 11.30000 11.40000 M I
## 714 362.0000 1305.0000 28.20000 34.30000 I
## 715 375.0000 975.0000 27.20000 31.80000 I
## 716 388.0000 1185.0000 28.90000 34.30000 I
## 717 392.0000 1030.0000 26.10000 30.50000 I
## 718 412.0000 1215.0000 28.70000 34.10000 I
## 719 371.0000 1075.0000 26.90000 32.80000 I
## 720 255.0000 960.0000 19.70000 42.80000 F A
## 721 391.0000 795.0000 24.30000 27.60000 I
## 722 190.0000 180.0000 12.20000 14.20000 F I
## 723 385.0000 1225.0000 27.80000 32.00000 I
## 724 166.0000 110.0000 10.00000 11.90000 M I
## 725 197.0000 165.0000 12.20000 14.90000 F A
## 726 370.0000 920.0000 26.30000 32.00000 I
## 727 190.0000 170.0000 12.00000 15.00000 F I
## 728 400.0000 1315.0000 29.60000 34.00000 I
## 729 162.0000 100.0000 9.40000 11.10000 M I
## 730 194.0000 155.0000 12.50000 14.50000 F I
## 731 395.0000 1155.0000 29.90000 34.40000 I
## 732 403.0000 1160.0000 29.00000 32.30000 I
## 733 386.0000 955.0000 27.90000 30.40000 I
## 734 193.0000 190.0000 13.10000 14.90000 F A
## 735 203.0000 180.0000 13.80000 14.70000 F A
## 736 159.0000 90.0000 10.00000 11.50000 M A
## 737 163.0000 100.0000 9.80000 11.70000 M I
## 738 191.0000 190.0000 12.40000 14.80000 M A
## 739 166.0000 105.0000 10.30000 12.00000 M I
## 740 361.0000 1030.0000 27.00000 30.50000 I
## 741 260.0000 565.0000 19.70000 54.50000 F A
## 742 234.0000 380.0000 12.40000 21.90000 M A
## 743 377.0000 1040.0000 28.10000 30.90000 I
## 744 361.0000 910.0000 24.30000 27.50000 I
## 745 375.0000 1005.0000 26.00000 32.50000 I
## 746 193.0000 180.0000 11.90000 14.30000 F I
## 747 196.0000 175.0000 12.40000 15.60000 F I
## 748 159.0000 105.0000 9.80000 11.00000 M I
## 749 192.0000 190.0000 11.80000 14.20000 F I
## 750 401.0000 1250.0000 28.20000 35.30000 I
## 751 198.0000 185.0000 12.60000 15.20000 F I
## 752 407.0000 1275.0000 27.50000 33.70000 I
## 753 162.0000 105.0000 9.80000 12.50000 M I
## 754 169.0000 640.0000 16.70000 23.60000 F A
## 755 168.0000 100.0000 10.50000 10.70000 M I
## 756 168.0000 105.0000 10.70000 11.60000 M A
## 757 223.0000 390.0000 15.90000 20.60000 M A
## 758 375.0000 1030.0000 26.90000 31.30000 I
## 759 406.0000 1290.0000 29.30000 33.30000 A
## 760 386.0000 1020.0000 26.90000 31.60000 I
## 761 160.0000 105.0000 9.90000 11.40000 M A
## 762 378.0000 1055.0000 26.50000 29.90000 I
## 763 193.0000 185.0000 12.30000 14.80000 F A
## 764 379.0000 1010.0000 25.00000 29.30000 I
## 765 364.0000 1015.0000 24.90000 29.50000 I
## 766 350.0000 1115.0000 29.50000 30.30000 A
## 767 380.0000 1320.0000 26.70000 31.60000 I
## 768 395.0000 1180.0000 30.30000 33.40000 A
## 769 372.0000 1145.0000 25.90000 32.20000 I
## 770 376.0000 995.0000 28.00000 30.20000 I
## 771 367.0000 1045.0000 26.10000 30.50000 I
## 772 230.0000 340.0000 16.00000 19.50000 M I
## 773 366.0000 935.0000 25.70000 27.10000 I
## 774 386.0000 1065.0000 26.10000 31.00000 I
## 775 375.0000 1110.0000 27.70000 31.30000 I
## 776 199.0000 190.0000 12.00000 15.20000 F I
## 777 405.0000 1255.0000 27.90000 31.80000 A
## 778 371.0000 1015.0000 24.90000 28.40000 A
## 779 193.0000 190.0000 12.20000 15.20000 F I
## 780 350.0000 960.0000 26.60000 29.90000 I
## 781 193.0000 200.0000 11.30000 13.50000 F I
## 782 368.0000 1090.0000 27.30000 30.40000 A
## 783 185.0000 170.0000 12.00000 14.70000 M I
## 784 372.0000 1085.0000 25.40000 29.80000 I
## 785 396.0000 1065.0000 27.70000 30.00000 I
## 786 365.0000 1125.0000 26.90000 29.30000 I
## 787 374.0000 1050.0000 25.50000 30.30000 I
## 788 253.0000 525.0000 19.50000 23.50000 F I
## 789 372.0000 980.0000 26.40000 29.00000 I
## 790 376.0000 1180.0000 24.40000 30.70000 I
## 791 166.0000 115.0000 9.90000 11.60000 M I
## 792 369.0000 1095.0000 26.60000 28.40000 I
## 793 391.0000 1330.0000 26.80000 30.10000 A
## 794 193.0000 185.0000 12.10000 14.90000 F I
## 795 397.0000 1100.0000 22.10000 28.80000 A
## 796 366.0000 1115.0000 27.10000 21.00000 I
## 797 385.0000 1400.0000 30.30000 33.30000 A
## 798 400.0000 1175.0000 27.60000 32.60000 I
## 799 198.0000 185.0000 11.80000 15.10000 F I
## 800 365.0000 970.0000 25.90000 31.60000 A
## 801 194.0000 170.0000 11.60000 14.00000 F I
## 802 195.0000 175.0000 12.00000 15.60000 F I
## 803 200.0000 165.0000 11.50000 14.50000 F I
## 804 384.0000 1260.0000 28.60000 32.50000 I
## 805 159.0000 110.0000 9.90000 11.10000 M I
## 806 161.0000 100.0000 9.30000 11.50000 M I
## 807 191.0000 190.0000 12.30000 14.80000 F I
## 808 216.0000 305.0000 16.00000 20.40000 M I
## 809 256.0000 510.0000 18.80000 23.30000 F I
## 810 161.0000 90.0000 9.50000 11.30000 M I
## 811 396.0000 1195.0000 27.00000 23.80000 A
## 812 391.0000 1035.0000 27.90000 33.10000 I
## 813 160.0000 90.0000 8.80000 11.40000 M I
## 814 183.0000 160.0000 12.70000 14.60000 M I
## 815 156.0000 85.0000 9.70000 11.00000 M I
## 816 393.0000 1155.0000 28.30000 30.90000 I
## 817 397.0000 1260.0000 27.80000 32.90000 I
## 818 159.0000 95.0000 8.90000 10.40000 M I
## 819 255.0000 440.0000 18.60000 22.80000 F I
## 820 197.0000 175.0000 10.00000 14.90000 M I
## 821 218.0000 295.0000 16.10000 19.40000 M I
## 822 196.0000 160.0000 12.60000 14.50000 F I
## 823 384.0000 1010.0000 26.80000 31.10000 I
## 824 385.0000 990.0000 26.00000 29.60000 I
## 825 181.0000 150.0000 11.40000 14.30000 M I
## 826 225.0000 300.0000 16.00000 20.10000 M I
## 827 379.0000 945.0000 24.50000 31.30000 I
## 828 201.0000 188.0000 11.70000 14.90000 F I
## 829 161.0000 95.0000 10.60000 11.50000 M I
## 830 230.0000 330.0000 15.70000 19.40000 M A
## 831 159.0000 95.0000 9.90000 11.20000 M I
## 832 367.0000 970.0000 26.40000 30.50000 I
## 833 396.0000 1240.0000 28.90000 32.80000 I
## 834 157.0000 105.0000 10.00000 11.50000 M I
## 835 191.0000 165.0000 11.50000 14.90000 F I
## 836 191.0000 170.0000 12.10000 15.10000 F I
## 837 168.0000 100.0000 10.20000 11.90000 M I
## 838 428.0000 1290.0000 28.40000 33.90000 I
## 839 252.0000 470.0000 19.50000 28.40000 F A
## 840 192.0000 175.0000 11.70000 14.20000 F A
## 841 195.0000 195.0000 13.60000 14.00000 F A
## 842 233.0000 335.0000 16.30000 21.30000 M A
## 843 364.0000 1150.0000 26.10000 28.20000 A
## 844 370.0000 960.0000 25.40000 30.40000 I
## 845 400.0000 1130.0000 28.30000 29.40000 I
## 846 375.0000 925.0000 25.40000 28.60000 I
## 847 398.0000 1205.0000 27.60000 33.40000 I
## 848 385.0000 1040.0000 27.20000 31.50000 I
## 849 156.0000 100.0000 9.90000 11.20000 M I
## 850 230.0000 335.0000 16.30000 19.70000 M I
## 851 220.0000 335.0000 16.20000 20.00000 M I
## 852 163.0000 105.0000 10.30000 11.70000 M I
## 853 376.0000 860.0000 25.60000 30.00000 I
## 854 360.0000 935.0000 25.80000 30.00000 I
## 855 372.0000 1010.0000 24.30000 29.00000 A
## 856 400.0000 1285.0000 29.70000 33.50000 I
## 857 194.0000 210.0000 13.00000 14.50000 F A
## 858 370.0000 830.0000 23.60000 27.80000 I
## 859 160.0000 95.0000 10.20000 11.20000 M I
## 860 403.0000 1350.0000 28.00000 32.80000 I
## 861 375.0000 1010.0000 25.00000 30.80000 I
## 862 373.0000 960.0000 27.70000 32.50000 I
## 863 385.0000 1370.0000 26.40000 29.20000 I
## 864 143.0000 170.0000 12.80000 13.90000 F I
## 865 162.0000 100.0000 8.70000 11.40000 M I
## 866 392.0000 1250.0000 28.60000 32.90000 I
## 867 372.0000 915.0000 24.70000 28.20000 I
## 868 375.0000 850.0000 25.00000 28.00000 I
## 869 415.0000 1285.0000 29.40000 34.00000 I
## 870 161.0000 95.0000 9.80000 11.70000 M A
## 871 380.0000 1005.0000 27.00000 31.60000 A
## 872 411.0000 1220.0000 28.10000 32.70000 A
## 873 161.0000 95.0000 9.60000 12.40000 M A
## 874 165.0000 100.0000 9.80000 12.00000 M I
## 875 393.0000 1265.0000 28.30000 32.70000 I
## 876 370.0000 1020.0000 24.60000 30.00000 I
## 877 230.0000 360.0000 16.00000 22.10000 M A
## 878 365.0000 895.0000 24.50000 28.90000 I
## 879 371.0000 1160.0000 25.70000 28.40000 I
## 880 400.0000 1585.0000 29.00000 33.80000 I
## 881 382.0000 1140.0000 24.90000 31.60000 A
## 882 371.0000 1115.0000 25.30000 29.20000 A
## 883 370.0000 1145.0000 25.40000 30.20000 A
## 884 194.0000 185.0000 12.80000 14.80000 F A
## 885 347.0000 990.0000 25.30000 29.80000 A
## 886 363.0000 945.0000 24.50000 32.23097 I
## 887 195.0000 165.0000 11.70000 14.50000 F I
## 888 392.0000 1030.0000 26.30000 28.10000 A
## 889 220.0000 320.0000 15.50000 19.50000 M I
## 890 193.0000 105.0000 13.00000 15.60000 F I
## 891 365.0000 990.0000 26.40000 30.00000 I
## 892 387.0000 1065.0000 28.00000 32.70000 A
## 893 400.0000 1050.0000 26.10000 29.70000 I
## 894 362.0000 840.0000 23.20000 26.10000 I
## 895 198.0000 190.0000 12.20000 15.80000 F I
## 896 190.0000 200.0000 12.70000 15.00000 F I
## 897 197.0000 185.0000 12.80000 15.60000 F I
## 898 370.0000 1000.0000 26.90000 31.40000 A
## 899 200.0000 185.0000 12.80000 15.20000 F I
## 900 360.0000 1325.0000 26.20000 30.60000 A
## 901 366.0000 945.0000 25.30000 27.20000 A
## 902 402.0000 1350.0000 28.70000 31.00000 A
## 903 366.0000 805.0000 23.50000 25.70000 I
## 904 380.0000 1525.0000 26.00000 27.60000 I
## 905 190.0000 175.0000 12.70000 15.40000 F I
## 906 360.0000 790.0000 21.90000 27.60000 I
## 907 369.0000 860.0000 25.20000 28.00000 I
## 908 199.0000 1290.0000 28.70000 32.10000 AIn our analysis, we selected two categorical variables to convert into numerical format using the dummy encoding method.
We assign binary values (0 and 1) to the Age categories (Adult = 1, Immature = 0) and Sex categories (Male = 1, Female = 0).
hawks_limpio2 <- hawks_limpio2 %>%
mutate(
Sex_M = ifelse(Sex == "M", 1, 0),
Sex_F = ifelse(Sex == "F", 1, 0),
Age_A = ifelse(Age == "A", 1, 0),
Age_I = ifelse(Age == "I", 1, 0)
)
print(hawks_limpio2)## Month Day Year CaptureTime ReleaseTime BandNumber Species Age Sex Wing
## 1 9 19 1992 13:30 877-76317 RT I 385.0000
## 2 9 22 1992 10:30 877-76318 RT I 376.0000
## 3 9 23 1992 12:45 877-76319 RT I 381.0000
## 4 9 23 1992 10:50 745-49508 CH I F 265.0000
## 5 9 27 1992 11:15 1253-98801 SS I F 205.0000
## 6 9 28 1992 11:25 1207-55910 RT I 412.0000
## 7 9 28 1992 13:30 877-76320 RT I 370.0000
## 8 9 29 1992 11:45 877-76321 RT A 375.0000
## 9 9 29 1992 15:35 877-76322 RT A 412.0000
## 10 9 30 1992 13:45 1207-55911 RT I 405.0000
## 11 10 5 1992 13:30 877-76323 RT I 393.0000
## 12 10 8 1992 13:45 877-76324 RT I 371.0000
## 13 10 9 1992 12:30 877-76325 RT A 390.0000
## 14 10 10 1992 11:05 1207-55917 RT A 393.0000
## 15 10 11 1992 11:00 1207-55912 RT I 416.0000
## 16 10 11 1992 11:45 1207-55913 RT A 436.0000
## 17 10 11 1992 12:40 877-76326 RT I 418.0000
## 18 10 11 1992 14:20 877-76327 RT A 381.0000
## 19 10 12 1992 13:40 877-76328 RT I 378.0000
## 20 10 13 1992 11:00 877-76329 RT I 396.0000
## 21 10 13 1992 14:50 877-76330 RT I 399.0000
## 22 10 14 1992 13:15 877-76331 RT I 416.0000
## 23 10 17 1992 12:10 877-76332 RT I 415.0000
## 24 10 22 1992 13:05 877-76333 RT A 392.0000
## 25 10 23 1992 11:45 877-76334 RT I 380.0000
## 26 10 23 1992 16:05 1173-19901 SS I M 173.0000
## 27 10 24 1992 14:35 877-76335 RT I 399.0000
## 28 10 25 1992 12:05 1207-55914 RT A 401.0000
## 29 10 27 1992 10:05 1253-98802 SS I F 205.0000
## 30 10 27 1992 10:45 608-48703 RT I 427.0000
## 31 10 27 1992 15:15 1207-55915 RT A 395.0000
## 32 10 30 1992 11:05 877-76336 RT I 362.0000
## 33 11 3 1992 10:15 1207-55916 RT A 396.0000
## 34 11 8 1992 11:45 1207-55918 RT A 391.0000
## 35 11 8 1992 13:30 1207-55919 RT A 413.0000
## 36 11 13 1992 10:45 987-53707 RT A 371.0000
## 37 11 16 1992 11:15 1207-55920 RT A 385.0000
## 38 11 21 1992 14:00 877-76337 RT A 378.0000
## 39 11 22 1992 10:08 1207-55921 RT A 416.0000
## 40 9 13 1993 14:25 173-19904 SS I M 193.0000
## 41 9 17 1993 15:25 193-19905 SS I M 171.0000
## 42 9 20 1993 13:45 120407-804 CH I 233.0000
## 43 9 21 1993 15:11 877-76339 RT I 384.0000
## 44 9 22 1993 13:50 877-76340 RT I 382.0000
## 45 9 22 1993 15:55 877-76341 RT I 390.0000
## 46 9 27 1993 12:15 877-76342 RT I 390.0000
## 47 9 27 1993 13:00 877-76344 RT I 393.0000
## 48 9 27 1993 13:20 877-76345 RT I 378.0000
## 49 9 27 1993 15:03 877-76346 RT I 398.0000
## 50 9 28 1993 11:50 877-76347 RT I 412.0000
## 51 9 28 1993 12:45 877-76348 RT I 400.0000
## 52 9 29 1993 9:53 877-76349 RT I 422.0000
## 53 9 29 1993 10:25 1253-98803 SS I F 202.0000
## 54 9 29 1993 15:30 877-76350 RT I 394.0000
## 55 9 30 1993 13:25 787-53708 RT I 369.0000
## 56 10 1 1993 10:20 745-49512 CH I F 252.0000
## 57 10 1 1993 10:45 745-49513 CH A M 240.0000
## 58 10 3 1993 13:35 1207-55922 RT I 410.0000
## 59 10 4 1993 11:25 1207-55923 RT I 241.0000
## 60 10 7 1993 14:40 1207-55924 RT I 408.0000
## 61 10 9 1993 9:38 877-76351 RT I 37.2000
## 62 10 9 1993 10:20 877-76552 RT I 380.0000
## 63 10 10 1993 11:25 1207-55927 RT I 396.0000
## 64 10 10 1993 13:27 877-76353 RT I 326.0000
## 65 10 11 1993 11:35 1173-19906 SS I M 158.0000
## 66 10 11 1993 14:00 877-76354 RT I 416.0000
## 67 10 12 1993 13:15 745-49515 CH I F 271.0000
## 68 10 13 1993 9:23 1173-19907 SS A M 176.0000
## 69 10 14 1993 14:05 1373-35272 SS A F 194.0000
## 70 10 21 1993 9:20 877-76355 RT A 390.0000
## 71 10 21 1993 15:30 877-76357 RT A 391.0000
## 72 10 22 1993 16:35 877-76358 RT A 387.0000
## 73 10 23 1993 13:05 1207-55941 RT I 420.0000
## 74 10 25 1993 14:12 877-76359 RT A 435.0000
## 75 10 26 1993 15:55 877-76360 RT A 400.0000
## 76 10 31 1993 11:35 1207-55947 RT I 398.0000
## 77 11 5 1993 11:00 877-76361 RT I 395.0000
## 78 11 18 1993 10:37 877-76362 RT I 410.0000
## 79 9 6 1994 9:55 1387-99101 RT I 369.0000
## 80 9 6 1994 10:40 1387-99102 RT I 372.0000
## 81 9 7 1994 12:27 1387-99104 RT I 415.0000
## 82 9 7 1994 13:35 1387-99103 RT I 412.0000
## 83 9 8 1994 12:10 1423-16201 SS I F 205.0000
## 84 9 9 1994 9:02 2003-58433 SS I F 204.0000
## 85 9 9 1994 10:47 872-09611 SS I M 170.0000
## 86 9 12 1994 11:24 1204-45804 CH A M 233.0000
## 87 9 12 1994 13:50 1387-97105 RT I 375.0000
## 88 9 13 1994 11:58 1387-79106 RT I 385.0000
## 89 9 15 1994 12:45 1207-64601 RT I 422.0000
## 90 9 15 1994 13:20 1387-79107 RT I 391.0000
## 91 9 15 1994 13:35 1387-79108 RT I 410.0000
## 92 9 16 1994 10:23 1387-79109 RT I 385.0000
## 93 9 16 1994 11:20 1387-79111 RT I 381.0000
## 94 8 18 1994 12:05 1207-64602 RT A 416.0000
## 95 9 18 1994 13:20 1207-64603 RT I 406.0000
## 96 9 19 1994 12:58 1207-64604 RT I 418.0000
## 97 9 19 1994 14:05 1207-64605 RT I 412.0000
## 98 9 20 1994 9:05 2003-58435 SS A F 208.0000
## 99 9 20 1994 9:33 2003-58436 SS I F 208.0000
## 100 9 20 1994 11:04 1423-16203 SS I M 175.0000
## 101 9 20 1994 12:10 1423-16204 SS I M 166.0000
## 102 9 29 1994 13:55 1387-79112 RT I 405.0000
## 103 9 20 1994 14:00 2003-58437 SS A F 198.0000
## 104 9 29 1994 14:45 2003-58438 SS I F 200.0000
## 105 9 21 1994 13:50 1387-79113 RT I 380.0000
## 106 9 23 1994 11:48 1387-79114 RT I 381.0000
## 107 9 26 1994 10:28 872-09612 SS I M 169.0000
## 108 9 26 1994 10:54 2206-35417 CH I F 260.0000
## 109 9 26 1994 12:10 1207-64606 RT I 428.0000
## 110 9 26 1994 14:02 1207-64607 RT I 400.0000
## 111 9 27 1994 8:00 1705-24603 CH I F 265.0000
## 112 9 27 1994 11:55 1423-16205 SS I M 177.0000
## 113 9 27 1994 15:40 1307-79115 RT I 381.0000
## 114 9 28 1994 9:25 1387-79116 RT I 403.0000
## 115 9 28 1994 11:10 1387-79117 RT I 382.0000
## 116 9 28 1994 11:38 1387-79118 RT I 382.0000
## 117 9 28 1994 13:02 1387-79119 RT I 399.0000
## 118 9 29 1994 13:55 1387-79120 RT I 380.0000
## 119 9 29 1994 13:16 1387-79121 RT I 375.0000
## 120 9 30 1994 10:39 1207-64608 RT I 420.0000
## 121 10 3 1994 11:13 872-09613 SS I M 170.0000
## 122 10 3 1994 13:07 872-09614 SS A M 177.0000
## 123 10 4 1994 13:37 1387-79122 RT I 375.0000
## 124 10 4 1994 14:45 1207-64609 RT I 395.0000
## 125 10 5 1994 11:55 872-09615 SS A M 170.0000
## 126 10 5 1994 13:55 1207-64610 RT I 406.0000
## 127 10 5 1994 15:17 1207-64611 RT I 414.0000
## 128 10 5 1994 16:00 872-09616 SS I M 173.0000
## 129 10 6 1994 10:45 2003-58439 SS I F 209.0000
## 130 10 6 1994 11:23 872-09617 SS I M 177.0000
## 131 10 7 1994 10:50 1387-79123 RT I 388.0000
## 132 10 7 1994 11:24 1387-79124 RT I 277.0000
## 133 10 7 1994 12:15 1207-64612 RT I 423.0000
## 134 10 7 1994 15:40 1387-79125 RT I 365.0000
## 135 10 7 1994 16:35 1387-79126 RT I 383.0000
## 136 10 10 1994 11:02 1387-79127 RT I 391.0000
## 137 10 10 1994 12:01 1387-79128 RT I 389.0000
## 138 10 10 1994 12:23 1387-79129 RT I 392.0000
## 139 10 10 1994 13:10 1387-79130 RT I 375.0000
## 140 10 10 1994 13:50 1207-64613 RT I 410.0000
## 141 10 10 1994 15:07 872-09618 SS I M 179.0000
## 142 10 11 1994 8:52 872-09619 SS I M 172.0000
## 143 10 11 1994 12:36 2003-58440 SS A F 202.0000
## 144 10 12 1994 11:15 1423-16206 SS I M 174.0000
## 145 10 13 1994 13:05 1207-64614 RT I 422.0000
## 146 10 13 1994 14:00 1387-79131 RT I 385.0000
## 147 10 16 1994 12:05 1387-79132 RT I 363.0000
## 148 10 16 1994 11:30 1207-64615 RT I 450.0000
## 149 10 18 1994 10:00 1287-79133 RT I 380.0000
## 150 10 18 1994 12:35 1387-79134 RT I 385.0000
## 151 10 18 1994 13:30 1387-79135 RT I 385.0000
## 152 10 19 1994 9:08 872-09620 SS I M 171.0000
## 153 10 19 1994 10:46 1387-79136 RT I 380.0000
## 154 10 19 1994 11:27 1387-79137 RT I 384.0000
## 155 10 19 1994 12:15 1387-79138 RT I 373.0000
## 156 10 19 1994 12:55 1387-79139 RT I 381.0000
## 157 10 19 1994 13:35 1387-79140 RT I 363.0000
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## 159 10 20 1994 12:00 1387-79142 RT A 390.0000
## 160 10 21 1994 10:12 2003-58441 SS I F 204.0000
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## 162 10 23 1994 11:06 1387-79143 RT I 420.0000
## 163 10 23 1994 11:36 1387-79144 RT I 381.0000
## 164 10 23 1994 13:09 1207-64616 RT I 408.0000
## 165 10 23 1994 14:25 1387079145 RT I 388.0000
## 166 10 23 1994 15:00 1387-79146 RT A 398.0000
## 167 10 24 1994 9:05 1423-16208 SS I F 209.0000
## 168 10 25 1994 10:25 2003-58442 SS I F 209.0000
## 169 10 25 1994 14:00 1387-079147 RT A 394.0000
## 170 10 25 1994 14:19 1423-11209 SS A F 204.0000
## 171 10 26 1994 9.12 1423-16210 SS I F 204.0000
## 172 10 26 1994 10:29 2003-58443 SS I F 209.0000
## 173 10 26 1994 11:39 1387-79148 RT I 394.0000
## 174 10 26 1994 14:55 1207-64617 RT I 416.0000
## 175 10 26 1994 15:40 1207-64618 RT I 445.0000
## 176 10 27 1994 9:15 2003-58444 SS I F 209.0000
## 177 10 27 1994 10:55 1387-79149 RT I 388.0000
## 178 10 27 1994 11:50 1387-79150 RT I 397.0000
## 179 10 27 1994 12:24 1387-79151 RT I 384.0000
## 180 10 27 1994 13:37 1387-79152 RT I 379.0000
## 181 10 28 1994 10:05 1387-79199 RT I 393.0000
## 182 10 28 1994 10:45 1387-79153 RT I 386.0000
## 183 10 29 1994 11:05 1387-79154 RT I 397.0000
## 184 10 29 1994 11:50 1387-79155 RT I 382.0000
## 185 11 1 1994 10:45 1387-79156 RT I 386.0000
## 186 11 1 1994 11:21 1387-79157 RT I 417.0000
## 187 11 2 1994 11:41 1387-79158 RT I 403.0000
## 188 11 2 1994 12:26 1204-45805 CH A M 239.0000
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## 190 11 2 1994 14:52 1387-79159 RT A 377.0000
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## 193 11 6 1994 11:40 1387-79160 RT I 381.0000
## 194 11 7 1994 11:22 1387-79161 RT I 403.0000
## 195 11 7 1994 12:47 1423-16211 SS I F 213.0000
## 196 11 9 1994 9:46 872-09621 SS I M 172.0000
## 197 11 9 1994 15:02 1807-53101 RT I 390.0000
## 198 11 11 1994 10:00 1423-16212 SS I F 204.0000
## 199 11 11 1994 11:59 1387-79162 RT A 386.0000
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## 201 11 11 1994 15:01 1423-16213 SS I F 201.0000
## 202 11 11 1994 15:23 1423-16214 SS I F 202.0000
## 203 11 15 1994 11:40 1387-79164 RT A 374.0000
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## 205 11 16 1994 12:19 1387-79165 RT I 370.0000
## 206 11 21 1994 10:40 1387-79166 RT I 390.0000
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## 208 9 8 1995 13:30 1387-170 RT I 360.0000
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## 213 9 15 1995 9:40 2003-58464 SS I M 175.0000
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## 250 10 11 1995 14:25 1387-79188 RT A 380.0000
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## 256 10 12 1995 14:30 1207-64631 RT A 384.0000
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## 272 10 18 1995 13:15 1807-53107 RT I 350.0000
## 273 10 18 1995 12:00 1387-79200 RT I 388.0000
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## 280 11 20 1995 14:10 1207-64639 RT I 396.0000
## 281 11 21 1995 11:45 8777-6382 RT I 363.0000
## 282 10 2 1996 9:47 1807-53108 RT I 360.0000
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## 541 9 30 2000 15:01 1207-74640 RT I 392.0000
## 542 10 1 2000 14:00 1705-37413 SS I M 250.0000
## 543 10 1 2000 14:50 1207-72641 RT I 418.0000
## 544 10 2 2000 13:20 1177-04641 RT I 370.0000
## 545 10 3 2000 10:52 1142-19233 SS A M 170.0000
## 546 10 3 2000 14:05 803-05935 SS A F 203.0000
## 547 10 4 2000 10:40 1177-04642 RT A 370.0000
## 548 10 4 2000 11:56 1207-72642 RT A 408.0000
## 549 10 6 2000 12:59 1207-72643 RT A 393.0000
## 550 10 7 2000 9:55 1177-04643 RT I 365.0000
## 551 10 7 2000 10:27 1207-72644 RT I 405.0000
## 552 10 7 2000 10:43 1207-72645 RT I 381.0000
## 553 10 7 2000 12:24 1177-04644 RT I 390.0000
## 554 10 7 2000 15:12 1207-72646 RT I 384.0000
## 555 10 8 2000 12:25 1177-04645 RT I 390.0000
## 556 10 8 2000 13:29 1177-04646 RT I 381.0000
## 557 10 9 2000 10:10 803-05936 SS A F 194.0000
## 558 10 9 2000 14:00 1807-82702 RT I 371.0000
## 559 10 9 2000 14:26 1177-04647 RT I 356.0000
## 560 10 9 2000 14:38 1177-04648 RT I 377.0000
## 561 10 10 2000 13:57 1177-04649 RT I 362.0000
## 562 10 11 2000 12:21 1142-19234 SS A M 165.0000
## 563 10 12 2000 10:10 1142-19235 SS A M 155.0000
## 564 10 12 2000 13:35 1207-72647 RT I 400.0000
## 565 10 13 2000 9:33 1142-19236 SS A M 161.0000
## 566 10 13 2000 9:58 1207-72648 RT I 387.0000
## 567 10 13 2000 11:08 1207-72649 RT I 409.0000
## 568 10 13 2000 12:35 2003-99320 SS A F 195.0000
## 569 10 13 2000 14:45 2003-99321 SS A F 196.0000
## 570 10 14 2000 11:35 1142-19237 SS A M 169.0000
## 571 10 14 2000 12:07 1177-04650 RT I 385.0000
## 572 10 14 2000 13:07 1807-82703 RT I 377.0000
## 573 10 14 2000 13:12 1177-04651 RT I 400.0000
## 574 10 15 2000 12:50 1142-19238 SS I M 164.0000
## 575 10 16 2000 14:30 1142-19239 SS A M 165.0000
## 576 10 17 2000 15:03 1177-04652 RT I 363.0000
## 577 10 18 2000 12:14 2206-35432 CH A F 266.0000
## 578 10 18 2000 14:28 1177-04653 RT I 403.0000
## 579 10 19 2000 12:14 1177-04654 RT I 375.0000
## 580 10 19 2000 13:38 1142-09240 SS A M 166.0000
## 581 10 20 2000 9:48 1177-04655 RT I 373.0000
## 582 10 20 2000 11:46 1177-04656 RT I 373.0000
## 583 10 20 2000 12:38 1142-09241 SS A M 170.0000
## 584 10 20 2000 14:12 1177-04657 RT A 373.0000
## 585 10 20 2000 14:27 1807-82704 RT I 354.0000
## 586 10 20 2000 14:45 1207-72650 RT I 394.0000
## 587 10 21 2000 9:22 1142-09242 SS I M 165.0000
## 588 10 21 2000 13:57 1705-24640 CH A F 261.0000
## 589 10 21 2000 14:12 1177-04658 RT I 377.0000
## 590 10 25 2000 12:51 1177-04659 RT I 364.0000
## 591 10 25 2000 13:45 1177-04660 RT I 385.0000
## 592 10 26 2000 9:21 1177-04661 RT I 390.0000
## 593 10 26 2000 10:53 1177-04662 RT A 383.0000
## 594 10 26 2000 12:53 1177-04663 RT I 365.0000
## 595 10 27 2000 10:49 803-05937 SS I F 201.0000
## 596 10 27 2000 13:15 1177-04664 RT I 376.0000
## 597 10 27 2000 14:49 1207-72651 RT A 402.0000
## 598 10 29 2000 9:45 1177-04665 RT I 394.0000
## 599 10 29 2000 13:36 1204-45871 CH I M 223.0000
## 600 10 30 2000 11:20 1177-04666 RT A 378.0000
## 601 11 1 2000 12:08 1177-04667 RT I 369.0000
## 602 11 1 2000 13:16 1177-04668 RT A 378.0000
## 603 11 2 2000 9:55 1177-04669 RT A 262.0000
## 604 11 2 2000 10:28 1142-19243 SS I M 165.0000
## 605 11 2 2000 12:47 1177-04670 RT A 379.0000
## 606 11 3 2000 9:42 1177-04671 RT I 380.0000
## 607 11 4 2000 11:20 1177-04672 RT A 380.0000
## 608 11 4 2000 13:10 1177-04673 RT I 393.0000
## 609 11 4 2000 13:24 1207-72652 RT A 389.0000
## 610 11 8 2000 10:31 1207-72653 RT I 395.0000
## 611 11 12 2000 13:50 2003-99233 SS I F 207.0000
## 612 11 14 2000 11:40 1807-82705 RT I 367.0000
## 613 11 14 2000 11:57 1177-04674 RT A 368.0000
## 614 11 18 2000 10:47 1177-04675 RT I 377.0000
## 615 11 20 2000 11:15 1177-04676 RT I 374.0000
## 616 11 21 2000 12:03 1177-04677 RT A 385.0000
## 617 9 3 2001 13:30 1177-04698 RT I 363.0000
## 618 9 9 2001 11:51 1142-19244 SS I M 164.0000
## 619 9 10 2001 9:39 2003-99323 SS A F 199.0000
## 620 9 10 2001 14:05 1177-04678 RT I 378.0000
## 621 9 12 2001 11:03 803-05938 SS I F 200.0000
## 622 9 12 2001 11:35 1207-72654 RT I 405.0000
## 623 9 13 2001 10:20 2003-99324 SS I F 194.0000
## 624 9 13 2001 11:00 2003-99325 SS I F 190.0000
## 625 9 13 2001 13:03 2003-99326 SS I F 195.0000
## 626 9 14 2001 10:35 1213-58903 SS I M 161.0000
## 627 9 14 2001 13:05 1213-58904 SS I M 168.0000
## 628 9 14 2001 13:55 1213-58905 SS I M 160.0000
## 629 9 16 2001 14:00 1177-04679 RT I 392.0000
## 630 9 19 2001 10:11 2003-99327 SS I F 201.0000
## 631 9 19 2001 11:55 1207-72655 RT I 395.0000
## 632 9 20 2001 12:50 1207-72656 RT I 390.0000
## 633 9 22 2001 9:45 1142-19245 SS I M 161.0000
## 634 9 22 2001 10:45 1705-24641 CH A M 230.0000
## 635 9 22 2001 14:57 2003-99328 SS I F 192.0000
## 636 9 24 2001 12:50 1213-58906 SS I M 156.0000
## 637 9 24 2001 14:20 1213-58907 SS I M 158.0000
## 638 9 26 2001 10:15 1142-19246 SS I M 167.0000
## 639 9 26 2001 12:20 804-00201 SS I F 199.0000
## 640 9 27 2001 13:40 1705-24642 CH I F 320.0000
## 641 9 30 2001 12:33 1207-72657 RT A 389.0000
## 642 10 2 2001 11:00 804-00202 CH I M 227.0000
## 643 10 2 2001 13:15 804-00203 CH A M 230.0000
## 644 10 3 2001 10:29 2003-99329 SS A F 199.0000
## 645 10 5 2001 14:29 1177-04680 RT I 378.0000
## 646 10 9 2001 13:25 1142-19247 SS I M 164.0000
## 647 10 9 2001 14:58 1207-72658 RT A 385.0000
## 648 10 14 2001 9:36 1177-04681 RT I 369.0000
## 649 10 14 2001 10:27 1177-04682 RT I 378.0000
## 650 10 14 2001 11:52 1177-04683 RT I 373.0000
## 651 10 14 2001 12:20 1177-04684 RT A 419.0000
## 652 10 14 2001 14:12 1177-04685 RT I 414.0000
## 653 10 15 2001 13:20 2003-99330 SS A F 203.0000
## 654 10 17 2001 9:50 1142-19248 SS A M 162.0000
## 655 10 17 2001 10:36 1142-19249 SS I M 165.0000
## 656 10 17 2001 10:58 1142-19250 SS A M 161.0000
## 657 10 17 2001 11:35 1142-19251 SS I M 161.0000
## 658 10 17 2001 12:59 1177-04686 RT I 404.0000
## 659 10 17 2001 13:48 1142-19252 SS I M 165.0000
## 660 10 17 2001 14:03 2003-99331 SS A F 199.0000
## 661 10 18 2001 9:24 1142-19253 SS I M 171.0000
## 662 10 18 2001 9:58 2003-99332 SS A F 213.0000
## 663 10 18 2001 10:11 1142-19254 SS A M 169.0000
## 664 10 18 2001 10:35 1207-72659 RT I 379.0000
## 665 10 18 2001 12:00 1207-72660 RT I 407.0000
## 666 10 18 2001 12:42 1177-04689 RT I 376.0000
## 667 10 18 2001 13:56 1177-04688 RT I 380.0000
## 668 10 18 2001 14:29 1142-19255 SS A M 172.0000
## 669 10 18 2001 15:30 1207-72661 RT I 408.0000
## 670 10 19 2001 11:53 1142-19256 SS A M 167.0000
## 671 10 19 2001 12:42 1177-04690 RT A 374.0000
## 672 10 21 2001 12:48 1177-04691 RT I 376.0000
## 673 10 23 2001 10:55 1705-24643 CH I F 258.0000
## 674 10 23 2001 12:24 1807-66307 RT I 370.0000
## 675 10 23 2001 12:55 2003-99333 SS A F 202.0000
## 676 10 25 2001 10:29 1807-66308 RT I 363.0000
## 677 10 25 2001 11:04 2003-99334 SS A F 200.0000
## 678 10 25 2001 11:50 1177-04692 RT I 372.0000
## 679 10 25 2001 12:55 1807-66309 RT A 378.0000
## 680 10 26 2001 12:20 1750-24644 CH A F 254.0000
## 681 10 26 2001 13:00 1177-04694 RT I 361.0000
## 682 10 28 2001 10:46 1177-04695 RT A 389.0000
## 683 10 28 2001 11:37 1207-72662 RT A 404.0000
## 684 10 31 2001 13:30 2003-99335 SS I F 195.0000
## 685 11 1 2001 11:45 2003-99336 SS I F 203.0000
## 686 11 1 2001 13:45 1705-24645 CH A F 253.0000
## 687 11 2 2001 9:41 2003-99337 SS I F 199.0000
## 688 11 3 2001 13:58 2003-99338 SS I F 194.0000
## 689 11 3 2001 14:23 2003-99339 SS A F 196.0000
## 690 11 5 2001 14:40 1142-19257 SS I M 168.0000
## 691 11 6 2001 13:05 1177-04696 RT A 395.0000
## 692 11 7 2001 11:15 1177-04697 RT I 368.0000
## 693 11 7 2001 13:15 803-05939 SS I F 210.0000
## 694 11 9 2001 9:40 1177-04700 RT I 401.0000
## 695 11 9 2001 10:40 1807-53134 RT I 355.0000
## 696 11 10 2001 10:27 1177-04701 RT A 377.0000
## 697 11 11 2001 9:44 2003-99340 SS I F 197.0000
## 698 11 14 2001 10:04 1142-19258 SS I M 171.0000
## 699 11 19 2001 9:48 1177-04702 RT A 277.0000
## 700 11 19 2001 14:05 1207-72663 RT A 435.0000
## 701 9 4 2002 10:00 1177-04703 RT I 372.0000
## 702 9 5 2002 12:45 1705-24648 CH A F 260.0000
## 703 9 8 2002 12:20 1177-04704 RT I 390.0000
## 704 9 8 2002 12:44 1177-04705 RT I 359.0000
## 705 9 10 2002 12:39 1177-04706 RT I 393.0000
## 706 9 12 2002 10:13 1207-72664 RT I 402.0000
## 707 9 12 2002 11:51 1177-04707 RT I 362.0000
## 708 9 13 2002 12:55 1705-14646 CH I M 227.0000
## 709 9 16 2002 13:14 1807-53135 RT A 359.0000
## 710 9 17 2002 11:20 1142-19259 SS I M 155.0000
## 711 9 18 2002 12:08 1705-24647 CH I F 261.0000
## 712 9 19 2002 9:30 1142-19260 SS I M 160.0000
## 713 9 19 2002 12:01 1142-19261 SS I M 166.0000
## 714 9 21 2002 13:38 1207-72665 RT I 362.0000
## 715 9 22 2002 10:50 1177-04708 RT I 375.0000
## 716 9 22 2002 11:57 1177-04709 RT I 388.0000
## 717 9 22 2002 13:47 1177-04710 RT I 392.0000
## 718 9 22 2002 14:29 1207-72666 RT I 412.0000
## 719 9 23 2002 13:15 1177-04711 RT I 371.0000
## 720 9 23 2002 14:23 1705-24649 CH A F 255.0000
## 721 9 24 2002 12:50 1807-53136 RT I 391.0000
## 722 9 24 2002 13:26 2003-99341 SS I F 190.0000
## 723 9 25 2002 12:36 1177-04712 RT I 385.0000
## 724 9 25 2002 14:05 1142-19262 SS I M 166.0000
## 725 9 26 2002 10:49 2003-99342 SS A F 197.0000
## 726 9 29 2002 10:10 1177-04713 RT I 370.0000
## 727 9 29 2002 10:50 2003-99345 SS I F 190.0000
## 728 9 29 2002 12:52 1207-72667 RT I 400.0000
## 729 9 29 2002 13:06 1142-19263 SS I M 162.0000
## 730 9 30 2002 11:26 2003-00344 SS I F 194.0000
## 731 9 30 2002 11:45 1207-72668 RT I 395.0000
## 732 9 30 2002 12:46 1207-72669 RT I 403.0000
## 733 10 3 2002 9:58 1177-04714 RT I 386.0000
## 734 10 4 2002 9:53 803-05940 SS A F 193.0000
## 735 10 4 2002 15:15 2003-99346 SS A F 203.0000
## 736 10 5 2002 8:34 1142-19264 SS A M 159.0000
## 737 10 5 2002 9:59 1142-19265 SS I M 163.0000
## 738 10 5 2002 10:34 2003-99348 SS A M 191.0000
## 739 10 5 2002 13:08 1142-19266 SS I M 166.0000
## 740 10 5 2002 13:30 1177-04715 RT I 361.0000
## 741 10 5 2002 14:27 1705-37416 CH A F 260.0000
## 742 10 6 2002 9:48 804-00205 CH A M 234.0000
## 743 10 6 2002 10:43 1177-04716 RT I 377.0000
## 744 10 6 2002 12:03 1807-53137 RT I 361.0000
## 745 10 6 2002 12:34 1177-04717 RT I 375.0000
## 746 10 6 2002 14:56 2003-99349 SS I F 193.0000
## 747 10 7 2002 9:40 803-05941 SS I F 196.0000
## 748 10 7 2002 13:25 1142-19267 SS I M 159.0000
## 749 10 7 2002 13:25 1213-58908 SS I F 192.0000
## 750 10 7 2002 13:29 1207-72670 RT I 401.0000
## 751 10 8 2002 14:40 2003-99350 SS I F 198.0000
## 752 10 10 2002 11:36 1177-04718 RT I 407.0000
## 753 10 10 2002 12:46 1142-19268 SS I M 162.0000
## 754 10 11 2002 11:23 2206-35435 CH A F 169.0000
## 755 10 11 2002 14:50 1142-19269 SS I M 168.0000
## 756 10 13 2002 9:38 1142-19270 SS A M 168.0000
## 757 10 13 2002 10:00 804-00206 CH A M 223.0000
## 758 10 13 2002 10:42 1177-04719 RT I 375.0000
## 759 10 13 2002 11:33 1177-04720 RT A 406.0000
## 760 10 14 2002 9:50 1177-04721 RT I 386.0000
## 761 10 14 2002 10:14 1142-19271 SS A M 160.0000
## 762 10 14 2002 12:59 1177-04722 RT I 378.0000
## 763 10 14 2002 14:16 803-05942 SS A F 193.0000
## 764 10 17 2002 9:46 1177-04723 RT I 379.0000
## 765 10 18 2002 10:00 1177-04724 RT I 364.0000
## 766 10 18 2002 12:50 1177-04725 RT A 350.0000
## 767 10 18 2002 13:10 1207-7267 RT I 380.0000
## 768 10 19 2002 10:34 1207-72672 RT A 395.0000
## 769 10 19 2002 11:22 1177-04726 RT I 372.0000
## 770 10 19 2002 13:22 1177-04727 RT I 376.0000
## 771 10 20 2002 13:24 1177-04728 RT I 367.0000
## 772 10 21 2002 11:05 1204-5874 CH I M 230.0000
## 773 10 21 2002 13:55 1807-53138 RT I 366.0000
## 774 10 23 2002 12:56 1177-04729 RT I 386.0000
## 775 10 26 2002 12:45 1177-04730 RT I 375.0000
## 776 10 30 2002 10:30 2003-99351 SS I F 199.0000
## 777 10 30 2002 12:40 1177-04731 RT A 405.0000
## 778 10 31 2002 10:18 1177-04732 RT A 371.0000
## 779 10 31 2002 12:00 2003-99352 SS I F 193.0000
## 780 10 31 2002 12:15 1177-04733 RT I 350.0000
## 781 10 31 2002 13:20 2003-99353 SS I F 193.0000
## 782 11 1 2002 10:50 1177-04734 RT A 368.0000
## 783 11 2 2002 10:34 2003-99354 SS I M 185.0000
## 784 11 2 2002 10:48 1177-04735 RT I 372.0000
## 785 11 2 2002 11:00 1177-04736 RT I 396.0000
## 786 11 2 2002 11:18 1177-04737 RT I 365.0000
## 787 11 3 2002 11:36 1177-04738 RT I 374.0000
## 788 11 4 2002 9:33 1705-24644 CH I F 253.0000
## 789 11 6 2002 12:06 1177-04739 RT I 372.0000
## 790 11 6 2002 14:06 1177-04740 RT I 376.0000
## 791 11 7 2002 10:20 1142-19272 SS I M 166.0000
## 792 11 7 2002 11:58 1177-04741 RT I 369.0000
## 793 11 7 2002 12:28 1207-72673 RT A 391.0000
## 794 11 7 2002 12:59 2003-99355 SS I F 193.0000
## 795 11 8 2002 11:45 1177-0472 RT A 397.0000
## 796 11 8 2002 14:29 1177-0473 RT I 366.0000
## 797 11 10 2002 11:35 1207-72674 RT A 385.0000
## 798 11 10 2002 12:35 1177-0744 RT I 400.0000
## 799 11 11 2002 11:48 2003-99356 SS I F 198.0000
## 800 9 5 2003 10:38 1177-0745 RT A 365.0000
## 801 9 14 2003 10:18 2003-99357 SS I F 194.0000
## 802 9 16 2003 10:15 803-05943 SS I F 195.0000
## 803 9 16 2003 10:57 2003-99358 SS I F 200.0000
## 804 9 16 2003 12:55 1207-72675 RT I 384.0000
## 805 9 17 2003 9:40 1142-19273 SS I M 159.0000
## 806 9 18 2003 10:17 1142-19274 SS I M 161.0000
## 807 9 18 2003 10:17 2003-99359 SS I F 191.0000
## 808 9 18 2003 11:55 1204-45879 CH I M 216.0000
## 809 9 18 2003 13:50 1705-37417 CH I F 256.0000
## 810 9 19 2003 10:59 1142-19275 SS I M 161.0000
## 811 9 20 2003 12:04 1207-99560 RT A 396.0000
## 812 9 20 2003 13:35 1177-04746 RT I 391.0000
## 813 9 20 2003 14:12 1142-19276 SS I M 160.0000
## 814 9 21 2003 9:52 2003-99360 SS I M 183.0000
## 815 9 22 2003 14:21 1142-19277 SS I M 156.0000
## 816 9 23 2003 10:44 1207-72676 RT I 393.0000
## 817 9 23 2003 11:16 1207-72677 RT I 397.0000
## 818 9 23 2003 13:13 1142-19278 SS I M 159.0000
## 819 9 23 2003 14:00 1705-37418 CH I F 255.0000
## 820 9 24 2003 9:35 2003-99362 SS I M 197.0000
## 821 9 24 2003 9:53 1204-45880 CH I M 218.0000
## 822 9 25 2003 9:49 2003-99363 SS I F 196.0000
## 823 9 25 2003 13:08 1177-04747 RT I 384.0000
## 824 9 25 2003 13:30 1177-04748 RT I 385.0000
## 825 9 26 2003 10:19 2003-99364 SS I M 181.0000
## 826 9 26 2003 11:27 1204-45881 CH I M 225.0000
## 827 9 17 2003 9:18 1177-04749 RT I 379.0000
## 828 9 27 2003 10:10 2003-99365 SS I F 201.0000
## 829 9 28 2003 9:36 1142-19279 SS I M 161.0000
## 830 9 28 2003 10:11 1705-37419 CH A M 230.0000
## 831 9 28 2003 12:12 1142-19280 SS I M 159.0000
## 832 9 29 2003 11:20 1177-04750 RT I 367.0000
## 833 9 29 2003 12:02 1207-72678 RT I 396.0000
## 834 9 29 2003 12:58 1142-19281 SS I M 157.0000
## 835 9 29 2003 13:51 2003-99366 SS I F 191.0000
## 836 9 29 2003 14:47 2003-99367 SS I F 191.0000
## 837 9 29 2003 15:15 1142-19282 SS I M 168.0000
## 838 9 29 2003 15:55 1207-72679 RT I 428.0000
## 839 9 30 2003 12:05 1705-37420 CH A F 252.0000
## 840 9 30 2003 12:53 2003-99368 SS A F 192.0000
## 841 9 30 2003 13:22 2003-99369 SS A F 195.0000
## 842 10 1 2003 10:07 1204-45882 CH A M 233.0000
## 843 10 1 2003 11:53 1177-04751 RT A 364.0000
## 844 10 1 2003 13:40 1177-04752 RT I 370.0000
## 845 10 1 2003 14:30 1207-72680 RT I 400.0000
## 846 10 3 2003 9:18 1177-04753 RT I 375.0000
## 847 10 3 2003 14:43 1207-72681 RT I 398.0000
## 848 10 4 2003 11:04 1177-04754 RT I 385.0000
## 849 10 4 2003 11:58 1142-19283 SS I M 156.0000
## 850 10 4 2003 12:46 1204-45883 CH I M 230.0000
## 851 10 5 2003 10:58 1204-45884 CH I M 220.0000
## 852 10 6 2003 14:12 1142-19284 SS I M 163.0000
## 853 10 7 2003 10:46 1807-53139 RT I 376.0000
## 854 10 7 2003 11:17 1177-04755 RT I 360.0000
## 855 10 7 2003 11:42 1177-04756 RT A 372.0000
## 856 10 7 2003 11:58 1207-72682 RT I 400.0000
## 857 10 7 2003 12:10 2003-99370 SS A F 194.0000
## 858 10 7 2003 12:49 1807-53140 RT I 370.0000
## 859 10 8 2003 10:31 1142-19285 SS I M 160.0000
## 860 10 8 2003 11:08 1207-72683 RT I 403.0000
## 861 10 8 2003 12:28 1177-04757 RT I 375.0000
## 862 10 8 2003 14:48 1177-04758 RT I 373.0000
## 863 10 10 2003 11:43 1177-04759 RT I 385.0000
## 864 10 12 2003 10:10 2003-99371 SS I F 143.0000
## 865 10 12 2003 11:30 1142-19286 SS I M 162.0000
## 866 10 12 2003 12:10 1207-72684 RT I 392.0000
## 867 10 12 2003 13:15 1807-53141 RT I 372.0000
## 868 10 13 2003 12:00 1177-04760 RT I 375.0000
## 869 10 13 2003 1207-72685 RT I 415.0000
## 870 10 14 2003 10:53 1142-19287 SS A M 161.0000
## 871 10 14 2003 12:24 1177-04761 RT A 380.0000
## 872 10 18 2003 12:45 788-36611 RT A 411.0000
## 873 10 21 2003 9:08 1142-19288 SS A M 161.0000
## 874 10 21 2003 10:19 1142-19289 SS I M 165.0000
## 875 10 21 2003 11:35 1207-72686 RT I 393.0000
## 876 10 21 2003 13:02 1177-04762 RT I 370.0000
## 877 10 22 2003 12:19 1204-45885 CH A M 230.0000
## 878 10 25 2003 11:07 1177-04763 RT I 365.0000
## 879 10 25 2003 11:53 1177-04764 RT I 371.0000
## 880 10 25 2003 12:47 1207-72687 RT I 400.0000
## 881 10 25 2003 12:55 1177-04765 RT A 382.0000
## 882 10 25 2003 13:27 1807-53142 RT A 371.0000
## 883 10 25 2003 13:40 1177-04766 RT A 370.0000
## 884 10 26 2003 11:35 2003-99372 SS A F 194.0000
## 885 10 26 2003 12:15 1177-04767 RT A 347.0000
## 886 10 30 2003 10:40 1177-04768 RT I 363.0000
## 887 10 30 2003 13:13 1213-58909 SS I F 195.0000
## 888 10 30 2003 13:35 1177-04769 RT A 392.0000
## 889 10 31 2003 11:20 1204-45886 CH I M 220.0000
## 890 11 6 2003 10:06 2003-99373 SS I F 193.0000
## 891 11 6 2003 13:02 1177-04770 RT I 365.0000
## 892 11 7 2003 12:30 1177-04771 RT A 387.0000
## 893 11 7 2003 13:45 1177-04772 RT I 400.0000
## 894 11 8 2003 13:01 1801-53143 RT I 362.0000
## 895 11 9 2003 12:00 803-05944 SS I F 198.0000
## 896 11 9 2003 13:31 2003-99374 SS I F 190.0000
## 897 11 11 2003 10:15 2003-99375 SS I F 197.0000
## 898 11 13 2003 14:00 1177-04773 RT A 370.0000
## 899 11 14 2003 13:35 1213-58910 SS I F 200.0000
## 900 11 17 2003 10:19 1177-04774 RT A 360.0000
## 901 11 18 2003 13:29 1177-04775 RT A 366.0000
## 902 11 18 2003 13:45 1177-04776 RT A 402.0000
## 903 11 18 2003 14:07 1207-53144 RT I 366.0000
## 904 11 18 2003 14:44 1177-04777 RT I 380.0000
## 905 11 19 2003 10:18 803-05985 SS I F 190.0000
## 906 11 19 2003 12:02 1807-53145 RT I 360.0000
## 907 11 20 2003 9:56 1177-04778 RT I 369.0000
## 908 11 20 2003 13:30 1207-53145 RT A 199.0000
## Weight Culmen Hallux Tail Sex_M Sex_F Age_A Age_I
## 1 920.0000 25.70000 30.10000 219 0 0 0 1
## 2 930.0000 26.81197 32.23097 221 0 0 0 1
## 3 990.0000 26.70000 31.30000 235 0 0 0 1
## 4 470.0000 18.70000 23.50000 220 0 1 0 1
## 5 170.0000 12.50000 14.30000 157 0 1 0 1
## 6 1090.0000 28.50000 32.20000 230 0 0 0 1
## 7 960.0000 25.30000 30.10000 212 0 0 0 1
## 8 855.0000 27.20000 30.00000 243 0 0 1 0
## 9 1210.0000 29.30000 31.30000 210 0 0 1 0
## 10 1120.0000 26.00000 30.20000 238 0 0 0 1
## 11 1010.0000 26.30000 30.80000 222 0 0 0 1
## 12 1010.0000 25.40000 29.70000 217 0 0 0 1
## 13 1120.0000 28.90000 30.90000 213 0 0 1 0
## 14 1161.4132 28.20000 30.60000 238 0 0 1 0
## 15 1170.0000 26.50000 34.00000 243 0 0 0 1
## 16 1390.0000 30.50000 34.00000 232 0 0 1 0
## 17 1150.0000 27.10000 31.00000 238 0 0 0 1
## 18 950.0000 28.90000 28.90000 202 0 0 1 0
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## 821 295.0000 16.10000 19.40000 183 1 0 0 1
## 822 160.0000 12.60000 14.50000 158 0 1 0 1
## 823 1010.0000 26.80000 31.10000 230 0 0 0 1
## 824 990.0000 26.00000 29.60000 225 0 0 0 1
## 825 150.0000 11.40000 14.30000 141 1 0 0 1
## 826 300.0000 16.00000 20.10000 183 1 0 0 1
## 827 945.0000 24.50000 31.30000 224 0 0 0 1
## 828 188.0000 11.70000 14.90000 162 0 1 0 1
## 829 95.0000 10.60000 11.50000 131 1 0 0 1
## 830 330.0000 15.70000 19.40000 188 1 0 1 0
## 831 95.0000 9.90000 11.20000 132 1 0 0 1
## 832 970.0000 26.40000 30.50000 215 0 0 0 1
## 833 1240.0000 28.90000 32.80000 237 0 0 0 1
## 834 105.0000 10.00000 11.50000 133 1 0 0 1
## 835 165.0000 11.50000 14.90000 156 0 1 0 1
## 836 170.0000 12.10000 15.10000 163 0 1 0 1
## 837 100.0000 10.20000 11.90000 134 1 0 0 1
## 838 1290.0000 28.40000 33.90000 253 0 0 0 1
## 839 470.0000 19.50000 28.40000 211 0 1 1 0
## 840 175.0000 11.70000 14.20000 160 0 1 1 0
## 841 195.0000 13.60000 14.00000 158 0 1 1 0
## 842 335.0000 16.30000 21.30000 187 1 0 1 0
## 843 1150.0000 26.10000 28.20000 196 0 0 1 0
## 844 960.0000 25.40000 30.40000 217 0 0 0 1
## 845 1130.0000 28.30000 29.40000 227 0 0 0 1
## 846 925.0000 25.40000 28.60000 220 0 0 0 1
## 847 1205.0000 27.60000 33.40000 227 0 0 0 1
## 848 1040.0000 27.20000 31.50000 238 0 0 0 1
## 849 100.0000 9.90000 11.20000 122 1 0 0 1
## 850 335.0000 16.30000 19.70000 201 1 0 0 1
## 851 335.0000 16.20000 20.00000 185 1 0 0 1
## 852 105.0000 10.30000 11.70000 137 1 0 0 1
## 853 860.0000 25.60000 30.00000 220 0 0 0 1
## 854 935.0000 25.80000 30.00000 212 0 0 0 1
## 855 1010.0000 24.30000 29.00000 197 0 0 1 0
## 856 1285.0000 29.70000 33.50000 230 0 0 0 1
## 857 210.0000 13.00000 14.50000 147 0 1 1 0
## 858 830.0000 23.60000 27.80000 233 0 0 0 1
## 859 95.0000 10.20000 11.20000 135 1 0 0 1
## 860 1350.0000 28.00000 32.80000 140 0 0 0 1
## 861 1010.0000 25.00000 30.80000 218 0 0 0 1
## 862 960.0000 27.70000 32.50000 222 0 0 0 1
## 863 1370.0000 26.40000 29.20000 233 0 0 0 1
## 864 170.0000 12.80000 13.90000 159 0 1 0 1
## 865 100.0000 8.70000 11.40000 136 1 0 0 1
## 866 1250.0000 28.60000 32.90000 222 0 0 0 1
## 867 915.0000 24.70000 28.20000 203 0 0 0 1
## 868 850.0000 25.00000 28.00000 218 0 0 0 1
## 869 1285.0000 29.40000 34.00000 242 0 0 0 1
## 870 95.0000 9.80000 11.70000 129 1 0 1 0
## 871 1005.0000 27.00000 31.60000 205 0 0 1 0
## 872 1220.0000 28.10000 32.70000 236 0 0 1 0
## 873 95.0000 9.60000 12.40000 121 1 0 1 0
## 874 100.0000 9.80000 12.00000 134 1 0 0 1
## 875 1265.0000 28.30000 32.70000 233 0 0 0 1
## 876 1020.0000 24.60000 30.00000 211 0 0 0 1
## 877 360.0000 16.00000 22.10000 186 1 0 1 0
## 878 895.0000 24.50000 28.90000 217 0 0 0 1
## 879 1160.0000 25.70000 28.40000 218 0 0 0 1
## 880 1585.0000 29.00000 33.80000 241 0 0 0 1
## 881 1140.0000 24.90000 31.60000 218 0 0 1 0
## 882 1115.0000 25.30000 29.20000 208 0 0 1 0
## 883 1145.0000 25.40000 30.20000 212 0 0 1 0
## 884 185.0000 12.80000 14.80000 152 0 1 1 0
## 885 990.0000 25.30000 29.80000 203 0 0 1 0
## 886 945.0000 24.50000 32.23097 218 0 0 0 1
## 887 165.0000 11.70000 14.50000 153 0 1 0 1
## 888 1030.0000 26.30000 28.10000 196 0 0 1 0
## 889 320.0000 15.50000 19.50000 184 1 0 0 1
## 890 105.0000 13.00000 15.60000 156 0 1 0 1
## 891 990.0000 26.40000 30.00000 217 0 0 0 1
## 892 1065.0000 28.00000 32.70000 212 0 0 1 0
## 893 1050.0000 26.10000 29.70000 237 0 0 0 1
## 894 840.0000 23.20000 26.10000 206 0 0 0 1
## 895 190.0000 12.20000 15.80000 158 0 1 0 1
## 896 200.0000 12.70000 15.00000 157 0 1 0 1
## 897 185.0000 12.80000 15.60000 157 0 1 0 1
## 898 1000.0000 26.90000 31.40000 201 0 0 1 0
## 899 185.0000 12.80000 15.20000 158 0 1 0 1
## 900 1325.0000 26.20000 30.60000 224 0 0 1 0
## 901 945.0000 25.30000 27.20000 199 0 0 1 0
## 902 1350.0000 28.70000 31.00000 219 0 0 1 0
## 903 805.0000 23.50000 25.70000 217 0 0 0 1
## 904 1525.0000 26.00000 27.60000 224 0 0 0 1
## 905 175.0000 12.70000 15.40000 150 0 1 0 1
## 906 790.0000 21.90000 27.60000 211 0 0 0 1
## 907 860.0000 25.20000 28.00000 207 0 0 0 1
## 908 1290.0000 28.70000 32.10000 222 0 0 1 0Now, we create a subset of the dataset containing only numerical variables, including categorical variables converted into numerical format using dummy encoding.
hawks_selected <- hawks_limpio2 %>%
select(Wing, Weight, Culmen, Hallux, Sex_M, Sex_F, Age_A, Age_I)
print(hawks_selected)## Wing Weight Culmen Hallux Sex_M Sex_F Age_A Age_I
## 1 385.0000 920.0000 25.70000 30.10000 0 0 0 1
## 2 376.0000 930.0000 26.81197 32.23097 0 0 0 1
## 3 381.0000 990.0000 26.70000 31.30000 0 0 0 1
## 4 265.0000 470.0000 18.70000 23.50000 0 1 0 1
## 5 205.0000 170.0000 12.50000 14.30000 0 1 0 1
## 6 412.0000 1090.0000 28.50000 32.20000 0 0 0 1
## 7 370.0000 960.0000 25.30000 30.10000 0 0 0 1
## 8 375.0000 855.0000 27.20000 30.00000 0 0 1 0
## 9 412.0000 1210.0000 29.30000 31.30000 0 0 1 0
## 10 405.0000 1120.0000 26.00000 30.20000 0 0 0 1
## 11 393.0000 1010.0000 26.30000 30.80000 0 0 0 1
## 12 371.0000 1010.0000 25.40000 29.70000 0 0 0 1
## 13 390.0000 1120.0000 28.90000 30.90000 0 0 1 0
## 14 393.0000 1161.4132 28.20000 30.60000 0 0 1 0
## 15 416.0000 1170.0000 26.50000 34.00000 0 0 0 1
## 16 436.0000 1390.0000 30.50000 34.00000 0 0 1 0
## 17 418.0000 1150.0000 27.10000 31.00000 0 0 0 1
## 18 381.0000 950.0000 28.90000 28.90000 0 0 1 0
## 19 378.0000 910.0000 25.70000 28.20000 0 0 0 1
## 20 396.0000 1010.0000 24.00000 26.90000 0 0 0 1
## 21 399.0000 1070.0000 26.40000 31.20000 0 0 0 1
## 22 416.0000 1190.0000 28.80000 31.60000 0 0 0 1
## 23 415.0000 101.0000 24.90000 30.70000 0 0 0 1
## 24 392.0000 1330.0000 27.00000 30.30000 0 0 1 0
## 25 380.0000 990.0000 26.00000 30.00000 0 0 0 1
## 26 173.0000 100.0000 11.41111 14.24101 1 0 0 1
## 27 399.0000 1100.0000 26.20000 32.50000 0 0 0 1
## 28 401.0000 1190.0000 28.60000 31.60000 0 0 1 0
## 29 205.0000 180.0000 11.70000 15.00000 0 1 0 1
## 30 427.0000 1490.0000 30.10000 32.40000 0 0 0 1
## 31 395.0000 1040.0000 27.10000 31.40000 0 0 1 0
## 32 362.0000 820.0000 24.90000 27.90000 0 0 0 1
## 33 396.0000 1030.0000 26.00000 29.70000 0 0 1 0
## 34 391.0000 1300.0000 25.50000 32.40000 0 0 1 0
## 35 413.0000 1500.0000 26.50000 31.30000 0 0 1 0
## 36 371.0000 1080.0000 25.30000 27.20000 0 0 1 0
## 37 385.0000 1320.0000 27.30000 30.10000 0 0 1 0
## 38 378.0000 1490.0000 25.40000 31.30000 0 0 1 0
## 39 416.0000 1500.0000 29.10000 30.80000 0 0 1 0
## 40 193.0000 100.0000 9.30000 14.24101 1 0 0 1
## 41 171.0000 88.0000 9.70000 11.50000 1 0 0 1
## 42 233.0000 324.0000 16.00000 19.30000 0 0 0 1
## 43 384.0000 1060.0000 26.10000 31.20000 0 0 0 1
## 44 382.0000 1140.0000 25.10000 29.40000 0 0 0 1
## 45 390.0000 1030.0000 27.60000 30.30000 0 0 0 1
## 46 390.0000 1000.0000 25.10000 28.30000 0 0 0 1
## 47 393.0000 1050.0000 28.70000 29.80000 0 0 0 1
## 48 378.0000 1040.0000 26.20000 31.20000 0 0 0 1
## 49 398.0000 1110.0000 26.50000 30.90000 0 0 0 1
## 50 412.0000 1300.0000 27.90000 31.55000 0 0 0 1
## 51 400.0000 980.0000 25.70000 29.30000 0 0 0 1
## 52 422.0000 1120.0000 26.40000 28.30000 0 0 0 1
## 53 202.0000 134.0000 12.40000 13.70000 0 1 0 1
## 54 394.0000 1270.0000 27.80000 31.60000 0 0 0 1
## 55 369.0000 880.0000 25.00000 26.50000 0 0 0 1
## 56 252.0000 340.0000 16.00000 20.80000 0 1 0 1
## 57 240.0000 340.0000 16.10000 19.30000 1 0 1 0
## 58 410.0000 1255.0000 29.70000 31.40000 0 0 0 1
## 59 241.0000 1320.0000 28.60000 36.40000 0 0 0 1
## 60 408.0000 1320.0000 30.00000 33.40000 0 0 0 1
## 61 37.2000 1180.0000 20.20000 26.65000 0 0 0 1
## 62 380.0000 760.0000 24.50000 26.10000 0 0 0 1
## 63 396.0000 1250.0000 26.60000 32.50000 0 0 0 1
## 64 326.0000 1076.4590 25.20000 27.70000 0 0 0 1
## 65 158.0000 100.0000 10.80000 10.50000 1 0 0 1
## 66 416.0000 1300.0000 27.30000 32.70000 0 0 0 1
## 67 271.0000 475.0000 18.20000 24.75000 0 1 0 1
## 68 176.0000 100.0000 9.80000 11.10000 1 0 1 0
## 69 194.0000 150.3824 11.40000 14.20000 0 1 1 0
## 70 390.0000 1080.0000 30.20000 29.10000 0 0 1 0
## 71 391.0000 1130.0000 26.40000 29.40000 0 0 1 0
## 72 387.0000 1160.0000 26.80000 31.00000 0 0 1 0
## 73 420.0000 1345.0000 29.50000 34.30000 0 0 0 1
## 74 435.0000 1385.0000 32.60000 30.60000 0 0 1 0
## 75 400.0000 1210.0000 25.50000 28.60000 0 0 1 0
## 76 398.0000 1455.0000 28.00000 31.50000 0 0 0 1
## 77 395.0000 1180.0000 25.00000 28.90000 0 0 0 1
## 78 410.0000 1500.0000 27.10000 33.20000 0 0 0 1
## 79 369.0000 1025.0000 27.10000 31.50000 0 0 0 1
## 80 372.0000 930.0000 26.10000 31.10000 0 0 0 1
## 81 415.0000 1360.0000 28.60000 33.50000 0 0 0 1
## 82 412.0000 1255.0000 27.70000 32.60000 0 0 0 1
## 83 205.0000 194.0000 12.60000 14.40000 0 1 0 1
## 84 204.0000 159.0000 12.50000 14.80000 0 1 0 1
## 85 170.0000 90.0000 9.50000 11.30000 1 0 0 1
## 86 233.0000 340.0000 17.80000 19.40000 1 0 1 0
## 87 375.0000 1065.0000 25.90000 30.00000 0 0 0 1
## 88 385.0000 1125.0000 19.60000 31.40000 0 0 0 1
## 89 422.0000 1340.0000 28.70000 32.00000 0 0 0 1
## 90 391.0000 1050.0000 26.60000 32.20000 0 0 0 1
## 91 410.0000 1210.0000 27.50000 32.23097 0 0 0 1
## 92 385.0000 980.0000 26.80000 27.80000 0 0 0 1
## 93 381.0000 1000.0000 25.50000 29.80000 0 0 0 1
## 94 416.0000 1390.0000 28.10000 31.30000 0 0 1 0
## 95 406.0000 1275.0000 29.00000 33.70000 0 0 0 1
## 96 418.0000 1180.0000 30.10000 32.23097 0 0 0 1
## 97 412.0000 1210.0000 29.30000 33.80000 0 0 0 1
## 98 208.0000 168.0000 12.70000 14.80000 0 1 1 0
## 99 208.0000 146.0000 11.80000 14.90000 0 1 0 1
## 100 175.0000 108.0000 10.00000 11.50000 1 0 0 1
## 101 166.0000 94.0000 9.50000 11.30000 1 0 0 1
## 102 405.0000 1085.0000 27.70000 29.90000 0 0 0 1
## 103 198.0000 188.0000 12.20000 16.94493 0 1 1 0
## 104 200.0000 154.0000 12.40000 14.40000 0 1 0 1
## 105 380.0000 810.0000 25.90000 28.70000 0 0 0 1
## 106 381.0000 905.0000 27.90000 29.10000 0 0 0 1
## 107 169.0000 94.0000 9.00000 10.20000 1 0 0 1
## 108 260.0000 420.0000 19.60000 23.90000 0 1 0 1
## 109 428.0000 1240.0000 29.10000 34.70000 0 0 0 1
## 110 400.0000 990.0000 26.90000 31.40000 0 0 0 1
## 111 265.0000 365.0000 16.80000 22.50000 0 1 0 1
## 112 177.0000 91.0000 10.20000 11.30000 1 0 0 1
## 113 381.0000 1010.0000 25.80000 31.70000 0 0 0 1
## 114 403.0000 980.0000 26.30000 29.70000 0 0 0 1
## 115 382.0000 860.0000 26.50000 29.00000 0 0 0 1
## 116 382.0000 970.0000 25.80000 29.00000 0 0 0 1
## 117 399.0000 980.0000 27.50000 29.90000 0 0 0 1
## 118 380.0000 985.0000 23.90000 29.00000 0 0 0 1
## 119 375.0000 990.0000 25.60000 30.60000 0 0 0 1
## 120 420.0000 1210.0000 27.80000 32.60000 0 0 0 1
## 121 170.0000 89.0000 8.60000 11.00000 1 0 0 1
## 122 177.0000 97.0000 10.00000 11.30000 1 0 1 0
## 123 375.0000 990.0000 28.00000 29.50000 0 0 0 1
## 124 395.0000 1170.0000 28.10000 31.70000 0 0 0 1
## 125 170.0000 93.0000 10.10000 11.20000 1 0 1 0
## 126 406.0000 1350.0000 30.50000 32.00000 0 0 0 1
## 127 414.0000 1370.0000 29.30000 33.00000 0 0 0 1
## 128 173.0000 103.0000 9.70000 19.40000 1 0 0 1
## 129 209.0000 151.0000 12.20000 13.90000 0 1 0 1
## 130 177.0000 101.0000 10.30000 12.10000 1 0 0 1
## 131 388.0000 985.0000 26.90000 29.80000 0 0 0 1
## 132 277.0000 940.0000 26.50000 30.40000 0 0 0 1
## 133 423.0000 1310.0000 27.40000 34.10000 0 0 0 1
## 134 365.0000 1035.0000 26.10000 30.80000 0 0 0 1
## 135 383.0000 965.0000 26.10000 31.80000 0 0 0 1
## 136 391.0000 1125.0000 25.40000 30.90000 0 0 0 1
## 137 389.0000 975.0000 26.40000 30.30000 0 0 0 1
## 138 392.0000 1140.0000 26.20000 29.80000 0 0 0 1
## 139 375.0000 950.0000 25.30000 29.90000 0 0 0 1
## 140 410.0000 1210.0000 28.10000 28.90000 0 0 0 1
## 141 179.0000 95.0000 10.80000 11.60000 1 0 0 1
## 142 172.0000 89.0000 9.40000 10.80000 1 0 0 1
## 143 202.0000 195.0000 12.40000 14.10000 0 1 1 0
## 144 174.0000 93.0000 9.50000 11.00000 1 0 0 1
## 145 422.0000 1205.0000 28.80000 31.30000 0 0 0 1
## 146 385.0000 1045.0000 27.60000 27.50000 0 0 0 1
## 147 363.0000 1090.0000 26.60000 28.80000 0 0 0 1
## 148 450.0000 1190.0000 30.30000 32.80000 0 0 0 1
## 149 380.0000 960.0000 25.60000 30.10000 0 0 0 1
## 150 385.0000 955.0000 26.30000 30.10000 0 0 0 1
## 151 385.0000 1110.0000 24.70000 30.20000 0 0 0 1
## 152 171.0000 100.0000 19.10000 11.50000 1 0 0 1
## 153 380.0000 900.0000 24.00000 26.50000 0 0 0 1
## 154 384.0000 1075.0000 26.50000 30.70000 0 0 0 1
## 155 373.0000 980.0000 27.90000 32.10000 0 0 0 1
## 156 381.0000 940.0000 27.80000 34.20000 0 0 0 1
## 157 363.0000 1070.0000 25.60000 30.40000 0 0 0 1
## 158 409.0000 1120.0000 29.40000 31.60000 0 0 0 1
## 159 390.0000 1060.0000 27.60000 29.00000 0 0 1 0
## 160 204.0000 168.0000 12.10000 14.30000 0 1 0 1
## 161 197.0000 211.0000 11.50000 13.90000 0 1 0 1
## 162 420.0000 1125.0000 27.20000 27.40000 0 0 0 1
## 163 381.0000 1100.0000 27.00000 28.20000 0 0 0 1
## 164 408.0000 1360.0000 30.00000 33.90000 0 0 0 1
## 165 388.0000 995.0000 26.70000 30.70000 0 0 0 1
## 166 398.0000 1095.0000 21.10000 31.40000 0 0 1 0
## 167 209.0000 196.0000 12.10000 14.60000 0 1 0 1
## 168 209.0000 176.0000 11.70000 15.10000 0 1 0 1
## 169 394.0000 1075.0000 25.50000 29.70000 0 0 1 0
## 170 204.0000 180.0000 12.30000 15.20000 0 1 1 0
## 171 204.0000 164.0000 12.30000 14.30000 0 1 0 1
## 172 209.0000 158.0000 12.20000 14.40000 0 1 0 1
## 173 394.0000 1140.0000 26.80000 29.20000 0 0 0 1
## 174 416.0000 1240.0000 27.90000 31.80000 0 0 0 1
## 175 445.0000 1465.0000 29.70000 34.60000 0 0 0 1
## 176 209.0000 169.0000 12.10000 14.50000 0 1 0 1
## 177 388.0000 1105.0000 26.70000 28.90000 0 0 0 1
## 178 397.0000 1010.0000 27.10000 31.40000 0 0 0 1
## 179 384.0000 1075.0000 26.30000 30.50000 0 0 0 1
## 180 379.0000 1060.0000 27.90000 30.90000 0 0 0 1
## 181 393.0000 1015.0000 27.60000 31.10000 0 0 0 1
## 182 386.0000 1100.0000 26.00000 30.20000 0 0 0 1
## 183 397.0000 1010.0000 25.00000 30.60000 0 0 0 1
## 184 382.0000 1000.0000 26.30000 30.10000 0 0 0 1
## 185 386.0000 980.0000 25.40000 30.20000 0 0 0 1
## 186 417.0000 1240.0000 28.70000 32.40000 0 0 0 1
## 187 403.0000 1360.0000 27.90000 33.10000 0 0 0 1
## 188 239.0000 183.0000 17.30000 19.20000 1 0 1 0
## 189 401.0000 1405.0000 29.10000 32.23097 0 0 0 1
## 190 377.0000 1055.0000 27.00000 29.10000 0 0 1 0
## 191 432.0000 1670.0000 27.10000 32.90000 0 0 1 0
## 192 390.0000 1250.0000 26.20000 30.50000 0 0 0 1
## 193 381.0000 1030.0000 25.30000 29.90000 0 0 0 1
## 194 403.0000 1040.0000 26.81197 29.90000 0 0 0 1
## 195 213.0000 190.0000 12.20000 15.50000 0 1 0 1
## 196 172.0000 105.0000 10.00000 10.80000 1 0 0 1
## 197 390.0000 1090.0000 26.20000 28.80000 0 0 0 1
## 198 204.0000 190.0000 11.80000 13.90000 0 1 0 1
## 199 386.0000 1050.0000 28.40000 29.40000 0 0 1 0
## 200 402.0000 1110.0000 26.10000 30.00000 0 0 0 1
## 201 201.0000 206.0000 12.10000 13.50000 0 1 0 1
## 202 202.0000 195.0000 12.10000 14.80000 0 1 0 1
## 203 374.0000 1010.0000 24.90000 30.10000 0 0 1 0
## 204 358.0000 880.0000 24.20000 28.70000 0 0 0 1
## 205 370.0000 1060.0000 24.30000 29.80000 0 0 0 1
## 206 390.0000 920.0000 25.70000 30.00000 0 0 0 1
## 207 398.0000 1195.0000 26.20000 29.80000 0 0 0 1
## 208 360.0000 890.0000 26.00000 28.40000 0 0 0 1
## 209 355.0000 900.0000 25.30000 29.00000 0 0 0 1
## 210 375.0000 1110.0000 22.20000 31.50000 0 0 1 0
## 211 200.0000 160.0000 10.20000 13.20000 0 1 0 1
## 212 179.0000 105.0000 10.10000 11.30000 1 0 0 1
## 213 175.0000 99.0000 9.60000 12.70000 1 0 0 1
## 214 203.0000 165.0000 12.00000 14.40000 0 1 0 1
## 215 205.0000 100.0000 12.00000 12.50000 0 1 0 1
## 216 213.0000 125.0000 11.50000 14.40000 0 1 0 1
## 217 409.0000 1100.0000 29.00000 32.60000 0 0 0 1
## 218 202.0000 147.0957 11.41111 14.24101 0 1 0 1
## 219 195.0000 155.0000 11.90000 14.60000 0 1 0 1
## 220 415.0000 1285.0000 29.50000 31.80000 0 0 0 1
## 221 236.0000 390.0000 15.10000 20.40000 1 0 1 0
## 222 363.0000 920.0000 26.80000 30.20000 0 0 0 1
## 223 381.0000 1025.0000 25.40000 30.80000 0 0 0 1
## 224 350.0000 940.0000 26.00000 29.10000 0 0 1 0
## 225 398.0000 1240.0000 28.50000 30.80000 0 0 0 1
## 226 412.0000 1160.0000 27.80000 33.00000 0 0 0 1
## 227 203.0000 150.0000 11.50000 13.90000 0 1 0 1
## 228 201.0000 130.0000 11.70000 14.40000 0 1 0 1
## 229 411.0000 1240.0000 26.80000 32.70000 0 0 0 1
## 230 373.0000 930.0000 24.40000 27.40000 0 0 0 1
## 231 178.0000 90.0000 10.90000 12.10000 1 0 0 1
## 232 415.0000 1240.0000 25.60000 31.20000 0 0 0 1
## 233 383.0000 1030.0000 25.20000 29.80000 0 0 0 1
## 234 223.0000 550.0000 18.80000 21.30000 1 0 0 1
## 235 390.0000 1250.0000 26.50000 32.00000 0 0 0 1
## 236 390.0000 999.0000 25.30000 29.80000 0 0 0 1
## 237 365.0000 1120.0000 26.50000 30.80000 0 0 1 0
## 238 345.0000 1000.0000 26.40000 30.10000 0 0 1 0
## 239 273.0000 530.0000 19.20000 24.70000 0 1 0 1
## 240 400.0000 1040.0000 27.70000 32.10000 0 0 0 1
## 241 380.0000 1150.0000 27.80000 31.10000 0 0 0 1
## 242 330.0000 1000.0000 25.90000 30.20000 0 0 0 1
## 243 410.0000 1360.0000 33.30000 28.60000 0 0 0 1
## 244 313.0000 930.0000 25.70000 28.90000 0 0 0 1
## 245 384.0000 980.0000 25.80000 30.40000 0 0 0 1
## 246 409.0000 1260.0000 27.70000 31.80000 0 0 0 1
## 247 390.0000 900.0000 27.50000 28.60000 0 0 0 1
## 248 411.0000 1300.0000 25.90000 31.90000 0 0 0 1
## 249 259.0000 470.0000 16.60000 23.40000 0 1 0 1
## 250 380.0000 1040.0000 26.40000 30.90000 0 0 1 0
## 251 370.0000 950.0000 27.30000 30.50000 0 0 0 1
## 252 415.0000 1320.0000 29.40000 33.90000 0 0 0 1
## 253 215.0000 180.0000 14.10000 12.70000 0 1 0 1
## 254 410.0000 1280.0000 27.90000 32.70000 0 0 0 1
## 255 412.0000 1310.0000 26.10000 31.10000 0 0 0 1
## 256 384.0000 910.0000 26.40000 28.40000 0 0 1 0
## 257 404.0000 1220.0000 28.60000 30.40000 0 0 0 1
## 258 375.0000 920.0000 23.80000 28.80000 0 0 0 1
## 259 410.0000 1135.0000 26.40000 32.40000 0 0 0 1
## 260 384.0000 940.0000 26.20000 29.80000 0 0 0 1
## 261 385.0000 920.0000 25.00000 32.20000 0 0 0 1
## 262 398.0000 1280.0000 28.00000 32.40000 0 0 0 1
## 263 242.4839 480.0000 17.70000 32.10000 0 0 1 0
## 264 425.0000 1220.0000 27.30000 33.00000 0 0 0 1
## 265 401.0000 1000.0000 26.70000 28.00000 0 0 0 1
## 266 387.0000 1120.0000 26.80000 50.20000 0 0 0 1
## 267 376.0000 925.0000 26.00000 30.80000 0 0 0 1
## 268 171.0000 90.0000 9.90000 11.90000 1 0 1 0
## 269 420.0000 1280.0000 27.50000 31.80000 0 0 1 0
## 270 385.0000 985.0000 27.50000 30.80000 0 0 0 1
## 271 405.0000 1350.0000 28.30000 32.60000 0 0 0 1
## 272 350.0000 730.0000 24.60000 25.70000 0 0 0 1
## 273 388.0000 890.0000 27.80000 31.20000 0 0 0 1
## 274 398.0000 1020.0000 26.50000 31.10000 0 0 0 1
## 275 410.0000 1000.0000 27.10000 30.60000 0 0 1 0
## 276 202.0000 150.0000 11.70000 14.10000 0 1 0 1
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## 646 164.0000 105.0000 10.20000 11.20000 1 0 0 1
## 647 385.0000 1085.0000 27.50000 30.80000 0 0 1 0
## 648 369.0000 970.0000 26.10000 30.40000 0 0 0 1
## 649 378.0000 1030.0000 28.50000 31.90000 0 0 0 1
## 650 373.0000 1015.0000 25.50000 29.60000 0 0 0 1
## 651 419.0000 1030.0000 29.20000 31.50000 0 0 1 0
## 652 414.0000 1215.0000 26.40000 29.20000 0 0 0 1
## 653 203.0000 185.0000 13.50000 14.20000 0 1 1 0
## 654 162.0000 95.0000 10.20000 11.00000 1 0 1 0
## 655 165.0000 95.0000 10.00000 11.00000 1 0 0 1
## 656 161.0000 95.0000 9.70000 11.00000 1 0 1 0
## 657 161.0000 110.0000 10.10000 11.80000 1 0 0 1
## 658 404.0000 1170.0000 28.40000 32.80000 0 0 0 1
## 659 165.0000 105.0000 10.40000 11.20000 1 0 0 1
## 660 199.0000 175.0000 12.80000 14.50000 0 1 1 0
## 661 171.0000 95.0000 10.90000 11.70000 1 0 0 1
## 662 213.0000 190.0000 13.70000 15.20000 0 1 1 0
## 663 169.0000 105.0000 10.20000 11.80000 1 0 1 0
## 664 379.0000 1435.0000 27.40000 32.70000 0 0 0 1
## 665 407.0000 1235.0000 30.10000 35.80000 0 0 0 1
## 666 376.0000 1055.0000 29.50000 32.20000 0 0 0 1
## 667 380.0000 1105.0000 22.00000 30.80000 0 0 0 1
## 668 172.0000 120.0000 9.80000 11.80000 1 0 1 0
## 669 408.0000 1390.0000 28.40000 32.70000 0 0 0 1
## 670 167.0000 105.0000 10.30000 10.80000 1 0 1 0
## 671 374.0000 1080.0000 26.50000 31.30000 0 0 1 0
## 672 376.0000 910.0000 26.10000 32.20000 0 0 0 1
## 673 258.0000 490.0000 18.00000 24.20000 0 1 0 1
## 674 370.0000 845.0000 25.00000 27.40000 0 0 0 1
## 675 202.0000 175.0000 13.30000 14.90000 0 1 1 0
## 676 363.0000 865.0000 25.60000 27.30000 0 0 0 1
## 677 200.0000 180.0000 11.90000 13.50000 0 1 1 0
## 678 372.0000 2030.0000 26.20000 30.20000 0 0 0 1
## 679 378.0000 960.0000 24.60000 30.00000 0 0 1 0
## 680 254.0000 515.0000 19.50000 23.80000 0 1 1 0
## 681 361.0000 970.0000 26.30000 30.70000 0 0 0 1
## 682 389.0000 1265.0000 26.60000 30.60000 0 0 1 0
## 683 404.0000 1300.0000 29.40000 32.80000 0 0 1 0
## 684 195.0000 170.0000 12.90000 14.70000 0 1 0 1
## 685 203.0000 191.0000 13.50000 15.50000 0 1 0 1
## 686 253.0000 540.0000 19.10000 22.60000 0 1 1 0
## 687 199.0000 185.0000 12.00000 14.90000 0 1 0 1
## 688 194.0000 165.0000 11.90000 14.40000 0 1 0 1
## 689 196.0000 205.0000 12.20000 14.00000 0 1 1 0
## 690 168.0000 95.0000 10.40000 12.10000 1 0 0 1
## 691 395.0000 1170.0000 25.80000 30.50000 0 0 1 0
## 692 368.0000 1075.0000 27.70000 31.70000 0 0 0 1
## 693 210.0000 200.0000 12.10000 15.30000 0 1 0 1
## 694 401.0000 965.0000 25.80000 29.10000 0 0 0 1
## 695 355.0000 785.0000 22.70000 25.00000 0 0 0 1
## 696 377.0000 1095.0000 25.60000 31.70000 0 0 1 0
## 697 197.0000 160.0000 12.00000 14.70000 0 1 0 1
## 698 171.0000 95.0000 9.10000 11.50000 1 0 0 1
## 699 277.0000 1500.0000 29.70000 32.10000 0 0 1 0
## 700 435.0000 1595.0000 27.40000 34.50000 0 0 1 0
## 701 372.0000 985.0000 25.40000 31.00000 0 0 0 1
## 702 260.0000 565.0000 20.00000 24.20000 0 1 1 0
## 703 390.0000 240.0000 25.20000 29.30000 0 0 0 1
## 704 359.0000 875.0000 26.00000 31.10000 0 0 0 1
## 705 393.0000 1225.0000 29.00000 33.40000 0 0 0 1
## 706 402.0000 1255.0000 30.60000 34.60000 0 0 0 1
## 707 362.0000 950.0000 26.80000 30.70000 0 0 0 1
## 708 227.0000 330.0000 16.00000 18.50000 1 0 0 1
## 709 359.0000 895.0000 27.50000 30.10000 0 0 1 0
## 710 155.0000 100.0000 9.80000 12.00000 1 0 0 1
## 711 261.0000 455.0000 17.10000 26.80000 0 1 0 1
## 712 160.0000 90.0000 10.30000 11.50000 1 0 0 1
## 713 166.0000 105.0000 11.30000 11.40000 1 0 0 1
## 714 362.0000 1305.0000 28.20000 34.30000 0 0 0 1
## 715 375.0000 975.0000 27.20000 31.80000 0 0 0 1
## 716 388.0000 1185.0000 28.90000 34.30000 0 0 0 1
## 717 392.0000 1030.0000 26.10000 30.50000 0 0 0 1
## 718 412.0000 1215.0000 28.70000 34.10000 0 0 0 1
## 719 371.0000 1075.0000 26.90000 32.80000 0 0 0 1
## 720 255.0000 960.0000 19.70000 42.80000 0 1 1 0
## 721 391.0000 795.0000 24.30000 27.60000 0 0 0 1
## 722 190.0000 180.0000 12.20000 14.20000 0 1 0 1
## 723 385.0000 1225.0000 27.80000 32.00000 0 0 0 1
## 724 166.0000 110.0000 10.00000 11.90000 1 0 0 1
## 725 197.0000 165.0000 12.20000 14.90000 0 1 1 0
## 726 370.0000 920.0000 26.30000 32.00000 0 0 0 1
## 727 190.0000 170.0000 12.00000 15.00000 0 1 0 1
## 728 400.0000 1315.0000 29.60000 34.00000 0 0 0 1
## 729 162.0000 100.0000 9.40000 11.10000 1 0 0 1
## 730 194.0000 155.0000 12.50000 14.50000 0 1 0 1
## 731 395.0000 1155.0000 29.90000 34.40000 0 0 0 1
## 732 403.0000 1160.0000 29.00000 32.30000 0 0 0 1
## 733 386.0000 955.0000 27.90000 30.40000 0 0 0 1
## 734 193.0000 190.0000 13.10000 14.90000 0 1 1 0
## 735 203.0000 180.0000 13.80000 14.70000 0 1 1 0
## 736 159.0000 90.0000 10.00000 11.50000 1 0 1 0
## 737 163.0000 100.0000 9.80000 11.70000 1 0 0 1
## 738 191.0000 190.0000 12.40000 14.80000 1 0 1 0
## 739 166.0000 105.0000 10.30000 12.00000 1 0 0 1
## 740 361.0000 1030.0000 27.00000 30.50000 0 0 0 1
## 741 260.0000 565.0000 19.70000 54.50000 0 1 1 0
## 742 234.0000 380.0000 12.40000 21.90000 1 0 1 0
## 743 377.0000 1040.0000 28.10000 30.90000 0 0 0 1
## 744 361.0000 910.0000 24.30000 27.50000 0 0 0 1
## 745 375.0000 1005.0000 26.00000 32.50000 0 0 0 1
## 746 193.0000 180.0000 11.90000 14.30000 0 1 0 1
## 747 196.0000 175.0000 12.40000 15.60000 0 1 0 1
## 748 159.0000 105.0000 9.80000 11.00000 1 0 0 1
## 749 192.0000 190.0000 11.80000 14.20000 0 1 0 1
## 750 401.0000 1250.0000 28.20000 35.30000 0 0 0 1
## 751 198.0000 185.0000 12.60000 15.20000 0 1 0 1
## 752 407.0000 1275.0000 27.50000 33.70000 0 0 0 1
## 753 162.0000 105.0000 9.80000 12.50000 1 0 0 1
## 754 169.0000 640.0000 16.70000 23.60000 0 1 1 0
## 755 168.0000 100.0000 10.50000 10.70000 1 0 0 1
## 756 168.0000 105.0000 10.70000 11.60000 1 0 1 0
## 757 223.0000 390.0000 15.90000 20.60000 1 0 1 0
## 758 375.0000 1030.0000 26.90000 31.30000 0 0 0 1
## 759 406.0000 1290.0000 29.30000 33.30000 0 0 1 0
## 760 386.0000 1020.0000 26.90000 31.60000 0 0 0 1
## 761 160.0000 105.0000 9.90000 11.40000 1 0 1 0
## 762 378.0000 1055.0000 26.50000 29.90000 0 0 0 1
## 763 193.0000 185.0000 12.30000 14.80000 0 1 1 0
## 764 379.0000 1010.0000 25.00000 29.30000 0 0 0 1
## 765 364.0000 1015.0000 24.90000 29.50000 0 0 0 1
## 766 350.0000 1115.0000 29.50000 30.30000 0 0 1 0
## 767 380.0000 1320.0000 26.70000 31.60000 0 0 0 1
## 768 395.0000 1180.0000 30.30000 33.40000 0 0 1 0
## 769 372.0000 1145.0000 25.90000 32.20000 0 0 0 1
## 770 376.0000 995.0000 28.00000 30.20000 0 0 0 1
## 771 367.0000 1045.0000 26.10000 30.50000 0 0 0 1
## 772 230.0000 340.0000 16.00000 19.50000 1 0 0 1
## 773 366.0000 935.0000 25.70000 27.10000 0 0 0 1
## 774 386.0000 1065.0000 26.10000 31.00000 0 0 0 1
## 775 375.0000 1110.0000 27.70000 31.30000 0 0 0 1
## 776 199.0000 190.0000 12.00000 15.20000 0 1 0 1
## 777 405.0000 1255.0000 27.90000 31.80000 0 0 1 0
## 778 371.0000 1015.0000 24.90000 28.40000 0 0 1 0
## 779 193.0000 190.0000 12.20000 15.20000 0 1 0 1
## 780 350.0000 960.0000 26.60000 29.90000 0 0 0 1
## 781 193.0000 200.0000 11.30000 13.50000 0 1 0 1
## 782 368.0000 1090.0000 27.30000 30.40000 0 0 1 0
## 783 185.0000 170.0000 12.00000 14.70000 1 0 0 1
## 784 372.0000 1085.0000 25.40000 29.80000 0 0 0 1
## 785 396.0000 1065.0000 27.70000 30.00000 0 0 0 1
## 786 365.0000 1125.0000 26.90000 29.30000 0 0 0 1
## 787 374.0000 1050.0000 25.50000 30.30000 0 0 0 1
## 788 253.0000 525.0000 19.50000 23.50000 0 1 0 1
## 789 372.0000 980.0000 26.40000 29.00000 0 0 0 1
## 790 376.0000 1180.0000 24.40000 30.70000 0 0 0 1
## 791 166.0000 115.0000 9.90000 11.60000 1 0 0 1
## 792 369.0000 1095.0000 26.60000 28.40000 0 0 0 1
## 793 391.0000 1330.0000 26.80000 30.10000 0 0 1 0
## 794 193.0000 185.0000 12.10000 14.90000 0 1 0 1
## 795 397.0000 1100.0000 22.10000 28.80000 0 0 1 0
## 796 366.0000 1115.0000 27.10000 21.00000 0 0 0 1
## 797 385.0000 1400.0000 30.30000 33.30000 0 0 1 0
## 798 400.0000 1175.0000 27.60000 32.60000 0 0 0 1
## 799 198.0000 185.0000 11.80000 15.10000 0 1 0 1
## 800 365.0000 970.0000 25.90000 31.60000 0 0 1 0
## 801 194.0000 170.0000 11.60000 14.00000 0 1 0 1
## 802 195.0000 175.0000 12.00000 15.60000 0 1 0 1
## 803 200.0000 165.0000 11.50000 14.50000 0 1 0 1
## 804 384.0000 1260.0000 28.60000 32.50000 0 0 0 1
## 805 159.0000 110.0000 9.90000 11.10000 1 0 0 1
## 806 161.0000 100.0000 9.30000 11.50000 1 0 0 1
## 807 191.0000 190.0000 12.30000 14.80000 0 1 0 1
## 808 216.0000 305.0000 16.00000 20.40000 1 0 0 1
## 809 256.0000 510.0000 18.80000 23.30000 0 1 0 1
## 810 161.0000 90.0000 9.50000 11.30000 1 0 0 1
## 811 396.0000 1195.0000 27.00000 23.80000 0 0 1 0
## 812 391.0000 1035.0000 27.90000 33.10000 0 0 0 1
## 813 160.0000 90.0000 8.80000 11.40000 1 0 0 1
## 814 183.0000 160.0000 12.70000 14.60000 1 0 0 1
## 815 156.0000 85.0000 9.70000 11.00000 1 0 0 1
## 816 393.0000 1155.0000 28.30000 30.90000 0 0 0 1
## 817 397.0000 1260.0000 27.80000 32.90000 0 0 0 1
## 818 159.0000 95.0000 8.90000 10.40000 1 0 0 1
## 819 255.0000 440.0000 18.60000 22.80000 0 1 0 1
## 820 197.0000 175.0000 10.00000 14.90000 1 0 0 1
## 821 218.0000 295.0000 16.10000 19.40000 1 0 0 1
## 822 196.0000 160.0000 12.60000 14.50000 0 1 0 1
## 823 384.0000 1010.0000 26.80000 31.10000 0 0 0 1
## 824 385.0000 990.0000 26.00000 29.60000 0 0 0 1
## 825 181.0000 150.0000 11.40000 14.30000 1 0 0 1
## 826 225.0000 300.0000 16.00000 20.10000 1 0 0 1
## 827 379.0000 945.0000 24.50000 31.30000 0 0 0 1
## 828 201.0000 188.0000 11.70000 14.90000 0 1 0 1
## 829 161.0000 95.0000 10.60000 11.50000 1 0 0 1
## 830 230.0000 330.0000 15.70000 19.40000 1 0 1 0
## 831 159.0000 95.0000 9.90000 11.20000 1 0 0 1
## 832 367.0000 970.0000 26.40000 30.50000 0 0 0 1
## 833 396.0000 1240.0000 28.90000 32.80000 0 0 0 1
## 834 157.0000 105.0000 10.00000 11.50000 1 0 0 1
## 835 191.0000 165.0000 11.50000 14.90000 0 1 0 1
## 836 191.0000 170.0000 12.10000 15.10000 0 1 0 1
## 837 168.0000 100.0000 10.20000 11.90000 1 0 0 1
## 838 428.0000 1290.0000 28.40000 33.90000 0 0 0 1
## 839 252.0000 470.0000 19.50000 28.40000 0 1 1 0
## 840 192.0000 175.0000 11.70000 14.20000 0 1 1 0
## 841 195.0000 195.0000 13.60000 14.00000 0 1 1 0
## 842 233.0000 335.0000 16.30000 21.30000 1 0 1 0
## 843 364.0000 1150.0000 26.10000 28.20000 0 0 1 0
## 844 370.0000 960.0000 25.40000 30.40000 0 0 0 1
## 845 400.0000 1130.0000 28.30000 29.40000 0 0 0 1
## 846 375.0000 925.0000 25.40000 28.60000 0 0 0 1
## 847 398.0000 1205.0000 27.60000 33.40000 0 0 0 1
## 848 385.0000 1040.0000 27.20000 31.50000 0 0 0 1
## 849 156.0000 100.0000 9.90000 11.20000 1 0 0 1
## 850 230.0000 335.0000 16.30000 19.70000 1 0 0 1
## 851 220.0000 335.0000 16.20000 20.00000 1 0 0 1
## 852 163.0000 105.0000 10.30000 11.70000 1 0 0 1
## 853 376.0000 860.0000 25.60000 30.00000 0 0 0 1
## 854 360.0000 935.0000 25.80000 30.00000 0 0 0 1
## 855 372.0000 1010.0000 24.30000 29.00000 0 0 1 0
## 856 400.0000 1285.0000 29.70000 33.50000 0 0 0 1
## 857 194.0000 210.0000 13.00000 14.50000 0 1 1 0
## 858 370.0000 830.0000 23.60000 27.80000 0 0 0 1
## 859 160.0000 95.0000 10.20000 11.20000 1 0 0 1
## 860 403.0000 1350.0000 28.00000 32.80000 0 0 0 1
## 861 375.0000 1010.0000 25.00000 30.80000 0 0 0 1
## 862 373.0000 960.0000 27.70000 32.50000 0 0 0 1
## 863 385.0000 1370.0000 26.40000 29.20000 0 0 0 1
## 864 143.0000 170.0000 12.80000 13.90000 0 1 0 1
## 865 162.0000 100.0000 8.70000 11.40000 1 0 0 1
## 866 392.0000 1250.0000 28.60000 32.90000 0 0 0 1
## 867 372.0000 915.0000 24.70000 28.20000 0 0 0 1
## 868 375.0000 850.0000 25.00000 28.00000 0 0 0 1
## 869 415.0000 1285.0000 29.40000 34.00000 0 0 0 1
## 870 161.0000 95.0000 9.80000 11.70000 1 0 1 0
## 871 380.0000 1005.0000 27.00000 31.60000 0 0 1 0
## 872 411.0000 1220.0000 28.10000 32.70000 0 0 1 0
## 873 161.0000 95.0000 9.60000 12.40000 1 0 1 0
## 874 165.0000 100.0000 9.80000 12.00000 1 0 0 1
## 875 393.0000 1265.0000 28.30000 32.70000 0 0 0 1
## 876 370.0000 1020.0000 24.60000 30.00000 0 0 0 1
## 877 230.0000 360.0000 16.00000 22.10000 1 0 1 0
## 878 365.0000 895.0000 24.50000 28.90000 0 0 0 1
## 879 371.0000 1160.0000 25.70000 28.40000 0 0 0 1
## 880 400.0000 1585.0000 29.00000 33.80000 0 0 0 1
## 881 382.0000 1140.0000 24.90000 31.60000 0 0 1 0
## 882 371.0000 1115.0000 25.30000 29.20000 0 0 1 0
## 883 370.0000 1145.0000 25.40000 30.20000 0 0 1 0
## 884 194.0000 185.0000 12.80000 14.80000 0 1 1 0
## 885 347.0000 990.0000 25.30000 29.80000 0 0 1 0
## 886 363.0000 945.0000 24.50000 32.23097 0 0 0 1
## 887 195.0000 165.0000 11.70000 14.50000 0 1 0 1
## 888 392.0000 1030.0000 26.30000 28.10000 0 0 1 0
## 889 220.0000 320.0000 15.50000 19.50000 1 0 0 1
## 890 193.0000 105.0000 13.00000 15.60000 0 1 0 1
## 891 365.0000 990.0000 26.40000 30.00000 0 0 0 1
## 892 387.0000 1065.0000 28.00000 32.70000 0 0 1 0
## 893 400.0000 1050.0000 26.10000 29.70000 0 0 0 1
## 894 362.0000 840.0000 23.20000 26.10000 0 0 0 1
## 895 198.0000 190.0000 12.20000 15.80000 0 1 0 1
## 896 190.0000 200.0000 12.70000 15.00000 0 1 0 1
## 897 197.0000 185.0000 12.80000 15.60000 0 1 0 1
## 898 370.0000 1000.0000 26.90000 31.40000 0 0 1 0
## 899 200.0000 185.0000 12.80000 15.20000 0 1 0 1
## 900 360.0000 1325.0000 26.20000 30.60000 0 0 1 0
## 901 366.0000 945.0000 25.30000 27.20000 0 0 1 0
## 902 402.0000 1350.0000 28.70000 31.00000 0 0 1 0
## 903 366.0000 805.0000 23.50000 25.70000 0 0 0 1
## 904 380.0000 1525.0000 26.00000 27.60000 0 0 0 1
## 905 190.0000 175.0000 12.70000 15.40000 0 1 0 1
## 906 360.0000 790.0000 21.90000 27.60000 0 0 0 1
## 907 369.0000 860.0000 25.20000 28.00000 0 0 0 1
## 908 199.0000 1290.0000 28.70000 32.10000 0 0 1 0As we can observe, the transformation was successfully applied.
Now, we just need to normalize this dataset.
We must consider that dummy numerical variables should not be scaled, so we exclude them from the scaling process.
Reference:
https://stackoverflow.com/questions/74365630/how-to-avoid-scaling-dummy-variables-in-dataframe-in-r
hawks_scaled <- hawks_selected %>%
mutate(
Wing = scale(Wing),
Weight = scale(Weight),
Culmen = scale(Culmen),
Hallux = scale(Hallux) )
print(hawks_scaled)## Wing Weight Culmen Hallux Sex_M Sex_F Age_A Age_I
## 1 0.72901533 0.323037860 0.53643756 0.58802795 0 0 0 1
## 2 0.63453308 0.344646534 0.68899769 0.84440031 0 0 0 1
## 3 0.68702322 0.474298581 0.67363520 0.73239710 0 0 0 1
## 4 -0.53074792 -0.649352494 -0.42394592 -0.20600240 0 1 0 1
## 5 -1.16062955 -1.297612730 -1.27457130 -1.31283258 0 1 0 1
## 6 1.01246206 0.690385326 0.92059096 0.84067397 0 0 0 1
## 7 0.57154492 0.409472558 0.48155851 0.58802795 0 0 0 1
## 8 0.62403506 0.182581475 0.74223402 0.57599719 0 0 1 0
## 9 1.01246206 0.949689421 1.03034907 0.73239710 0 0 1 0
## 10 0.93897587 0.755211350 0.57759685 0.60005871 0 0 0 1
## 11 0.81299955 0.517515930 0.61875615 0.67224329 0 0 0 1
## 12 0.58204295 0.517515930 0.49527827 0.53990490 0 0 0 1
## 13 0.78150546 0.755211350 0.97547001 0.68427405 0 0 1 0
## 14 0.81299955 0.844699836 0.87943166 0.64818176 0 0 1 0
## 15 1.05445417 0.863254723 0.64619568 1.05722770 0 0 0 1
## 16 1.26441471 1.338645562 1.19498624 1.05722770 0 0 1 0
## 17 1.07545022 0.820037374 0.72851426 0.69630482 0 0 0 1
## 18 0.68702322 0.387863883 0.97547001 0.44365880 0 0 1 0
## 19 0.65552914 0.301429185 0.53643756 0.35944346 0 0 0 1
## 20 0.84449363 0.517515930 0.30320157 0.20304354 0 0 0 1
## 21 0.87598771 0.647167977 0.63247591 0.72036634 0 0 0 1
## 22 1.05445417 0.906472072 0.96175025 0.76848939 0 0 0 1
## 23 1.04395614 -1.446712584 0.42667945 0.66021253 0 0 0 1
## 24 0.80250152 1.208993515 0.71479450 0.61208948 0 0 1 0
## 25 0.67652519 0.474298581 0.57759685 0.57599719 0 0 0 1
## 26 -1.49656641 -1.448873451 -1.42396428 -1.31993010 1 0 0 1
## 27 0.87598771 0.711994001 0.60503638 0.87676626 0 0 0 1
## 28 0.89698376 0.906472072 0.93431072 0.76848939 0 0 1 0
## 29 -1.16062955 -1.276004055 -1.38432941 -1.22861724 0 1 0 1
## 30 1.16993247 1.554732307 1.14010718 0.86473550 0 0 0 1
## 31 0.83399560 0.582341954 0.72851426 0.74442787 0 0 1 0
## 32 0.48756071 0.106951114 0.42667945 0.32335117 0 0 0 1
## 33 0.84449363 0.560733279 0.57759685 0.53990490 0 0 1 0
## 34 0.79200349 1.144167491 0.50899803 0.86473550 0 0 1 0
## 35 1.02296009 1.576340982 0.64619568 0.73239710 0 0 1 0
## 36 0.58204295 0.668776652 0.48155851 0.23913583 0 0 1 0
## 37 0.72901533 1.187384840 0.75595379 0.58802795 0 0 1 0
## 38 0.65552914 1.554732307 0.49527827 0.73239710 0 0 1 0
## 39 1.05445417 1.576340982 1.00290954 0.67224329 0 0 1 0
## 40 -1.28660587 -1.448873451 -1.71360375 -1.31993010 1 0 0 1
## 41 -1.51756247 -1.474803861 -1.65872469 -1.64969394 1 0 0 1
## 42 -0.86668479 -0.964839142 -0.79437955 -0.71129444 0 0 0 1
## 43 0.71851730 0.625559303 0.59131662 0.72036634 0 0 0 1
## 44 0.69752125 0.798428699 0.45411898 0.50381261 0 0 0 1
## 45 0.78150546 0.560733279 0.79711308 0.61208948 0 0 0 1
## 46 0.78150546 0.495907256 0.45411898 0.37147422 0 0 0 1
## 47 0.81299955 0.603950628 0.94803048 0.55193566 0 0 0 1
## 48 0.65552914 0.582341954 0.60503638 0.72036634 0 0 0 1
## 49 0.86548968 0.733602675 0.64619568 0.68427405 0 0 0 1
## 50 1.01246206 1.144167491 0.83827237 0.76247401 0 0 0 1
## 51 0.88648573 0.452689907 0.53643756 0.49178185 0 0 0 1
## 52 1.11744233 0.755211350 0.63247591 0.37147422 0 0 0 1
## 53 -1.19212363 -1.375403958 -1.28829106 -1.38501716 0 1 0 1
## 54 0.82349757 1.079341468 0.82455261 0.76848939 0 0 0 1
## 55 0.56104690 0.236603161 0.44039921 0.15492049 0 0 0 1
## 56 -0.66722227 -0.930265263 -0.79437955 -0.53083300 0 1 0 1
## 57 -0.79319860 -0.930265263 -0.78065979 -0.71129444 1 0 1 0
## 58 0.99146601 1.046928456 1.08522813 0.74442787 0 0 0 1
## 59 -0.78270057 1.187384840 0.93431072 1.34596601 0 0 0 1
## 60 0.97046995 1.187384840 1.12638742 0.98504313 0 0 0 1
## 61 -2.92219849 0.884863397 -0.21814946 0.17296663 0 0 0 1
## 62 0.67652519 -0.022700933 0.37180039 0.10679744 0 0 0 1
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## 825 -1.41258220 -1.340830079 -1.42548870 -1.31283258 1 0 0 1
## 826 -0.95066901 -1.016699961 -0.79437955 -0.61504834 1 0 0 1
## 827 0.66602717 0.377059546 0.37180039 0.73239710 0 0 0 1
## 828 -1.20262166 -1.258717116 -1.38432941 -1.24064801 0 1 0 1
## 829 -1.62254274 -1.459677789 -1.53524681 -1.64969394 1 0 0 1
## 830 -0.89817887 -0.951873937 -0.83553885 -0.69926368 1 0 1 0
## 831 -1.64353879 -1.459677789 -1.63128516 -1.68578623 1 0 0 1
## 832 0.54005084 0.431081232 0.63247591 0.63615100 0 0 0 1
## 833 0.84449363 1.014515444 0.97547001 0.91285855 0 0 0 1
## 834 -1.66453485 -1.438069114 -1.61756540 -1.64969394 1 0 0 1
## 835 -1.30760193 -1.308417067 -1.41176894 -1.24064801 0 1 0 1
## 836 -1.30760193 -1.297612730 -1.32945035 -1.21658648 0 1 0 1
## 837 -1.54905655 -1.448873451 -1.59012587 -1.60157089 1 0 0 1
## 838 1.18043049 1.122558817 0.90687119 1.04519694 0 0 0 1
## 839 -0.66722227 -0.649352494 -0.31418781 0.38350498 0 1 1 0
## 840 -1.29710390 -1.286808392 -1.38432941 -1.32486335 0 1 1 0
## 841 -1.26560982 -1.243591043 -1.12365389 -1.34892487 0 1 1 0
## 842 -0.86668479 -0.941069600 -0.75322026 -0.47067918 1 0 1 0
## 843 0.50855676 0.820037374 0.59131662 0.35944346 0 0 1 0
## 844 0.57154492 0.409472558 0.49527827 0.62412024 0 0 0 1
## 845 0.88648573 0.776820025 0.89315143 0.50381261 0 0 0 1
## 846 0.62403506 0.333842197 0.49527827 0.40756651 0 0 0 1
## 847 0.86548968 0.938885083 0.79711308 0.98504313 0 0 0 1
## 848 0.72901533 0.582341954 0.74223402 0.75645863 0 0 0 1
## 849 -1.67503287 -1.448873451 -1.63128516 -1.68578623 1 0 0 1
## 850 -0.89817887 -0.941069600 -0.75322026 -0.66317139 1 0 0 1
## 851 -1.00315914 -0.941069600 -0.76694002 -0.62707910 1 0 0 1
## 852 -1.60154668 -1.438069114 -1.57640611 -1.62563242 1 0 0 1
## 853 0.63453308 0.193385812 0.52271780 0.57599719 0 0 0 1
## 854 0.46656465 0.355450871 0.55015733 0.57599719 0 0 0 1
## 855 0.59254098 0.517515930 0.34436087 0.45568956 0 0 1 0
## 856 0.88648573 1.111754480 1.08522813 0.99707389 0 0 0 1
## 857 -1.27610784 -1.211178032 -1.20597248 -1.28877106 0 1 1 0
## 858 0.57154492 0.128559789 0.24832252 0.31132040 0 0 0 1
## 859 -1.63304077 -1.459677789 -1.59012587 -1.68578623 1 0 0 1
## 860 0.91797982 1.252210864 0.85199214 0.91285855 0 0 0 1
## 861 0.62403506 0.517515930 0.44039921 0.67224329 0 0 0 1
## 862 0.60303900 0.409472558 0.81083284 0.87676626 0 0 0 1
## 863 0.72901533 1.295428213 0.63247591 0.47975108 0 0 0 1
## 864 -1.81150723 -1.297612730 -1.23341200 -1.36095563 0 1 0 1
## 865 -1.61204471 -1.448873451 -1.79592233 -1.66172471 1 0 0 1
## 866 0.80250152 1.036124119 0.93431072 0.92488931 0 0 0 1
## 867 0.59254098 0.312233522 0.39923992 0.35944346 0 0 0 1
## 868 0.62403506 0.171777138 0.44039921 0.33538193 0 0 0 1
## 869 1.04395614 1.111754480 1.04406883 1.05722770 0 0 0 1
## 870 -1.62254274 -1.459677789 -1.64500493 -1.62563242 1 0 1 0
## 871 0.67652519 0.506711593 0.71479450 0.76848939 0 0 1 0
## 872 1.00196403 0.971298095 0.86571190 0.90082778 0 0 1 0
## 873 -1.62254274 -1.459677789 -1.67244445 -1.54141708 1 0 1 0
## 874 -1.58055063 -1.448873451 -1.64500493 -1.58954013 1 0 0 1
## 875 0.81299955 1.068537131 0.89315143 0.90082778 0 0 0 1
## 876 0.57154492 0.539124605 0.38552016 0.57599719 0 0 0 1
## 877 -0.89817887 -0.887047914 -0.79437955 -0.37443308 1 0 1 0
## 878 0.51905479 0.269016173 0.37180039 0.44365880 0 0 0 1
## 879 0.58204295 0.841646048 0.53643756 0.38350498 0 0 0 1
## 880 0.88648573 1.760014715 0.98918978 1.03316618 0 0 0 1
## 881 0.69752125 0.798428699 0.42667945 0.76848939 0 0 1 0
## 882 0.58204295 0.744407013 0.48155851 0.47975108 0 0 1 0
## 883 0.57154492 0.809233036 0.49527827 0.60005871 0 0 1 0
## 884 -1.27610784 -1.265199718 -1.23341200 -1.25267877 0 1 1 0
## 885 0.33009030 0.474298581 0.48155851 0.55193566 0 0 1 0
## 886 0.49805873 0.377059546 0.37180039 0.84440031 0 0 0 1
## 887 -1.26560982 -1.308417067 -1.38432941 -1.28877106 0 1 0 1
## 888 0.80250152 0.560733279 0.61875615 0.34741269 0 0 1 0
## 889 -1.00315914 -0.973482612 -0.86297837 -0.68723291 1 0 0 1
## 890 -1.28660587 -1.438069114 -1.20597248 -1.15643267 0 1 0 1
## 891 0.51905479 0.474298581 0.63247591 0.57599719 0 0 0 1
## 892 0.75001138 0.636363640 0.85199214 0.90082778 0 0 1 0
## 893 0.88648573 0.603950628 0.59131662 0.53990490 0 0 0 1
## 894 0.48756071 0.150168463 0.19344346 0.10679744 0 0 0 1
## 895 -1.23411574 -1.254395381 -1.31573059 -1.13237114 0 1 0 1
## 896 -1.31809995 -1.232786706 -1.24713177 -1.22861724 0 1 0 1
## 897 -1.24461376 -1.265199718 -1.23341200 -1.15643267 0 1 0 1
## 898 0.57154492 0.495907256 0.70107473 0.74442787 0 0 1 0
## 899 -1.21311968 -1.265199718 -1.23341200 -1.20455572 0 1 0 1
## 900 0.46656465 1.198189178 0.60503638 0.64818176 0 0 1 0
## 901 0.52955281 0.377059546 0.48155851 0.23913583 0 0 1 0
## 902 0.90748179 1.252210864 0.94803048 0.69630482 0 0 1 0
## 903 0.52955281 0.074538103 0.23460275 0.05867438 0 0 0 1
## 904 0.67652519 1.630362668 0.57759685 0.28725888 0 0 0 1
## 905 -1.31809995 -1.286808392 -1.24713177 -1.18049419 0 1 0 1
## 906 0.46656465 0.042125091 0.01508653 0.28725888 0 0 0 1
## 907 0.56104690 0.193385812 0.46783874 0.33538193 0 0 0 1
## 908 -1.22361771 1.122558817 0.94803048 0.82864321 0 0 1 0We have prepared our dataset for the K-Means clustering study by following a series of steps:
- Dataset Cleaning:
- Missing values were either removed or imputed with the mean, considering that the number of missing attributes was low.
- Variable Normalization:
- All numerical variables were normalized to ensure they contribute equally to the analysis.
- Creation of Dummy Variables:
- Dummy variables were generated for categorical features, specifically for two categorical attributes.
With the cleaned and prepared dataset, we now proceed with the K-Means analysis.
To do this, we will conduct three tests using 2, 3, and 5 clusters.
This approach will allow us to evaluate how the data clusters under different scenarios and help determine the optimal number of clusters for our analysis.
set.seed(123)
dos_grupos <- 2
kmeans2_result <- kmeans(hawks_scaled, centers = dos_grupos)
tres_grupos <- 3
kmeans3_result <- kmeans(hawks_scaled, centers = tres_grupos)
cinco_grupos <- 5
kmeans5_result <- kmeans(hawks_scaled, centers = cinco_grupos)
hawks_limpio2$Cluster2 <- as.factor(kmeans2_result$cluster)
hawks_limpio2$Cluster3 <- as.factor(kmeans3_result$cluster)
hawks_limpio2$Cluster5 <- as.factor(kmeans5_result$cluster)Now, we will visualize the clusters and draw conclusions based on the results.
ggplot(hawks_limpio2, aes(x = Wing, y = Weight, color = Cluster2)) +
geom_point() +
labs(title = "K-Means Clustering (2 Groups)",
x = "Wing Size (mm)",
y = "Weight (g)") +
theme_minimal()
ggplot(hawks_limpio2, aes(x = Wing, y = Culmen, color = Cluster2)) +
geom_point() +
labs(title = "K-Means Clustering (2 Groups)",
x = "Wing Size (mm)",
y = "Beak Size (mm)") +
theme_minimal()
ggplot(hawks_limpio2, aes(x = Wing, y = Hallux, color = Cluster2)) +
geom_point() +
labs(title = "K-Means Clustering (2 Groups)",
x = "Wing Size (mm)",
y = "Spur Size (mm)") +
theme_minimal()
ggplot(hawks_limpio2, aes(x = Cluster2, fill = Cluster2)) +
geom_bar() +
labs(title = "Cluster Distribution (2 Groups)",
x = "Cluster",
y = "Count") +
theme_minimal()
Our 2-cluster option seems like a good choice, as the distribution appears well-defined, clearly showing two groups.
However, we will continue our analysis with 3 clusters to further evaluate the data.
ggplot(hawks_limpio2, aes(x = Wing, y = Weight, color = Cluster3)) +
geom_point() +
labs(title = "K-Means Clustering (3 Groups)",
x = "Wing Size (mm)",
y = "Weight (g)") +
theme_minimal()
ggplot(hawks_limpio2, aes(x = Wing, y = Culmen, color = Cluster3)) +
geom_point() +
labs(title = "K-Means Clustering (3 Groups)",
x = "Wing Size (mm)",
y = "Beak Size (mm)") +
theme_minimal()
ggplot(hawks_limpio2, aes(x = Wing, y = Hallux, color = Cluster3)) +
geom_point() +
labs(title = "K-Means Clustering (3 Groups)",
x = "Wing Size (mm)",
y = "Spur Size (mm)") +
theme_minimal()
ggplot(hawks_limpio2, aes(x = Cluster3, fill = Cluster3)) +
geom_bar() +
labs(title = "Cluster Distribution (3 Groups)",
x = "Cluster",
y = "Count") +
theme_minimal()
Comparing with the 2-cluster model, the
3-cluster approach seems to make more
sense.
Additionally, considering that we have 3 species, this is likely the most logical reason to use 3 clusters.
However, as we are conducting multiple tests, we will continue to evaluate whether more clusters are a viable option.
Next, we test with 5 clusters to determine if further segmentation improves the analysis or if it becomes less meaningful.
ggplot(hawks_limpio2, aes(x = Wing, y = Weight, color = Cluster5)) +
geom_point() +
labs(title = "K-Means Clustering (5 Groups)",
x = "Wing Size (mm)",
y = "Weight (g)") +
theme_minimal()
ggplot(hawks_limpio2, aes(x = Wing, y = Culmen, color = Cluster5)) +
geom_point() +
labs(title = "K-Means Clustering (5 Groups)",
x = "Wing Size (mm)",
y = "Beak Size (mm)") +
theme_minimal()
ggplot(hawks_limpio2, aes(x = Wing, y = Hallux, color = Cluster5)) +
geom_point() +
labs(title = "K-Means Clustering (5 Groups)",
x = "Wing Size (mm)",
y = "Spur Size (mm)") +
theme_minimal()
ggplot(hawks_limpio2, aes(x = Cluster5, fill = Cluster5)) +
geom_bar() +
labs(title = "Cluster Distribution (5 Groups)",
x = "Cluster",
y = "Count") +
theme_minimal()
We clearly observe that 5 clusters is too many.
Although there is no exact definition of the optimal number of clusters to distinguish significant differences among the selected variables, we will apply several methods taught in the Multivariate Analysis course from previous semesters.
These methods include:
- Elbow Method
- Silhouette Method
- Gap Statistic
From our observations, the optimal number of clusters is between 2 and 3, but the best choice is 3, as we have three species.
dfnumeric <- hawks_limpio2 %>%
select(Wing, Weight, Culmen, Hallux, Sex_M, Sex_F, Age_A, Age_I)
# Elbow Method
wss <- sapply(1:10, function(k) {
kmeans(dfnumeric, k, nstart = 10)$tot.withinss
})
plot(1:10, wss, type = "b", pch = 19, frame = FALSE,
xlab = "Number of Clusters K", ylab = "Total Within-Cluster Sum of Squares")
# Silhouette Method
avg_sil <- sapply(2:10, function(k) {
km <- kmeans(dfnumeric, centers = k, nstart = 10)
ss <- silhouette(km$cluster, dist(dfnumeric))
mean(ss[, 3])
})
plot(2:10, avg_sil, type = "b", pch = 19, frame = FALSE,
xlab = "Number of Clusters K", ylab = "Average Silhouette Width")
# Gap Statistic Method
gap_stat <- clusGap(dfnumeric, FUN = kmeans, nstart = 25, K.max = 10, B = 50)## Warning: did not converge in 10 iterationsfviz_gap_stat(gap_stat)
Finally, we create a hierarchical clustering plot using
the selected number of clusters: 3.
dj <- dist(dfnumeric)
cc <- hclust(dj, method = "complete")
plot(cc, main = "Hierarchical Clustering of Birds")
rect.hclust(cc, k = 3, border = "red")
## Final Conclusions
The measurements of wing length and beak size allow for clear species separation, whereas weight does not.
When analyzing the weight variable, we observe that observations overlap, making it less effective for clustering.
As noted in our initial exploratory analysis, we have more juvenile hawks compared to adults, which may be a key factor influencing the cluster distribution.
The number of species (3) serves as a key indicator for selecting 3 clusters.
However, much of our analysis also suggests that 2 clusters would not be an incorrect choice.
Final Verdict:
After thoroughly analyzing the data and obtaining strong results, we conclude that the lack of clear separation in the dataset implies that K-Means may not be the most suitable clustering method for this dataset.
Section 2: Study Using DBSCAN and OPTICS
Data Preparation
Before proceeding, we need to understand both clustering algorithms.
We found the following information:
- The OPTICS algorithm (Ordering Points to
Identify the Clustering Structure) is a density-based
clustering method.
- It is similar to DBSCAN but more flexible.
- OPTICS orders data points so that closer
points are grouped first.
- It uses two parameters:
- ε (maximum radius)
- MinPts (minimum number of points to form a
cluster)
- ε (maximum radius)
- Each point receives a reachability distance,
representing the density required to form a
cluster.
- OPTICS is particularly useful for detecting clusters in datasets with varying densities.
We chose MinPts = 10, based on the example exercise and the following reference:
How to Determine Epsilon and MinPts for DBSCAN
- In practice and literature, a MinPts value
between 5 and 10 is commonly used.
- This range balances sensitivity to clusters and resistance
to outliers.
- A MinPts of 10 provides enough flexibility to adapt to data variability.
We will use the normalized dataset, excluding dummy variables.
After the initial analysis, we will assess whether repeating the experiment with dummy variables is necessary.
hawks_scaled2 <- hawks_scaled %>%
select(Wing, Weight, Culmen, Hallux)
hawks_scaled2## Wing Weight Culmen Hallux
## 1 0.72901533 0.323037860 0.53643756 0.58802795
## 2 0.63453308 0.344646534 0.68899769 0.84440031
## 3 0.68702322 0.474298581 0.67363520 0.73239710
## 4 -0.53074792 -0.649352494 -0.42394592 -0.20600240
## 5 -1.16062955 -1.297612730 -1.27457130 -1.31283258
## 6 1.01246206 0.690385326 0.92059096 0.84067397
## 7 0.57154492 0.409472558 0.48155851 0.58802795
## 8 0.62403506 0.182581475 0.74223402 0.57599719
## 9 1.01246206 0.949689421 1.03034907 0.73239710
## 10 0.93897587 0.755211350 0.57759685 0.60005871
## 11 0.81299955 0.517515930 0.61875615 0.67224329
## 12 0.58204295 0.517515930 0.49527827 0.53990490
## 13 0.78150546 0.755211350 0.97547001 0.68427405
## 14 0.81299955 0.844699836 0.87943166 0.64818176
## 15 1.05445417 0.863254723 0.64619568 1.05722770
## 16 1.26441471 1.338645562 1.19498624 1.05722770
## 17 1.07545022 0.820037374 0.72851426 0.69630482
## 18 0.68702322 0.387863883 0.97547001 0.44365880
## 19 0.65552914 0.301429185 0.53643756 0.35944346
## 20 0.84449363 0.517515930 0.30320157 0.20304354
## 21 0.87598771 0.647167977 0.63247591 0.72036634
## 22 1.05445417 0.906472072 0.96175025 0.76848939
## 23 1.04395614 -1.446712584 0.42667945 0.66021253
## 24 0.80250152 1.208993515 0.71479450 0.61208948
## 25 0.67652519 0.474298581 0.57759685 0.57599719
## 26 -1.49656641 -1.448873451 -1.42396428 -1.31993010
## 27 0.87598771 0.711994001 0.60503638 0.87676626
## 28 0.89698376 0.906472072 0.93431072 0.76848939
## 29 -1.16062955 -1.276004055 -1.38432941 -1.22861724
## 30 1.16993247 1.554732307 1.14010718 0.86473550
## 31 0.83399560 0.582341954 0.72851426 0.74442787
## 32 0.48756071 0.106951114 0.42667945 0.32335117
## 33 0.84449363 0.560733279 0.57759685 0.53990490
## 34 0.79200349 1.144167491 0.50899803 0.86473550
## 35 1.02296009 1.576340982 0.64619568 0.73239710
## 36 0.58204295 0.668776652 0.48155851 0.23913583
## 37 0.72901533 1.187384840 0.75595379 0.58802795
## 38 0.65552914 1.554732307 0.49527827 0.73239710
## 39 1.05445417 1.576340982 1.00290954 0.67224329
## 40 -1.28660587 -1.448873451 -1.71360375 -1.31993010
## 41 -1.51756247 -1.474803861 -1.65872469 -1.64969394
## 42 -0.86668479 -0.964839142 -0.79437955 -0.71129444
## 43 0.71851730 0.625559303 0.59131662 0.72036634
## 44 0.69752125 0.798428699 0.45411898 0.50381261
## 45 0.78150546 0.560733279 0.79711308 0.61208948
## 46 0.78150546 0.495907256 0.45411898 0.37147422
## 47 0.81299955 0.603950628 0.94803048 0.55193566
## 48 0.65552914 0.582341954 0.60503638 0.72036634
## 49 0.86548968 0.733602675 0.64619568 0.68427405
## 50 1.01246206 1.144167491 0.83827237 0.76247401
## 51 0.88648573 0.452689907 0.53643756 0.49178185
## 52 1.11744233 0.755211350 0.63247591 0.37147422
## 53 -1.19212363 -1.375403958 -1.28829106 -1.38501716
## 54 0.82349757 1.079341468 0.82455261 0.76848939
## 55 0.56104690 0.236603161 0.44039921 0.15492049
## 56 -0.66722227 -0.930265263 -0.79437955 -0.53083300
## 57 -0.79319860 -0.930265263 -0.78065979 -0.71129444
## 58 0.99146601 1.046928456 1.08522813 0.74442787
## 59 -0.78270057 1.187384840 0.93431072 1.34596601
## 60 0.97046995 1.187384840 1.12638742 0.98504313
## 61 -2.92219849 0.884863397 -0.21814946 0.17296663
## 62 0.67652519 -0.022700933 0.37180039 0.10679744
## 63 0.84449363 1.036124119 0.65991544 0.87676626
## 64 0.10963173 0.661124977 0.46783874 0.29928964
## 65 -1.65403682 -1.448873451 -1.50780728 -1.77000157
## 66 1.05445417 1.144167491 0.75595379 0.90082778
## 67 -0.46775976 -0.638548157 -0.49254474 -0.05561786
## 68 -1.46507233 -1.448873451 -1.64500493 -1.69781700
## 69 -1.27610784 -1.340003865 -1.42548870 -1.32486335
## 70 0.78150546 0.668776652 1.15382695 0.46772032
## 71 0.79200349 0.776820025 0.63247591 0.50381261
## 72 0.75001138 0.841646048 0.68735497 0.69630482
## 73 1.09644628 1.241406527 1.05778860 1.09331999
## 74 1.25391668 1.327841225 1.48310128 0.64818176
## 75 0.88648573 0.949689421 0.50899803 0.40756651
## 76 0.86548968 1.479101947 0.85199214 0.75645863
## 77 0.83399560 0.884863397 0.44039921 0.44365880
## 78 0.99146601 1.576340982 0.72851426 0.96098160
## 79 0.56104690 0.549928942 0.72851426 0.75645863
## 80 0.59254098 0.344646534 0.59131662 0.70833558
## 81 1.04395614 1.273819539 0.93431072 0.99707389
## 82 1.01246206 1.046928456 0.81083284 0.88879702
## 83 -1.16062955 -1.245751911 -1.26085153 -1.30080182
## 84 -1.17112757 -1.321382272 -1.27457130 -1.25267877
## 85 -1.52806050 -1.470482126 -1.68616422 -1.67375547
## 86 -0.86668479 -0.930265263 -0.54742380 -0.69926368
## 87 0.62403506 0.636363640 0.56387709 0.57599719
## 88 0.72901533 0.766015687 -0.30046805 0.74442787
## 89 1.11744233 1.230602190 0.94803048 0.81661244
## 90 0.79200349 0.603950628 0.65991544 0.84067397
## 91 0.99146601 0.949689421 0.78339332 0.84440031
## 92 0.72901533 0.452689907 0.68735497 0.31132040
## 93 0.68702322 0.495907256 0.50899803 0.55193566
## 94 1.05445417 1.338645562 0.86571190 0.73239710
## 95 0.94947390 1.090145805 0.98918978 1.02113541
## 96 1.07545022 0.884863397 1.14010718 0.84440031
## 97 1.01246206 0.949689421 1.03034907 1.03316618
## 98 -1.12913547 -1.301934465 -1.24713177 -1.25267877
## 99 -1.12913547 -1.349473549 -1.37060964 -1.24064801
## 100 -1.47557036 -1.431586512 -1.61756540 -1.64969394
## 101 -1.57005260 -1.461838656 -1.68616422 -1.67375547
## 102 0.93897587 0.679580989 0.81083284 0.56396642
## 103 -1.23411574 -1.258717116 -1.31573059 -0.99462762
## 104 -1.21311968 -1.332186609 -1.28829106 -1.30080182
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## 691 0.83399560 0.863254723 0.55015733 0.63615100
## 692 0.55054887 0.657972315 0.81083284 0.78052016
## 693 -1.10813941 -1.232786706 -1.32945035 -1.19252495
## 694 0.89698376 0.420276895 0.55015733 0.46772032
## 695 0.41407452 0.031320753 0.12484464 -0.02554096
## 696 0.64503111 0.701189664 0.52271780 0.78052016
## 697 -1.24461376 -1.319221404 -1.34317012 -1.26470953
## 698 -1.51756247 -1.459677789 -1.74104327 -1.64969394
## 699 -0.40477160 1.576340982 1.08522813 0.82864321
## 700 1.25391668 1.781623390 0.76967355 1.11738152
## 701 0.59254098 0.463494244 0.49527827 0.69630482
## 702 -0.58323806 -0.444070086 -0.24558899 -0.12178706
## 703 0.78150546 -1.146352008 0.46783874 0.49178185
## 704 0.45606662 0.225798824 0.57759685 0.70833558
## 705 0.81299955 0.982102432 0.98918978 0.98504313
## 706 0.90748179 1.046928456 1.20870600 1.12941228
## 707 0.48756071 0.387863883 0.68735497 0.66021253
## 708 -0.92967295 -0.951873937 -0.79437955 -0.80754054
## 709 0.45606662 0.269016173 0.78339332 0.58802795
## 710 -1.68553090 -1.448873451 -1.64500493 -1.58954013
## 711 -0.57274003 -0.681765506 -0.64346215 0.19101278
## 712 -1.63304077 -1.470482126 -1.57640611 -1.64969394
## 713 -1.57005260 -1.438069114 -1.43920846 -1.66172471
## 714 0.48756071 1.154971829 0.87943166 1.09331999
## 715 0.62403506 0.441885569 0.74223402 0.79255092
## 716 0.76050941 0.895667734 0.97547001 1.09331999
## 717 0.80250152 0.560733279 0.59131662 0.63615100
## 718 1.01246206 0.960493758 0.94803048 1.06925847
## 719 0.58204295 0.657972315 0.70107473 0.91285855
## 720 -0.63572819 0.409472558 -0.28674828 2.11593483
## 721 0.79200349 0.052929428 0.34436087 0.28725888
## 722 -1.31809995 -1.276004055 -1.31573059 -1.32486335
## 723 0.72901533 0.982102432 0.82455261 0.81661244
## 724 -1.57005260 -1.427264777 -1.61756540 -1.60157089
## 725 -1.24461376 -1.308417067 -1.31573059 -1.24064801
## 726 0.57154492 0.323037860 0.61875615 0.81661244
## 727 -1.31809995 -1.297612730 -1.34317012 -1.22861724
## 728 0.88648573 1.176580503 1.07150836 1.05722770
## 729 -1.61204471 -1.448873451 -1.69988398 -1.69781700
## 730 -1.27610784 -1.330025742 -1.27457130 -1.28877106
## 731 0.83399560 0.830841711 1.11266765 1.10535075
## 732 0.91797982 0.841646048 0.98918978 0.85270473
## 733 0.73951336 0.398668220 0.83827237 0.62412024
## 734 -1.28660587 -1.254395381 -1.19225271 -1.24064801
## 735 -1.18162560 -1.276004055 -1.09621436 -1.26470953
## 736 -1.64353879 -1.470482126 -1.61756540 -1.64969394
## 737 -1.60154668 -1.448873451 -1.64500493 -1.62563242
## 738 -1.30760193 -1.254395381 -1.28829106 -1.25267877
## 739 -1.57005260 -1.438069114 -1.57640611 -1.58954013
## 740 0.47706268 0.560733279 0.71479450 0.63615100
## 741 -0.58323806 -0.444070086 -0.28674828 3.52353409
## 742 -0.85618676 -0.843830565 -1.28829106 -0.39849461
## 743 0.64503111 0.582341954 0.86571190 0.68427405
## 744 0.47706268 0.301429185 0.34436087 0.27522812
## 745 0.62403506 0.506711593 0.57759685 0.87676626
## 746 -1.28660587 -1.276004055 -1.35688988 -1.31283258
## 747 -1.25511179 -1.286808392 -1.28829106 -1.15643267
## 748 -1.64353879 -1.438069114 -1.64500493 -1.70984776
## 749 -1.29710390 -1.254395381 -1.37060964 -1.32486335
## 750 0.89698376 1.036124119 0.87943166 1.21362762
## 751 -1.23411574 -1.265199718 -1.26085153 -1.20455572
## 752 0.95997192 1.090145805 0.78339332 1.02113541
## 753 -1.61204471 -1.438069114 -1.64500493 -1.52938631
## 754 -1.53855852 -0.282005027 -0.69834120 -0.19397164
## 755 -1.54905655 -1.448873451 -1.54896658 -1.74594005
## 756 -1.54905655 -1.438069114 -1.52152705 -1.63766318
## 757 -0.97166506 -0.822221890 -0.80809932 -0.55489452
## 758 0.62403506 0.560733279 0.70107473 0.73239710
## 759 0.94947390 1.122558817 1.03034907 0.97301236
## 760 0.73951336 0.539124605 0.70107473 0.76848939
## 761 -1.63304077 -1.438069114 -1.63128516 -1.66172471
## 762 0.65552914 0.614754966 0.64619568 0.56396642
## 763 -1.28660587 -1.265199718 -1.30201082 -1.25267877
## 764 0.66602717 0.517515930 0.44039921 0.49178185
## 765 0.50855676 0.528320267 0.42667945 0.51584337
## 766 0.36158438 0.744407013 1.05778860 0.61208948
## 767 0.67652519 1.187384840 0.67363520 0.76848939
## 768 0.83399560 0.884863397 1.16754671 0.98504313
## 769 0.59254098 0.809233036 0.56387709 0.84067397
## 770 0.63453308 0.485102918 0.85199214 0.60005871
## 771 0.54005084 0.593146291 0.59131662 0.63615100
## 772 -0.89817887 -0.930265263 -0.79437955 -0.68723291
## 773 0.52955281 0.355450871 0.53643756 0.22710506
## 774 0.73951336 0.636363640 0.59131662 0.69630482
## 775 0.62403506 0.733602675 0.81083284 0.73239710
## 776 -1.22361771 -1.254395381 -1.34317012 -1.20455572
## 777 0.93897587 1.046928456 0.83827237 0.79255092
## 778 0.58204295 0.528320267 0.42667945 0.38350498
## 779 -1.28660587 -1.254395381 -1.31573059 -1.20455572
## 780 0.36158438 0.409472558 0.65991544 0.56396642
## 781 -1.28660587 -1.232786706 -1.43920846 -1.40907869
## 782 0.55054887 0.690385326 0.75595379 0.62412024
## 783 -1.37059009 -1.297612730 -1.34317012 -1.26470953
## 784 0.59254098 0.679580989 0.49527827 0.55193566
## 785 0.84449363 0.636363640 0.81083284 0.57599719
## 786 0.51905479 0.766015687 0.70107473 0.49178185
## 787 0.61353703 0.603950628 0.50899803 0.61208948
## 788 -0.65672425 -0.530504784 -0.31418781 -0.20600240
## 789 0.59254098 0.452689907 0.63247591 0.45568956
## 790 0.63453308 0.884863397 0.35808063 0.66021253
## 791 -1.57005260 -1.416460440 -1.63128516 -1.63766318
## 792 0.56104690 0.701189664 0.65991544 0.38350498
## 793 0.79200349 1.208993515 0.68735497 0.58802795
## 794 -1.28660587 -1.265199718 -1.32945035 -1.24064801
## 795 0.85499165 0.711994001 0.04252606 0.43162803
## 796 0.52955281 0.744407013 0.72851426 -0.50677147
## 797 0.72901533 1.360254237 1.16754671 0.97301236
## 798 0.88648573 0.874059060 0.79711308 0.88879702
## 799 -1.23411574 -1.265199718 -1.37060964 -1.21658648
## 800 0.51905479 0.431081232 0.56387709 0.76848939
## 801 -1.27610784 -1.297612730 -1.39804917 -1.34892487
## 802 -1.26560982 -1.286808392 -1.34317012 -1.15643267
## 803 -1.21311968 -1.308417067 -1.41176894 -1.28877106
## 804 0.71851730 1.057732793 0.93431072 0.87676626
## 805 -1.64353879 -1.427264777 -1.63128516 -1.69781700
## 806 -1.62254274 -1.448873451 -1.71360375 -1.64969394
## 807 -1.30760193 -1.254395381 -1.30201082 -1.25267877
## 808 -1.04515125 -1.005895624 -0.79437955 -0.57895605
## 809 -0.62523017 -0.562917796 -0.41022616 -0.23006392
## 810 -1.62254274 -1.470482126 -1.68616422 -1.67375547
## 811 0.84449363 0.917276409 0.71479450 -0.16991011
## 812 0.79200349 0.571537617 0.83827237 0.94895084
## 813 -1.63304077 -1.470482126 -1.78220257 -1.66172471
## 814 -1.39158614 -1.319221404 -1.24713177 -1.27674029
## 815 -1.67503287 -1.481286463 -1.65872469 -1.70984776
## 816 0.81299955 0.830841711 0.89315143 0.68427405
## 817 0.85499165 1.057732793 0.82455261 0.92488931
## 818 -1.64353879 -1.459677789 -1.76848280 -1.78203234
## 819 -0.63572819 -0.714178518 -0.43766569 -0.29021774
## 820 -1.24461376 -1.286808392 -1.61756540 -1.24064801
## 821 -1.02415519 -1.027504298 -0.78065979 -0.69926368
## 822 -1.25511179 -1.319221404 -1.26085153 -1.28877106
## 823 0.71851730 0.517515930 0.68735497 0.70833558
## 824 0.72901533 0.474298581 0.57759685 0.52787414
## 825 -1.41258220 -1.340830079 -1.42548870 -1.31283258
## 826 -0.95066901 -1.016699961 -0.79437955 -0.61504834
## 827 0.66602717 0.377059546 0.37180039 0.73239710
## 828 -1.20262166 -1.258717116 -1.38432941 -1.24064801
## 829 -1.62254274 -1.459677789 -1.53524681 -1.64969394
## 830 -0.89817887 -0.951873937 -0.83553885 -0.69926368
## 831 -1.64353879 -1.459677789 -1.63128516 -1.68578623
## 832 0.54005084 0.431081232 0.63247591 0.63615100
## 833 0.84449363 1.014515444 0.97547001 0.91285855
## 834 -1.66453485 -1.438069114 -1.61756540 -1.64969394
## 835 -1.30760193 -1.308417067 -1.41176894 -1.24064801
## 836 -1.30760193 -1.297612730 -1.32945035 -1.21658648
## 837 -1.54905655 -1.448873451 -1.59012587 -1.60157089
## 838 1.18043049 1.122558817 0.90687119 1.04519694
## 839 -0.66722227 -0.649352494 -0.31418781 0.38350498
## 840 -1.29710390 -1.286808392 -1.38432941 -1.32486335
## 841 -1.26560982 -1.243591043 -1.12365389 -1.34892487
## 842 -0.86668479 -0.941069600 -0.75322026 -0.47067918
## 843 0.50855676 0.820037374 0.59131662 0.35944346
## 844 0.57154492 0.409472558 0.49527827 0.62412024
## 845 0.88648573 0.776820025 0.89315143 0.50381261
## 846 0.62403506 0.333842197 0.49527827 0.40756651
## 847 0.86548968 0.938885083 0.79711308 0.98504313
## 848 0.72901533 0.582341954 0.74223402 0.75645863
## 849 -1.67503287 -1.448873451 -1.63128516 -1.68578623
## 850 -0.89817887 -0.941069600 -0.75322026 -0.66317139
## 851 -1.00315914 -0.941069600 -0.76694002 -0.62707910
## 852 -1.60154668 -1.438069114 -1.57640611 -1.62563242
## 853 0.63453308 0.193385812 0.52271780 0.57599719
## 854 0.46656465 0.355450871 0.55015733 0.57599719
## 855 0.59254098 0.517515930 0.34436087 0.45568956
## 856 0.88648573 1.111754480 1.08522813 0.99707389
## 857 -1.27610784 -1.211178032 -1.20597248 -1.28877106
## 858 0.57154492 0.128559789 0.24832252 0.31132040
## 859 -1.63304077 -1.459677789 -1.59012587 -1.68578623
## 860 0.91797982 1.252210864 0.85199214 0.91285855
## 861 0.62403506 0.517515930 0.44039921 0.67224329
## 862 0.60303900 0.409472558 0.81083284 0.87676626
## 863 0.72901533 1.295428213 0.63247591 0.47975108
## 864 -1.81150723 -1.297612730 -1.23341200 -1.36095563
## 865 -1.61204471 -1.448873451 -1.79592233 -1.66172471
## 866 0.80250152 1.036124119 0.93431072 0.92488931
## 867 0.59254098 0.312233522 0.39923992 0.35944346
## 868 0.62403506 0.171777138 0.44039921 0.33538193
## 869 1.04395614 1.111754480 1.04406883 1.05722770
## 870 -1.62254274 -1.459677789 -1.64500493 -1.62563242
## 871 0.67652519 0.506711593 0.71479450 0.76848939
## 872 1.00196403 0.971298095 0.86571190 0.90082778
## 873 -1.62254274 -1.459677789 -1.67244445 -1.54141708
## 874 -1.58055063 -1.448873451 -1.64500493 -1.58954013
## 875 0.81299955 1.068537131 0.89315143 0.90082778
## 876 0.57154492 0.539124605 0.38552016 0.57599719
## 877 -0.89817887 -0.887047914 -0.79437955 -0.37443308
## 878 0.51905479 0.269016173 0.37180039 0.44365880
## 879 0.58204295 0.841646048 0.53643756 0.38350498
## 880 0.88648573 1.760014715 0.98918978 1.03316618
## 881 0.69752125 0.798428699 0.42667945 0.76848939
## 882 0.58204295 0.744407013 0.48155851 0.47975108
## 883 0.57154492 0.809233036 0.49527827 0.60005871
## 884 -1.27610784 -1.265199718 -1.23341200 -1.25267877
## 885 0.33009030 0.474298581 0.48155851 0.55193566
## 886 0.49805873 0.377059546 0.37180039 0.84440031
## 887 -1.26560982 -1.308417067 -1.38432941 -1.28877106
## 888 0.80250152 0.560733279 0.61875615 0.34741269
## 889 -1.00315914 -0.973482612 -0.86297837 -0.68723291
## 890 -1.28660587 -1.438069114 -1.20597248 -1.15643267
## 891 0.51905479 0.474298581 0.63247591 0.57599719
## 892 0.75001138 0.636363640 0.85199214 0.90082778
## 893 0.88648573 0.603950628 0.59131662 0.53990490
## 894 0.48756071 0.150168463 0.19344346 0.10679744
## 895 -1.23411574 -1.254395381 -1.31573059 -1.13237114
## 896 -1.31809995 -1.232786706 -1.24713177 -1.22861724
## 897 -1.24461376 -1.265199718 -1.23341200 -1.15643267
## 898 0.57154492 0.495907256 0.70107473 0.74442787
## 899 -1.21311968 -1.265199718 -1.23341200 -1.20455572
## 900 0.46656465 1.198189178 0.60503638 0.64818176
## 901 0.52955281 0.377059546 0.48155851 0.23913583
## 902 0.90748179 1.252210864 0.94803048 0.69630482
## 903 0.52955281 0.074538103 0.23460275 0.05867438
## 904 0.67652519 1.630362668 0.57759685 0.28725888
## 905 -1.31809995 -1.286808392 -1.24713177 -1.18049419
## 906 0.46656465 0.042125091 0.01508653 0.28725888
## 907 0.56104690 0.193385812 0.46783874 0.33538193
## 908 -1.22361771 1.122558817 0.94803048 0.82864321OPTICS
res <- optics(hawks_scaled2, minPts = 10)
res## OPTICS ordering/clustering for 908 objects.
## Parameters: minPts = 10, eps = 3.07488223798005, eps_cl = NA, xi = NA
## Available fields: order, reachdist, coredist, predecessor, minPts, eps,
## eps_cl, xiThe data indicates that 3.07488223798005 is the maximum neighborhood size to consider when determining proximity between data points.
res$order## [1] 1 571 390 267 260 245 620 185 184 150 149 137 93 824 764 650 408 233
## [19] 193 25 236 487 481 426 378 317 787 771 594 467 281 12 87 134 119 278
## [37] 203 765 334 861 844 701 471 223 283 116 648 891 832 707 681 547 508 337
## [55] 762 579 139 251 80 7 165 555 365 532 131 11 402 784 295 364 206 515
## [73] 457 876 561 550 391 33 222 774 717 552 292 403 372 250 823 506 460 179
## [91] 154 48 43 758 589 871 848 671 450 79 898 760 473 3 113 715 423 483
## [109] 438 427 270 647 135 90 31 696 782 740 590 182 323 190 157 342 800 465
## [127] 338 180 178 679 181 354 556 778 726 528 437 526 45 355 743 649 582 336
## [145] 155 544 855 309 615 854 893 169 274 585 240 110 21 572 433 183 692 862
## [163] 2 51 286 789 733 324 719 846 560 505 478 867 878 576 466 434 380 230
## [181] 19 853 489 504 114 194 617 136 138 71 709 258 770 290 205 237 596 780
## [199] 775 602 600 601 581 397 745 117 907 868 674 676 537 32 553 412 177 173
## [217] 49 200 672 606 593 151 559 605 881 769 496 531 888 197 159 123 385 883
## [235] 882 614 540 901 744 558 369 497 209 208 204 455 694 275 609 514 367 608
## [253] 892 812 631 566 501 405 300 785 199 47 224 72 691 207 10 294 46 153
## [271] 118 430 147 55 27 163 241 816 591 444 377 124 551 485 428 384 351 28
## [289] 14 798 847 658 872 548 289 254 186 174 120 91 777 262 246 82 229 66
## [307] 54 50 335 732 529 522 226 421 875 866 833 817 705 632 517 269 641 752
## [325] 388 492 804 573 225 716 502 389 564 541 350 13 441 869 856 759 728 683
## [343] 578 252 95 60 567 480 164 291 293 597 127 81 73 126 409 718 482 257
## [361] 22 9 97 536 271 860 669 468 187 616 92 792 827 723 463 217 158 344
## [379] 238 768 446 145 472 8 543 220 885 462 115 106 280 666 525 786 102 256
## [397] 586 6 435 592 452 89 499 387 264 773 44 58 886 261 189 470 704 247
## [415] 63 845 538 879 273 731 392 534 469 298 440 18 105 607 242 96 598 790
## [433] 303 17 750 133 192 75 494 366 682 902 418 140 652 339 382 146 77 613
## [451] 109 407 510 94 706 235 843 838 265 664 401 610 651 858 259 406 491 539
## [469] 248 512 34 894 410 793 24 767 584 37 76 36 507 285 15 332 474 484
## [487] 297 373 665 376 863 156 20 333 436 721 70 255 629 16 343 396 232 900
## [505] 39 52 399 348 903 549 498 30 331 797 612 906 62 695 35 272 244 78
## [523] 346 880 175 554 162 282 381 296 479 766 148 714 38 456 64 210 345 667
## [541] 700 411 322 795 166 88 904 359 356 349 347 191 132 74 811 796 622 476
## [559] 243 414 603 398 326 362 908 59 699 445 819 809 788 686 680 673 459 400
## [577] 310 4 588 353 239 108 67 415 702 577 542 249 530 711 111 234 634 839
## [595] 877 842 851 889 850 830 826 772 643 424 371 57 42 708 533 599 821 808
## [613] 524 757 443 299 221 393 288 56 86 188 642 742 442 327 263 287 662 735
## [631] 841 685 899 897 884 896 763 836 807 794 779 738 727 725 697 887 688 639
## [649] 623 416 316 284 219 621 104 840 746 475 313 595 523 500 630 214 822 730
## [667] 619 776 751 687 370 170 803 828 799 202 801 749 722 516 783 458 374 69
## [685] 84 29 276 301 228 461 171 5 624 176 160 905 448 375 172 644 802 306
## [703] 734 684 660 625 519 439 835 447 404 143 83 895 747 486 454 431 689 557
## [721] 312 857 395 488 413 340 98 513 477 464 167 129 611 198 218 675 546 814
## [739] 168 99 693 518 227 568 195 201 161 420 653 569 383 677 53 781 216 825
## [757] 26 103 211 277 352 890 820 215 360 315 618 357 40 341 253 329 545 837
## [775] 739 724 874 791 663 580 570 562 852 657 587 451 495 737 575 565 308 646
## [793] 659 655 654 626 503 859 831 761 736 712 527 422 849 805 748 636 520 307
## [811] 304 656 314 311 627 449 535 429 419 870 834 638 417 125 810 729 628 302
## [829] 633 829 386 268 815 690 101 670 394 41 604 806 368 755 196 756 144 85
## [847] 668 379 432 574 710 68 637 493 873 509 142 753 100 212 122 112 813 563
## [865] 698 661 865 713 130 65 231 141 818 107 363 121 213 864 320 635 425 583
## [883] 319 128 305 328 152 318 640 754 321 521 325 511 358 678 330 703 645 490
## [901] 23 453 266 361 279 720 741 61The OPTICS point ordering arranges data based on density, revealing the cluster structure.
To better visualize the valleys, we will plot the reachability plot, making it clearer to determine the optimal number of clusters.
We observe two large valleys (first indication, similar to K-Means) and three smaller ones, with one being more prominent, leading to a preliminary conclusion of 3 clusters.
If we consider all valleys, we might identify 5 clusters.
plot(res, main= "Diagram reachability plot")
Now, we will visualize the clusters using the
variables from our normalized dataset.
hawks_plot <- data.frame(
Wing = hawks_scaled2$Wing,
Weight = hawks_scaled2$Weight,
Culmen = hawks_scaled2$Culmen,
Hallux = hawks_scaled2$Hallux,
Order = res$order
)
ggplot(hawks_plot, aes(x = Wing, y = Weight)) +
geom_point(color = "grey") +
geom_polygon(aes(x = Wing[Order], y = Weight[Order]), fill = NA, color = "blue") +
ggtitle("Wing-Weight Traces") +
xlab("Wing Size") +
ylab("Weight") +
theme_minimal()
ggplot(hawks_plot, aes(x = Wing, y = Culmen)) +
geom_point(color = "grey") +
geom_polygon(aes(x = Wing[Order], y = Culmen[Order]), fill = NA, color = "green") +
ggtitle("Wing-Beak Traces") +
xlab("Wing Size") +
ylab("Beak Size") +
theme_minimal()
ggplot(hawks_plot, aes(x = Wing, y = Hallux)) +
geom_point(color = "grey") +
geom_polygon(aes(x = Wing[Order], y = Hallux[Order]), fill = NA, color = "red") +
ggtitle("Wing-Spur Traces") +
xlab("Wing Size") +
ylab("Spur Size") +
theme_minimal()
ggplot(hawks_plot, aes(x = Weight, y = Culmen)) +
geom_point(color = "grey") +
geom_polygon(aes(x = Weight[Order], y = Culmen[Order]), fill = NA, color = "purple") +
ggtitle("Weight-Beak Traces") +
xlab("Weight") +
ylab("Beak Size") +
theme_minimal()
ggplot(hawks_plot, aes(x = Weight, y = Hallux)) +
geom_point(color = "grey") +
geom_polygon(aes(x = Weight[Order], y = Hallux[Order]), fill = NA, color = "orange") +
ggtitle("Weight-Spur Traces") +
xlab("Weight") +
ylab("Spur Size") +
theme_minimal()
ggplot(hawks_plot, aes(x = Culmen, y = Hallux)) +
geom_point(color = "grey") +
geom_polygon(aes(x = Culmen[Order], y = Hallux[Order]), fill = NA, color = "pink") +
ggtitle("Beak-Spur Traces") +
xlab("Beak Size") +
ylab("Spur Size") +
theme_minimal()
This type of chart is complex to interpret, so we created another one where we grouped everything to observe clearer patterns.
hawks_long <- hawks_plot %>%
pivot_longer(cols = c(Wing, Weight, Culmen, Hallux), names_to = "variable", values_to = "value")
ggplot(hawks_long, aes(x = Order, y = value, color = variable)) +
geom_point() +
geom_line(aes(group = variable)) +
facet_wrap(~ variable, scales = "free_y") +
ggtitle("Variables by Density Order (OPTICS)") +
theme_minimal()
Wing vs. Weight Relationship
We can see clear groupings in the Wing vs. Weight plots. This
suggests that wing size and weight are characteristics that may help
distinguish between hawk species. For example, larger and heavier hawks
might belong to a specific species, while smaller and lighter ones may
belong to another.
Wing vs. Culmen Relationship
The Wing vs. Culmen plot also shows groupings, indicating that
wing size and beak size are correlated. This can be particularly useful
for identifying species with specific beak and wing characteristics,
such as cooperative hawks.
Wing vs. Hallux Relationship
Although less obvious, the Wing vs. Hallux plot still shows
some grouping patterns. The length of the spur, along with wing size,
may differentiate certain species or ages within the same species.
Weight vs. Culmen and Weight vs. Hallux
Relationships
These plots show less clear differentiation, suggesting that weight is
not as strong of an independent predictor for beak and spur
characteristics. However, when combined with other variables, it can
still provide valuable insights.
Species and Clusters
Finally, by including these measurements in the clustering analysis, we
can infer that there are three main clusters corresponding to the three
hawk species. The grouping observed in the plots confirms that physical
characteristics have a significant impact on species classification.
DBSCAN
Now, let’s move on to the second algorithm, DBSCAN.
We are not sure what epsilon value to use, so we referred to this
reference: How
to find optimal epsilon value
Looking at the k-distance graph (we used 9 as indicated by
minPts - 1 = k), we can see that the curve remains
relatively flat for most of the points but starts to increase sharply
towards the end. The point where the slope of the graph changes sharply
is between 0.4 and 0.7 on the axis. This suggests that the mean should
be around 0.55.
k <- 9
kNNdistplot(hawks_scaled2, k = k)
The clusters contain 559, 60, and
258 points respectively, highlighting the structure of
the data in specific densities and confirming the effectiveness of this
epsilon value.
res <- extractDBSCAN(res, eps_cl = 0.55)
res## OPTICS ordering/clustering for 908 objects.
## Parameters: minPts = 10, eps = 3.07488223798005, eps_cl = 0.55, xi = NA
## The clustering contains 3 cluster(s) and 31 noise points.
##
## 0 1 2 3
## 31 559 60 258
##
## Available fields: order, reachdist, coredist, predecessor, minPts, eps,
## eps_cl, xi, clusterWe plotted the data and can clearly see the 3 clusters and the corresponding noise.
plot(res)
We also plotted it additionally, where it is even clearer.
hullplot(hawks_scaled2, res)
We will perform the same process but including our dummy variables for sex and age.
hawks_scaled## Wing Weight Culmen Hallux Sex_M Sex_F Age_A Age_I
## 1 0.72901533 0.323037860 0.53643756 0.58802795 0 0 0 1
## 2 0.63453308 0.344646534 0.68899769 0.84440031 0 0 0 1
## 3 0.68702322 0.474298581 0.67363520 0.73239710 0 0 0 1
## 4 -0.53074792 -0.649352494 -0.42394592 -0.20600240 0 1 0 1
## 5 -1.16062955 -1.297612730 -1.27457130 -1.31283258 0 1 0 1
## 6 1.01246206 0.690385326 0.92059096 0.84067397 0 0 0 1
## 7 0.57154492 0.409472558 0.48155851 0.58802795 0 0 0 1
## 8 0.62403506 0.182581475 0.74223402 0.57599719 0 0 1 0
## 9 1.01246206 0.949689421 1.03034907 0.73239710 0 0 1 0
## 10 0.93897587 0.755211350 0.57759685 0.60005871 0 0 0 1
## 11 0.81299955 0.517515930 0.61875615 0.67224329 0 0 0 1
## 12 0.58204295 0.517515930 0.49527827 0.53990490 0 0 0 1
## 13 0.78150546 0.755211350 0.97547001 0.68427405 0 0 1 0
## 14 0.81299955 0.844699836 0.87943166 0.64818176 0 0 1 0
## 15 1.05445417 0.863254723 0.64619568 1.05722770 0 0 0 1
## 16 1.26441471 1.338645562 1.19498624 1.05722770 0 0 1 0
## 17 1.07545022 0.820037374 0.72851426 0.69630482 0 0 0 1
## 18 0.68702322 0.387863883 0.97547001 0.44365880 0 0 1 0
## 19 0.65552914 0.301429185 0.53643756 0.35944346 0 0 0 1
## 20 0.84449363 0.517515930 0.30320157 0.20304354 0 0 0 1
## 21 0.87598771 0.647167977 0.63247591 0.72036634 0 0 0 1
## 22 1.05445417 0.906472072 0.96175025 0.76848939 0 0 0 1
## 23 1.04395614 -1.446712584 0.42667945 0.66021253 0 0 0 1
## 24 0.80250152 1.208993515 0.71479450 0.61208948 0 0 1 0
## 25 0.67652519 0.474298581 0.57759685 0.57599719 0 0 0 1
## 26 -1.49656641 -1.448873451 -1.42396428 -1.31993010 1 0 0 1
## 27 0.87598771 0.711994001 0.60503638 0.87676626 0 0 0 1
## 28 0.89698376 0.906472072 0.93431072 0.76848939 0 0 1 0
## 29 -1.16062955 -1.276004055 -1.38432941 -1.22861724 0 1 0 1
## 30 1.16993247 1.554732307 1.14010718 0.86473550 0 0 0 1
## 31 0.83399560 0.582341954 0.72851426 0.74442787 0 0 1 0
## 32 0.48756071 0.106951114 0.42667945 0.32335117 0 0 0 1
## 33 0.84449363 0.560733279 0.57759685 0.53990490 0 0 1 0
## 34 0.79200349 1.144167491 0.50899803 0.86473550 0 0 1 0
## 35 1.02296009 1.576340982 0.64619568 0.73239710 0 0 1 0
## 36 0.58204295 0.668776652 0.48155851 0.23913583 0 0 1 0
## 37 0.72901533 1.187384840 0.75595379 0.58802795 0 0 1 0
## 38 0.65552914 1.554732307 0.49527827 0.73239710 0 0 1 0
## 39 1.05445417 1.576340982 1.00290954 0.67224329 0 0 1 0
## 40 -1.28660587 -1.448873451 -1.71360375 -1.31993010 1 0 0 1
## 41 -1.51756247 -1.474803861 -1.65872469 -1.64969394 1 0 0 1
## 42 -0.86668479 -0.964839142 -0.79437955 -0.71129444 0 0 0 1
## 43 0.71851730 0.625559303 0.59131662 0.72036634 0 0 0 1
## 44 0.69752125 0.798428699 0.45411898 0.50381261 0 0 0 1
## 45 0.78150546 0.560733279 0.79711308 0.61208948 0 0 0 1
## 46 0.78150546 0.495907256 0.45411898 0.37147422 0 0 0 1
## 47 0.81299955 0.603950628 0.94803048 0.55193566 0 0 0 1
## 48 0.65552914 0.582341954 0.60503638 0.72036634 0 0 0 1
## 49 0.86548968 0.733602675 0.64619568 0.68427405 0 0 0 1
## 50 1.01246206 1.144167491 0.83827237 0.76247401 0 0 0 1
## 51 0.88648573 0.452689907 0.53643756 0.49178185 0 0 0 1
## 52 1.11744233 0.755211350 0.63247591 0.37147422 0 0 0 1
## 53 -1.19212363 -1.375403958 -1.28829106 -1.38501716 0 1 0 1
## 54 0.82349757 1.079341468 0.82455261 0.76848939 0 0 0 1
## 55 0.56104690 0.236603161 0.44039921 0.15492049 0 0 0 1
## 56 -0.66722227 -0.930265263 -0.79437955 -0.53083300 0 1 0 1
## 57 -0.79319860 -0.930265263 -0.78065979 -0.71129444 1 0 1 0
## 58 0.99146601 1.046928456 1.08522813 0.74442787 0 0 0 1
## 59 -0.78270057 1.187384840 0.93431072 1.34596601 0 0 0 1
## 60 0.97046995 1.187384840 1.12638742 0.98504313 0 0 0 1
## 61 -2.92219849 0.884863397 -0.21814946 0.17296663 0 0 0 1
## 62 0.67652519 -0.022700933 0.37180039 0.10679744 0 0 0 1
## 63 0.84449363 1.036124119 0.65991544 0.87676626 0 0 0 1
## 64 0.10963173 0.661124977 0.46783874 0.29928964 0 0 0 1
## 65 -1.65403682 -1.448873451 -1.50780728 -1.77000157 1 0 0 1
## 66 1.05445417 1.144167491 0.75595379 0.90082778 0 0 0 1
## 67 -0.46775976 -0.638548157 -0.49254474 -0.05561786 0 1 0 1
## 68 -1.46507233 -1.448873451 -1.64500493 -1.69781700 1 0 1 0
## 69 -1.27610784 -1.340003865 -1.42548870 -1.32486335 0 1 1 0
## 70 0.78150546 0.668776652 1.15382695 0.46772032 0 0 1 0
## 71 0.79200349 0.776820025 0.63247591 0.50381261 0 0 1 0
## 72 0.75001138 0.841646048 0.68735497 0.69630482 0 0 1 0
## 73 1.09644628 1.241406527 1.05778860 1.09331999 0 0 0 1
## 74 1.25391668 1.327841225 1.48310128 0.64818176 0 0 1 0
## 75 0.88648573 0.949689421 0.50899803 0.40756651 0 0 1 0
## 76 0.86548968 1.479101947 0.85199214 0.75645863 0 0 0 1
## 77 0.83399560 0.884863397 0.44039921 0.44365880 0 0 0 1
## 78 0.99146601 1.576340982 0.72851426 0.96098160 0 0 0 1
## 79 0.56104690 0.549928942 0.72851426 0.75645863 0 0 0 1
## 80 0.59254098 0.344646534 0.59131662 0.70833558 0 0 0 1
## 81 1.04395614 1.273819539 0.93431072 0.99707389 0 0 0 1
## 82 1.01246206 1.046928456 0.81083284 0.88879702 0 0 0 1
## 83 -1.16062955 -1.245751911 -1.26085153 -1.30080182 0 1 0 1
## 84 -1.17112757 -1.321382272 -1.27457130 -1.25267877 0 1 0 1
## 85 -1.52806050 -1.470482126 -1.68616422 -1.67375547 1 0 0 1
## 86 -0.86668479 -0.930265263 -0.54742380 -0.69926368 1 0 1 0
## 87 0.62403506 0.636363640 0.56387709 0.57599719 0 0 0 1
## 88 0.72901533 0.766015687 -0.30046805 0.74442787 0 0 0 1
## 89 1.11744233 1.230602190 0.94803048 0.81661244 0 0 0 1
## 90 0.79200349 0.603950628 0.65991544 0.84067397 0 0 0 1
## 91 0.99146601 0.949689421 0.78339332 0.84440031 0 0 0 1
## 92 0.72901533 0.452689907 0.68735497 0.31132040 0 0 0 1
## 93 0.68702322 0.495907256 0.50899803 0.55193566 0 0 0 1
## 94 1.05445417 1.338645562 0.86571190 0.73239710 0 0 1 0
## 95 0.94947390 1.090145805 0.98918978 1.02113541 0 0 0 1
## 96 1.07545022 0.884863397 1.14010718 0.84440031 0 0 0 1
## 97 1.01246206 0.949689421 1.03034907 1.03316618 0 0 0 1
## 98 -1.12913547 -1.301934465 -1.24713177 -1.25267877 0 1 1 0
## 99 -1.12913547 -1.349473549 -1.37060964 -1.24064801 0 1 0 1
## 100 -1.47557036 -1.431586512 -1.61756540 -1.64969394 1 0 0 1
## 101 -1.57005260 -1.461838656 -1.68616422 -1.67375547 1 0 0 1
## 102 0.93897587 0.679580989 0.81083284 0.56396642 0 0 0 1
## 103 -1.23411574 -1.258717116 -1.31573059 -0.99462762 0 1 1 0
## 104 -1.21311968 -1.332186609 -1.28829106 -1.30080182 0 1 0 1
## 105 0.67652519 0.085342440 0.56387709 0.41959727 0 0 0 1
## 106 0.68702322 0.290624848 0.83827237 0.46772032 0 0 0 1
## 107 -1.53855852 -1.461838656 -1.75476304 -1.80609386 1 0 0 1
## 108 -0.58323806 -0.757395867 -0.30046805 -0.15787935 0 1 0 1
## 109 1.18043049 1.014515444 1.00290954 1.14144304 0 0 0 1
## 110 0.88648573 0.474298581 0.70107473 0.74442787 0 0 0 1
## 111 -0.53074792 -0.876243577 -0.68462144 -0.32631003 0 1 0 1
## 112 -1.45457431 -1.468321258 -1.59012587 -1.67375547 1 0 0 1
## 113 0.68702322 0.517515930 0.55015733 0.78052016 0 0 0 1
## 114 0.91797982 0.452689907 0.61875615 0.53990490 0 0 0 1
## 115 0.69752125 0.193385812 0.64619568 0.45568956 0 0 0 1
## 116 0.69752125 0.431081232 0.55015733 0.45568956 0 0 0 1
## 117 0.87598771 0.452689907 0.78339332 0.56396642 0 0 0 1
## 118 0.67652519 0.463494244 0.28948181 0.45568956 0 0 0 1
## 119 0.62403506 0.474298581 0.52271780 0.64818176 0 0 0 1
## 120 1.09644628 0.949689421 0.82455261 0.88879702 0 0 0 1
## 121 -1.52806050 -1.472642993 -1.80964209 -1.70984776 1 0 0 1
## 122 -1.45457431 -1.455356054 -1.61756540 -1.67375547 1 0 1 0
## 123 0.62403506 0.474298581 0.85199214 0.51584337 0 0 0 1
## 124 0.83399560 0.863254723 0.86571190 0.78052016 0 0 0 1
## 125 -1.52806050 -1.463999524 -1.60384563 -1.68578623 1 0 1 0
## 126 0.94947390 1.252210864 1.19498624 0.81661244 0 0 0 1
## 127 1.03345811 1.295428213 1.03034907 0.93692007 0 0 0 1
## 128 -1.49656641 -1.442390849 -1.65872469 -0.69926368 1 0 0 1
## 129 -1.11863744 -1.338669211 -1.31573059 -1.36095563 0 1 0 1
## 130 -1.45457431 -1.446712584 -1.57640611 -1.57750937 1 0 0 1
## 131 0.76050941 0.463494244 0.70107473 0.55193566 0 0 0 1
## 132 -0.40477160 0.366255209 0.64619568 0.62412024 0 0 0 1
## 133 1.12794036 1.165776166 0.76967355 1.06925847 0 0 0 1
## 134 0.51905479 0.571537617 0.59131662 0.67224329 0 0 0 1
## 135 0.70801927 0.420276895 0.59131662 0.79255092 0 0 0 1
## 136 0.79200349 0.766015687 0.49527827 0.68427405 0 0 0 1
## 137 0.77100744 0.441885569 0.63247591 0.61208948 0 0 0 1
## 138 0.80250152 0.798428699 0.60503638 0.55193566 0 0 0 1
## 139 0.62403506 0.387863883 0.48155851 0.56396642 0 0 0 1
## 140 0.99146601 0.949689421 0.86571190 0.44365880 0 0 0 1
## 141 -1.43357825 -1.459677789 -1.50780728 -1.63766318 1 0 0 1
## 142 -1.50706444 -1.472642993 -1.69988398 -1.73390928 1 0 0 1
## 143 -1.19212363 -1.243591043 -1.28829106 -1.33689411 0 1 1 0
## 144 -1.48606839 -1.463999524 -1.68616422 -1.70984776 1 0 0 1
## 145 1.11744233 0.938885083 0.96175025 0.73239710 0 0 0 1
## 146 0.72901533 0.593146291 0.79711308 0.27522812 0 0 0 1
## 147 0.49805873 0.690385326 0.65991544 0.43162803 0 0 0 1
## 148 1.41138709 0.906472072 1.16754671 0.91285855 0 0 0 1
## 149 0.67652519 0.409472558 0.52271780 0.58802795 0 0 0 1
## 150 0.72901533 0.398668220 0.61875615 0.58802795 0 0 0 1
## 151 0.72901533 0.733602675 0.39923992 0.60005871 0 0 0 1
## 152 -1.51756247 -1.448873451 -0.36906687 -1.64969394 1 0 0 1
## 153 0.67652519 0.279820510 0.30320157 0.15492049 0 0 0 1
## 154 0.71851730 0.657972315 0.64619568 0.66021253 0 0 0 1
## 155 0.60303900 0.452689907 0.83827237 0.82864321 0 0 0 1
## 156 0.68702322 0.366255209 0.82455261 1.08128923 0 0 0 1
## 157 0.49805873 0.647167977 0.52271780 0.62412024 0 0 0 1
## 158 0.98096798 0.755211350 1.04406883 0.76848939 0 0 0 1
## 159 0.78150546 0.625559303 0.79711308 0.45568956 0 0 1 0
## 160 -1.17112757 -1.301934465 -1.32945035 -1.31283258 0 1 0 1
## 161 -1.24461376 -1.209017164 -1.41176894 -1.36095563 0 1 0 1
## 162 1.09644628 0.766015687 0.74223402 0.26319735 0 0 0 1
## 163 0.68702322 0.711994001 0.71479450 0.35944346 0 0 0 1
## 164 0.97046995 1.273819539 1.12638742 1.04519694 0 0 0 1
## 165 0.76050941 0.485102918 0.67363520 0.66021253 0 0 0 1
## 166 0.86548968 0.701189664 -0.09467158 0.74442787 0 0 1 0
## 167 -1.11863744 -1.241430176 -1.32945035 -1.27674029 0 1 0 1
## 168 -1.11863744 -1.284647525 -1.38432941 -1.21658648 0 1 0 1
## 169 0.82349757 0.657972315 0.50899803 0.53990490 0 0 1 0
## 170 -1.17112757 -1.276004055 -1.30201082 -1.20455572 0 1 1 0
## 171 -1.17112757 -1.310577934 -1.30201082 -1.31283258 0 1 0 1
## 172 -1.11863744 -1.323543139 -1.31573059 -1.30080182 0 1 0 1
## 173 0.82349757 0.798428699 0.68735497 0.47975108 0 0 0 1
## 174 1.05445417 1.014515444 0.83827237 0.79255092 0 0 0 1
## 175 1.35889695 1.500710621 1.08522813 1.12941228 0 0 0 1
## 176 -1.11863744 -1.299773597 -1.32945035 -1.28877106 0 1 0 1
## 177 0.76050941 0.722798338 0.67363520 0.44365880 0 0 0 1
## 178 0.85499165 0.517515930 0.72851426 0.74442787 0 0 0 1
## 179 0.71851730 0.657972315 0.61875615 0.63615100 0 0 0 1
## 180 0.66602717 0.625559303 0.83827237 0.68427405 0 0 0 1
## 181 0.81299955 0.528320267 0.79711308 0.70833558 0 0 0 1
## 182 0.73951336 0.711994001 0.57759685 0.60005871 0 0 0 1
## 183 0.85499165 0.517515930 0.44039921 0.64818176 0 0 0 1
## 184 0.69752125 0.495907256 0.61875615 0.58802795 0 0 0 1
## 185 0.73951336 0.452689907 0.49527827 0.60005871 0 0 0 1
## 186 1.06495220 1.014515444 0.94803048 0.86473550 0 0 0 1
## 187 0.91797982 1.273819539 0.83827237 0.94895084 0 0 0 1
## 188 -0.80369663 -1.269521453 -0.61602262 -0.72332520 1 0 1 0
## 189 0.89698376 1.371058574 1.00290954 0.84440031 0 0 0 1
## 190 0.64503111 0.614754966 0.71479450 0.46772032 0 0 1 0
## 191 1.22242260 1.943688449 0.72851426 0.92488931 0 0 1 0
## 192 0.78150546 1.036124119 0.60503638 0.63615100 0 0 0 1
## 193 0.68702322 0.560733279 0.48155851 0.56396642 0 0 0 1
## 194 0.91797982 0.582341954 0.68899769 0.56396642 0 0 0 1
## 195 -1.07664533 -1.254395381 -1.31573059 -1.16846343 0 1 0 1
## 196 -1.50706444 -1.438069114 -1.61756540 -1.73390928 1 0 0 1
## 197 0.78150546 0.690385326 0.60503638 0.43162803 0 0 0 1
## 198 -1.17112757 -1.254395381 -1.37060964 -1.36095563 0 1 0 1
## 199 0.73951336 0.603950628 0.90687119 0.50381261 0 0 1 0
## 200 0.90748179 0.733602675 0.59131662 0.57599719 0 0 0 1
## 201 -1.20262166 -1.219821501 -1.32945035 -1.40907869 0 1 0 1
## 202 -1.19212363 -1.243591043 -1.32945035 -1.25267877 0 1 0 1
## 203 0.61353703 0.517515930 0.42667945 0.58802795 0 0 1 0
## 204 0.44556860 0.236603161 0.33064110 0.41959727 0 0 0 1
## 205 0.57154492 0.625559303 0.34436087 0.55193566 0 0 0 1
## 206 0.78150546 0.323037860 0.53643756 0.57599719 0 0 0 1
## 207 0.86548968 0.917276409 0.60503638 0.55193566 0 0 0 1
## 208 0.46656465 0.258211836 0.57759685 0.38350498 0 0 0 1
## 209 0.41407452 0.279820510 0.48155851 0.45568956 0 0 0 1
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## 722 -1.31809995 -1.276004055 -1.31573059 -1.32486335 0 1 0 1
## 723 0.72901533 0.982102432 0.82455261 0.81661244 0 0 0 1
## 724 -1.57005260 -1.427264777 -1.61756540 -1.60157089 1 0 0 1
## 725 -1.24461376 -1.308417067 -1.31573059 -1.24064801 0 1 1 0
## 726 0.57154492 0.323037860 0.61875615 0.81661244 0 0 0 1
## 727 -1.31809995 -1.297612730 -1.34317012 -1.22861724 0 1 0 1
## 728 0.88648573 1.176580503 1.07150836 1.05722770 0 0 0 1
## 729 -1.61204471 -1.448873451 -1.69988398 -1.69781700 1 0 0 1
## 730 -1.27610784 -1.330025742 -1.27457130 -1.28877106 0 1 0 1
## 731 0.83399560 0.830841711 1.11266765 1.10535075 0 0 0 1
## 732 0.91797982 0.841646048 0.98918978 0.85270473 0 0 0 1
## 733 0.73951336 0.398668220 0.83827237 0.62412024 0 0 0 1
## 734 -1.28660587 -1.254395381 -1.19225271 -1.24064801 0 1 1 0
## 735 -1.18162560 -1.276004055 -1.09621436 -1.26470953 0 1 1 0
## 736 -1.64353879 -1.470482126 -1.61756540 -1.64969394 1 0 1 0
## 737 -1.60154668 -1.448873451 -1.64500493 -1.62563242 1 0 0 1
## 738 -1.30760193 -1.254395381 -1.28829106 -1.25267877 1 0 1 0
## 739 -1.57005260 -1.438069114 -1.57640611 -1.58954013 1 0 0 1
## 740 0.47706268 0.560733279 0.71479450 0.63615100 0 0 0 1
## 741 -0.58323806 -0.444070086 -0.28674828 3.52353409 0 1 1 0
## 742 -0.85618676 -0.843830565 -1.28829106 -0.39849461 1 0 1 0
## 743 0.64503111 0.582341954 0.86571190 0.68427405 0 0 0 1
## 744 0.47706268 0.301429185 0.34436087 0.27522812 0 0 0 1
## 745 0.62403506 0.506711593 0.57759685 0.87676626 0 0 0 1
## 746 -1.28660587 -1.276004055 -1.35688988 -1.31283258 0 1 0 1
## 747 -1.25511179 -1.286808392 -1.28829106 -1.15643267 0 1 0 1
## 748 -1.64353879 -1.438069114 -1.64500493 -1.70984776 1 0 0 1
## 749 -1.29710390 -1.254395381 -1.37060964 -1.32486335 0 1 0 1
## 750 0.89698376 1.036124119 0.87943166 1.21362762 0 0 0 1
## 751 -1.23411574 -1.265199718 -1.26085153 -1.20455572 0 1 0 1
## 752 0.95997192 1.090145805 0.78339332 1.02113541 0 0 0 1
## 753 -1.61204471 -1.438069114 -1.64500493 -1.52938631 1 0 0 1
## 754 -1.53855852 -0.282005027 -0.69834120 -0.19397164 0 1 1 0
## 755 -1.54905655 -1.448873451 -1.54896658 -1.74594005 1 0 0 1
## 756 -1.54905655 -1.438069114 -1.52152705 -1.63766318 1 0 1 0
## 757 -0.97166506 -0.822221890 -0.80809932 -0.55489452 1 0 1 0
## 758 0.62403506 0.560733279 0.70107473 0.73239710 0 0 0 1
## 759 0.94947390 1.122558817 1.03034907 0.97301236 0 0 1 0
## 760 0.73951336 0.539124605 0.70107473 0.76848939 0 0 0 1
## 761 -1.63304077 -1.438069114 -1.63128516 -1.66172471 1 0 1 0
## 762 0.65552914 0.614754966 0.64619568 0.56396642 0 0 0 1
## 763 -1.28660587 -1.265199718 -1.30201082 -1.25267877 0 1 1 0
## 764 0.66602717 0.517515930 0.44039921 0.49178185 0 0 0 1
## 765 0.50855676 0.528320267 0.42667945 0.51584337 0 0 0 1
## 766 0.36158438 0.744407013 1.05778860 0.61208948 0 0 1 0
## 767 0.67652519 1.187384840 0.67363520 0.76848939 0 0 0 1
## 768 0.83399560 0.884863397 1.16754671 0.98504313 0 0 1 0
## 769 0.59254098 0.809233036 0.56387709 0.84067397 0 0 0 1
## 770 0.63453308 0.485102918 0.85199214 0.60005871 0 0 0 1
## 771 0.54005084 0.593146291 0.59131662 0.63615100 0 0 0 1
## 772 -0.89817887 -0.930265263 -0.79437955 -0.68723291 1 0 0 1
## 773 0.52955281 0.355450871 0.53643756 0.22710506 0 0 0 1
## 774 0.73951336 0.636363640 0.59131662 0.69630482 0 0 0 1
## 775 0.62403506 0.733602675 0.81083284 0.73239710 0 0 0 1
## 776 -1.22361771 -1.254395381 -1.34317012 -1.20455572 0 1 0 1
## 777 0.93897587 1.046928456 0.83827237 0.79255092 0 0 1 0
## 778 0.58204295 0.528320267 0.42667945 0.38350498 0 0 1 0
## 779 -1.28660587 -1.254395381 -1.31573059 -1.20455572 0 1 0 1
## 780 0.36158438 0.409472558 0.65991544 0.56396642 0 0 0 1
## 781 -1.28660587 -1.232786706 -1.43920846 -1.40907869 0 1 0 1
## 782 0.55054887 0.690385326 0.75595379 0.62412024 0 0 1 0
## 783 -1.37059009 -1.297612730 -1.34317012 -1.26470953 1 0 0 1
## 784 0.59254098 0.679580989 0.49527827 0.55193566 0 0 0 1
## 785 0.84449363 0.636363640 0.81083284 0.57599719 0 0 0 1
## 786 0.51905479 0.766015687 0.70107473 0.49178185 0 0 0 1
## 787 0.61353703 0.603950628 0.50899803 0.61208948 0 0 0 1
## 788 -0.65672425 -0.530504784 -0.31418781 -0.20600240 0 1 0 1
## 789 0.59254098 0.452689907 0.63247591 0.45568956 0 0 0 1
## 790 0.63453308 0.884863397 0.35808063 0.66021253 0 0 0 1
## 791 -1.57005260 -1.416460440 -1.63128516 -1.63766318 1 0 0 1
## 792 0.56104690 0.701189664 0.65991544 0.38350498 0 0 0 1
## 793 0.79200349 1.208993515 0.68735497 0.58802795 0 0 1 0
## 794 -1.28660587 -1.265199718 -1.32945035 -1.24064801 0 1 0 1
## 795 0.85499165 0.711994001 0.04252606 0.43162803 0 0 1 0
## 796 0.52955281 0.744407013 0.72851426 -0.50677147 0 0 0 1
## 797 0.72901533 1.360254237 1.16754671 0.97301236 0 0 1 0
## 798 0.88648573 0.874059060 0.79711308 0.88879702 0 0 0 1
## 799 -1.23411574 -1.265199718 -1.37060964 -1.21658648 0 1 0 1
## 800 0.51905479 0.431081232 0.56387709 0.76848939 0 0 1 0
## 801 -1.27610784 -1.297612730 -1.39804917 -1.34892487 0 1 0 1
## 802 -1.26560982 -1.286808392 -1.34317012 -1.15643267 0 1 0 1
## 803 -1.21311968 -1.308417067 -1.41176894 -1.28877106 0 1 0 1
## 804 0.71851730 1.057732793 0.93431072 0.87676626 0 0 0 1
## 805 -1.64353879 -1.427264777 -1.63128516 -1.69781700 1 0 0 1
## 806 -1.62254274 -1.448873451 -1.71360375 -1.64969394 1 0 0 1
## 807 -1.30760193 -1.254395381 -1.30201082 -1.25267877 0 1 0 1
## 808 -1.04515125 -1.005895624 -0.79437955 -0.57895605 1 0 0 1
## 809 -0.62523017 -0.562917796 -0.41022616 -0.23006392 0 1 0 1
## 810 -1.62254274 -1.470482126 -1.68616422 -1.67375547 1 0 0 1
## 811 0.84449363 0.917276409 0.71479450 -0.16991011 0 0 1 0
## 812 0.79200349 0.571537617 0.83827237 0.94895084 0 0 0 1
## 813 -1.63304077 -1.470482126 -1.78220257 -1.66172471 1 0 0 1
## 814 -1.39158614 -1.319221404 -1.24713177 -1.27674029 1 0 0 1
## 815 -1.67503287 -1.481286463 -1.65872469 -1.70984776 1 0 0 1
## 816 0.81299955 0.830841711 0.89315143 0.68427405 0 0 0 1
## 817 0.85499165 1.057732793 0.82455261 0.92488931 0 0 0 1
## 818 -1.64353879 -1.459677789 -1.76848280 -1.78203234 1 0 0 1
## 819 -0.63572819 -0.714178518 -0.43766569 -0.29021774 0 1 0 1
## 820 -1.24461376 -1.286808392 -1.61756540 -1.24064801 1 0 0 1
## 821 -1.02415519 -1.027504298 -0.78065979 -0.69926368 1 0 0 1
## 822 -1.25511179 -1.319221404 -1.26085153 -1.28877106 0 1 0 1
## 823 0.71851730 0.517515930 0.68735497 0.70833558 0 0 0 1
## 824 0.72901533 0.474298581 0.57759685 0.52787414 0 0 0 1
## 825 -1.41258220 -1.340830079 -1.42548870 -1.31283258 1 0 0 1
## 826 -0.95066901 -1.016699961 -0.79437955 -0.61504834 1 0 0 1
## 827 0.66602717 0.377059546 0.37180039 0.73239710 0 0 0 1
## 828 -1.20262166 -1.258717116 -1.38432941 -1.24064801 0 1 0 1
## 829 -1.62254274 -1.459677789 -1.53524681 -1.64969394 1 0 0 1
## 830 -0.89817887 -0.951873937 -0.83553885 -0.69926368 1 0 1 0
## 831 -1.64353879 -1.459677789 -1.63128516 -1.68578623 1 0 0 1
## 832 0.54005084 0.431081232 0.63247591 0.63615100 0 0 0 1
## 833 0.84449363 1.014515444 0.97547001 0.91285855 0 0 0 1
## 834 -1.66453485 -1.438069114 -1.61756540 -1.64969394 1 0 0 1
## 835 -1.30760193 -1.308417067 -1.41176894 -1.24064801 0 1 0 1
## 836 -1.30760193 -1.297612730 -1.32945035 -1.21658648 0 1 0 1
## 837 -1.54905655 -1.448873451 -1.59012587 -1.60157089 1 0 0 1
## 838 1.18043049 1.122558817 0.90687119 1.04519694 0 0 0 1
## 839 -0.66722227 -0.649352494 -0.31418781 0.38350498 0 1 1 0
## 840 -1.29710390 -1.286808392 -1.38432941 -1.32486335 0 1 1 0
## 841 -1.26560982 -1.243591043 -1.12365389 -1.34892487 0 1 1 0
## 842 -0.86668479 -0.941069600 -0.75322026 -0.47067918 1 0 1 0
## 843 0.50855676 0.820037374 0.59131662 0.35944346 0 0 1 0
## 844 0.57154492 0.409472558 0.49527827 0.62412024 0 0 0 1
## 845 0.88648573 0.776820025 0.89315143 0.50381261 0 0 0 1
## 846 0.62403506 0.333842197 0.49527827 0.40756651 0 0 0 1
## 847 0.86548968 0.938885083 0.79711308 0.98504313 0 0 0 1
## 848 0.72901533 0.582341954 0.74223402 0.75645863 0 0 0 1
## 849 -1.67503287 -1.448873451 -1.63128516 -1.68578623 1 0 0 1
## 850 -0.89817887 -0.941069600 -0.75322026 -0.66317139 1 0 0 1
## 851 -1.00315914 -0.941069600 -0.76694002 -0.62707910 1 0 0 1
## 852 -1.60154668 -1.438069114 -1.57640611 -1.62563242 1 0 0 1
## 853 0.63453308 0.193385812 0.52271780 0.57599719 0 0 0 1
## 854 0.46656465 0.355450871 0.55015733 0.57599719 0 0 0 1
## 855 0.59254098 0.517515930 0.34436087 0.45568956 0 0 1 0
## 856 0.88648573 1.111754480 1.08522813 0.99707389 0 0 0 1
## 857 -1.27610784 -1.211178032 -1.20597248 -1.28877106 0 1 1 0
## 858 0.57154492 0.128559789 0.24832252 0.31132040 0 0 0 1
## 859 -1.63304077 -1.459677789 -1.59012587 -1.68578623 1 0 0 1
## 860 0.91797982 1.252210864 0.85199214 0.91285855 0 0 0 1
## 861 0.62403506 0.517515930 0.44039921 0.67224329 0 0 0 1
## 862 0.60303900 0.409472558 0.81083284 0.87676626 0 0 0 1
## 863 0.72901533 1.295428213 0.63247591 0.47975108 0 0 0 1
## 864 -1.81150723 -1.297612730 -1.23341200 -1.36095563 0 1 0 1
## 865 -1.61204471 -1.448873451 -1.79592233 -1.66172471 1 0 0 1
## 866 0.80250152 1.036124119 0.93431072 0.92488931 0 0 0 1
## 867 0.59254098 0.312233522 0.39923992 0.35944346 0 0 0 1
## 868 0.62403506 0.171777138 0.44039921 0.33538193 0 0 0 1
## 869 1.04395614 1.111754480 1.04406883 1.05722770 0 0 0 1
## 870 -1.62254274 -1.459677789 -1.64500493 -1.62563242 1 0 1 0
## 871 0.67652519 0.506711593 0.71479450 0.76848939 0 0 1 0
## 872 1.00196403 0.971298095 0.86571190 0.90082778 0 0 1 0
## 873 -1.62254274 -1.459677789 -1.67244445 -1.54141708 1 0 1 0
## 874 -1.58055063 -1.448873451 -1.64500493 -1.58954013 1 0 0 1
## 875 0.81299955 1.068537131 0.89315143 0.90082778 0 0 0 1
## 876 0.57154492 0.539124605 0.38552016 0.57599719 0 0 0 1
## 877 -0.89817887 -0.887047914 -0.79437955 -0.37443308 1 0 1 0
## 878 0.51905479 0.269016173 0.37180039 0.44365880 0 0 0 1
## 879 0.58204295 0.841646048 0.53643756 0.38350498 0 0 0 1
## 880 0.88648573 1.760014715 0.98918978 1.03316618 0 0 0 1
## 881 0.69752125 0.798428699 0.42667945 0.76848939 0 0 1 0
## 882 0.58204295 0.744407013 0.48155851 0.47975108 0 0 1 0
## 883 0.57154492 0.809233036 0.49527827 0.60005871 0 0 1 0
## 884 -1.27610784 -1.265199718 -1.23341200 -1.25267877 0 1 1 0
## 885 0.33009030 0.474298581 0.48155851 0.55193566 0 0 1 0
## 886 0.49805873 0.377059546 0.37180039 0.84440031 0 0 0 1
## 887 -1.26560982 -1.308417067 -1.38432941 -1.28877106 0 1 0 1
## 888 0.80250152 0.560733279 0.61875615 0.34741269 0 0 1 0
## 889 -1.00315914 -0.973482612 -0.86297837 -0.68723291 1 0 0 1
## 890 -1.28660587 -1.438069114 -1.20597248 -1.15643267 0 1 0 1
## 891 0.51905479 0.474298581 0.63247591 0.57599719 0 0 0 1
## 892 0.75001138 0.636363640 0.85199214 0.90082778 0 0 1 0
## 893 0.88648573 0.603950628 0.59131662 0.53990490 0 0 0 1
## 894 0.48756071 0.150168463 0.19344346 0.10679744 0 0 0 1
## 895 -1.23411574 -1.254395381 -1.31573059 -1.13237114 0 1 0 1
## 896 -1.31809995 -1.232786706 -1.24713177 -1.22861724 0 1 0 1
## 897 -1.24461376 -1.265199718 -1.23341200 -1.15643267 0 1 0 1
## 898 0.57154492 0.495907256 0.70107473 0.74442787 0 0 1 0
## 899 -1.21311968 -1.265199718 -1.23341200 -1.20455572 0 1 0 1
## 900 0.46656465 1.198189178 0.60503638 0.64818176 0 0 1 0
## 901 0.52955281 0.377059546 0.48155851 0.23913583 0 0 1 0
## 902 0.90748179 1.252210864 0.94803048 0.69630482 0 0 1 0
## 903 0.52955281 0.074538103 0.23460275 0.05867438 0 0 0 1
## 904 0.67652519 1.630362668 0.57759685 0.28725888 0 0 0 1
## 905 -1.31809995 -1.286808392 -1.24713177 -1.18049419 0 1 0 1
## 906 0.46656465 0.042125091 0.01508653 0.28725888 0 0 0 1
## 907 0.56104690 0.193385812 0.46783874 0.33538193 0 0 0 1
## 908 -1.22361771 1.122558817 0.94803048 0.82864321 0 0 1 0res2 <- optics(hawks_scaled, minPts = 10)
res2## OPTICS ordering/clustering for 908 objects.
## Parameters: minPts = 10, eps = 3.40653377439247, eps_cl = NA, xi = NA
## Available fields: order, reachdist, coredist, predecessor, minPts, eps,
## eps_cl, xiThe data indicates that 3.47 is the maximum size to
consider the neighborhood between the data points, so the size has been
slightly increased.
We will print the order again for this new analysis.
res2$order## [1] 1 571 390 267 260 245 620 185 184 150 149 137 93 824 764 650 408 233
## [19] 193 25 236 481 426 467 317 787 771 594 281 12 87 378 134 119 861 844
## [37] 701 471 223 648 283 762 765 334 139 7 165 555 116 891 832 681 508 579
## [55] 532 131 11 784 295 206 876 561 364 80 323 337 157 823 717 473 270 3
## [73] 760 758 715 427 135 848 589 506 450 423 79 48 774 552 292 154 113 43
## [91] 403 182 179 556 526 178 90 355 544 740 707 309 726 528 437 342 854 550
## [109] 391 572 465 183 181 274 51 286 789 615 515 354 222 251 893 585 743 692
## [127] 582 483 649 336 155 180 338 853 489 110 733 504 45 617 770 560 290 2
## [145] 867 878 846 576 478 466 434 380 230 19 862 596 780 601 581 324 258 907
## [163] 240 868 674 117 676 537 32 205 21 412 200 177 173 138 49 672 559 114
## [181] 505 457 745 590 531 385 151 136 397 497 123 744 209 208 204 194 367 614
## [199] 540 558 369 153 694 118 719 147 55 608 775 207 10 92 344 472 197 27
## [217] 785 115 106 46 452 102 462 47 499 496 44 827 470 704 247 455 163 273
## [235] 886 261 812 566 501 392 105 773 631 798 847 658 632 485 428 300 226 124
## [253] 91 816 553 551 384 377 351 421 875 866 833 817 705 522 517 804 573 335
## [271] 732 529 262 492 388 54 564 541 350 716 502 441 254 752 389 246 174 82
## [289] 66 50 229 186 120 723 446 271 463 482 257 225 22 444 860 869 856 578
## [307] 220 97 95 60 728 567 252 164 127 81 73 217 158 718 592 6 591 241
## [325] 145 669 387 187 543 264 189 63 280 435 586 89 731 606 666 430 845 303
## [343] 17 792 750 133 769 534 366 418 140 786 109 652 382 192 510 879 790 706
## [361] 235 58 838 126 610 265 96 858 298 598 339 491 77 248 259 512 15 469
## [379] 146 297 373 894 156 20 721 76 767 484 333 629 407 343 665 376 255 232
## [397] 242 399 348 903 331 906 410 62 863 695 30 52 272 664 78 346 162 381
## [415] 554 714 244 612 148 456 64 880 345 479 667 175 411 498 904 296 282 88
## [433] 349 347 132 622 243 796 414 362 59 538 536 433 678 703 645 23 326 453
## [451] 266 33 888 487 855 778 679 402 365 696 883 881 671 898 782 647 460 871
## [469] 602 600 438 250 31 372 278 237 609 72 14 593 547 190 159 13 199 169
## [487] 285 203 800 605 294 892 616 525 405 691 682 71 514 882 275 28 872 777
## [505] 759 548 683 409 291 289 9 480 293 269 641 902 597 94 440 18 709 8
## [523] 75 332 70 843 36 607 468 436 256 406 401 24 793 584 37 34 901 768
## [541] 224 238 797 885 549 613 494 900 507 474 39 35 651 396 16 766 210 38
## [559] 795 74 191 700 166 356 811 359 603 476 398 539 322 699 908 490 361 330
## [577] 321 889 851 850 826 821 772 708 599 533 371 808 524 299 642 234 319 542
## [595] 814 825 820 783 618 488 360 315 284 26 231 837 874 852 829 739 724 791
## [613] 737 657 633 535 810 527 859 831 849 805 748 636 520 503 307 304 712 646
## [631] 626 422 314 308 655 419 659 311 417 627 587 834 628 815 302 638 495 41
## [649] 101 729 806 394 368 755 379 196 432 690 85 604 637 509 144 142 753 710
## [667] 574 100 698 865 813 661 112 212 130 818 65 107 363 141 121 713 213 40
## [685] 341 357 128 287 152 429 42 56 819 809 788 673 415 400 310 353 239 108
## [703] 67 4 249 530 711 111 640 327 328 685 899 897 751 779 836 807 802 794
## [721] 776 727 624 448 370 747 828 799 687 697 887 803 746 688 639 623 500 475
## [739] 313 219 523 416 621 214 630 595 202 801 749 29 374 276 722 228 176 171
## [757] 375 172 160 104 84 5 822 730 301 835 306 413 83 167 129 895 611 198
## [775] 905 896 218 168 99 227 684 464 312 625 340 161 693 53 781 195 201 216
## [793] 420 890 277 215 211 253 425 635 329 305 320 864 318 325 493 668 663 756
## [811] 580 575 570 562 870 761 565 451 449 670 654 125 268 386 736 656 122 68
## [829] 873 563 545 738 583 424 842 877 830 757 643 443 221 86 57 288 634 188
## [847] 742 358 763 884 857 734 660 519 513 458 439 431 675 518 461 404 143 619
## [865] 725 644 486 447 316 170 395 98 454 477 557 689 516 841 653 568 840 569
## [883] 546 735 677 69 662 103 383 352 393 702 839 686 680 588 577 459 445 442
## [901] 521 754 511 263 279 720 741 61It is clear that the number of valleys has increased considerably, as well as their size.
plot(res2, main= "Diagram reachability plot")
k <- 9
kNNdistplot(hawks_scaled, k = k)
We can see that the elbow continues to rise drastically, even a bit
later from 0.6 to 0.8, shifting to a mean of
0.7. We will introduce this new change in epsilon.
res2 <- extractDBSCAN(res2, eps_cl = 0.7)
res2## OPTICS ordering/clustering for 908 objects.
## Parameters: minPts = 10, eps = 3.40653377439247, eps_cl = 0.7, xi = NA
## The clustering contains 8 cluster(s) and 51 noise points.
##
## 0 1 2 3 4 5 6 7 8
## 51 438 115 110 18 93 27 14 42
##
## Available fields: order, reachdist, coredist, predecessor, minPts, eps,
## eps_cl, xi, clusterAs expected, the number of clusters changes radically, we now have 8 clusters and much more noise, as seen in the plot.
plot(res2)
Upon plotting, we see that the clusters themselves overlap, concluding that this analysis is not valid and is erroneous.
hullplot(hawks_scaled2, res2)## Warning in hullplot(hawks_scaled2, res2): Not enough colors. Some colors will
## be reused.
We return to our normalized dataset without the dummy attributes and change the epsilon value to 0.6 and 0.61, determining if we see significant changes since we are right on the limit.
res06 <- extractDBSCAN(res, eps_cl = 0.6)
res06## OPTICS ordering/clustering for 908 objects.
## Parameters: minPts = 10, eps = 3.07488223798005, eps_cl = 0.6, xi = NA
## The clustering contains 3 cluster(s) and 29 noise points.
##
## 0 1 2 3
## 29 559 61 259
##
## Available fields: order, reachdist, coredist, predecessor, minPts, eps,
## eps_cl, xi, clusterres61 <- extractDBSCAN(res, eps_cl = 0.61)
res61## OPTICS ordering/clustering for 908 objects.
## Parameters: minPts = 10, eps = 3.07488223798005, eps_cl = 0.61, xi = NA
## The clustering contains 2 cluster(s) and 28 noise points.
##
## 0 1 2
## 28 559 321
##
## Available fields: order, reachdist, coredist, predecessor, minPts, eps,
## eps_cl, xi, clusterConclusions ESP
The tests with eps_cl values of 0.55, 0.6, and 0.61 for the OPTICS algorithm provide a clear insight into the sensitivity of the epsilon parameter in cluster identification. With eps_cl = 0.55 and eps_cl = 0.6, OPTICS identifies 3 clusters, with a small variation in the number of noise points (31 and 29, respectively). However, when increasing eps_cl to 0.61, the number of clusters reduces to 2, and the noise points decrease to 28.
This indicates that the epsilon value within the range of 0.55 to 0.61 is a critical margin where small changes can significantly affect the clustering structure. This behavior suggests that the data has variable density, which is sensitive to epsilon adjustments, affecting the algorithm’s ability to differentiate between dense clusters and noise points.
In comparison, the DBSCAN and OPTICS methods show greater stability
and clarity in the clustering structure, consistently identifying three
main clusters with different eps_cl values. The average number of noise
points varied slightly, but the overall result was consistent with the
data structure.
This stability suggests that density-based methods like DBSCAN and
OPTICS may be more suitable for these specific data compared to
partition-based methods like k-means, especially due to their ability to
handle density variations and detect noise points.
Exercise 3: Comparison of k-means and DBSCAN Methods
- https://blogdatlas.wordpress.com/2024/04/06/clusterizacion-espacial-k-means-vs-dbscan-descripcion-y-ejemplo-practico-con-qgis-columna-de-investigacion-datlas/
- https://www.geeksforgeeks.org/difference-between-k-means-and-dbscan-clustering/
- https://www.kaggle.com/code/ahmedmohameddawoud/dbscan-vs-k-means-visualizing-the-difference
- https://hex.tech/blog/comparing-density-based-methods/
Comparison of k-means and DBSCAN Methods
Each of these clustering algorithms has its pros and cons. Choosing the best one depends on the structure and characteristics of the dataset and the purpose of the clustering. For example, if we want to group customers and need all the data to belong to a group, K-means is useful because it guarantees that each data point will belong to a cluster. On the other hand, if we want to filter noise and focus only on certain subsets, DBSCAN is better, as it allows ignoring isolated data points and focusing only on the most relevant ones, such as in an analysis of areas with prospect potential.
Comparison of Algorithms
K-means forms spherical clusters and requires specifying the number of groups beforehand. It is efficient with large datasets and is not affected by the variation in densities between points. However, it is sensitive to noise and outliers, which can distort the formation of clusters and make anomaly detection difficult. It only needs to define one parameter: the desired number of clusters (K).
On the other hand, DBSCAN creates irregularly shaped clusters of variable sizes without needing to specify the number of groups beforehand. Although not as efficient with high-dimensional data, it handles noise well and can mark certain points as “noise” or out of the clusters, making anomaly detection easier. However, it is sensitive to the choice of its two parameters: the neighborhood radius (R) and the minimum number of points (M) in that neighborhood, and it doesn’t perform well with sparse data or with highly variable densities.
Both algorithms have strengths: K-means works well on large, uniform data, while DBSCAN excels with complex densities and noise. The choice between them should be based on the type of data and the specific needs of the analysis.
Real-world Comparison
In a study conducted by Schubert et al. (2017), K-Means and DBSCAN
were compared on simulated datasets with different density and shape
configurations. The results showed that DBSCAN outperformed K-Means in
situations where clusters had different shapes and sizes, while K-Means
was more efficient in uniformly distributed data. This study illustrates
how the choice of algorithm can significantly affect data
interpretation.
A practical use case is in analyzing customer data in the retail sector.
If K-Means is used, the segmentation may be appropriate if customers
group consistently and without significant outliers. However, if the
data contains customers with extreme behaviors, DBSCAN could provide
better insights by identifying those outliers and preserving the
integrity of the main clusters.
Conclusion
The choice between K-Means and DBSCAN depends on the type of data and the application context. K-Means is preferable for well-structured and spherical data, while DBSCAN is the best choice for data with complex shapes and the presence of outliers. Understanding the characteristics of each algorithm allows analysts to select the most suitable one, thus improving the quality of the results and data-driven decision-making.
Comparison of k-means and DBSCAN Methods in Our Analysis
The analysis conducted concludes that, in the dataset used, three heterogeneous groups were identified, and DBSCAN and OPTICS methods outperformed K-means, especially in a dataset with much noise and variability. However, the results were not entirely satisfactory.
Comparison of Clustering Methods: K-means and DBSCAN
K-means: A prototype-based clustering method that seeks to minimize the variance within each group. While simple and effective, it requires knowing the number of clusters beforehand and tends to form circular clusters, which limits its usefulness in noisy datasets or datasets with complex shapes.
DBSCAN: A density-based method that groups points with a high concentration in their neighborhood, allowing the identification of non-linear clusters and handling noise and outliers well. However, it is sensitive to the input parameters, and its performance can be affected in high-dimensional datasets.
OPTICS was explored as an extension of DBSCAN, which allows identifying clusters with variable densities and represents the results graphically, facilitating analysis in contexts where clustering patterns are not obvious.
Final Conclusions in Comparison of Results
When applying both methods to a dataset of raptor birds, it was observed that K-means generated uniform clusters with good separation, while DBSCAN identified more complex and dense clusters and handled noise better. OPTICS provided a useful visual representation of the structure and density of the data.
Regarding cluster validation, both techniques showed good cohesion and separation according to the average silhouette index, indicating less compactness and separation between clusters.
Both methods can be useful, depending on the nature of the dataset and the research questions.