The project comes from a North Carolina, US company that manages workers’ compensation claims for other clients (name & location protected for confidentiality). This company wants you to advise them on how data analytics can be used to identify major drivers of costs of claims and the time to process claims. The company is interested in using data analytics to become efficient and responsive to claimants. The gist of workers’ compensation is as follows: When a worker of a participating company is injured in performance of her/his job, she/he can file a claim for the medical expenses and loss of wages related to the injury. When a claim is filed for the first time, a unique claim identifier is created and the details of the claims are recorded. The claim details are updated as payments are made to settle the claim. Payments can be made for various activities related to a claim, such as doctor visit, pharmacy, etc.

#Llamar Librerías
library(dplyr)
## 
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
library(ggplot2)
library(factoextra)
## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBa
library(rpart)
library(rpart.plot)
library(lubridate)
## 
## Attaching package: 'lubridate'
## The following objects are masked from 'package:base':
## 
##     date, intersect, setdiff, union
library(cluster)

Limpiar Base de Datos

bd1 <- read.csv("/Users/araquezada/Documents/Tec/7mo Semestre/Analítica para Negocios/Modulo 4/Actividad Análisis /ClaimsData2018 (1).csv")
bd2 <- read.csv("/Users/araquezada/Documents/Tec/7mo Semestre/Analítica para Negocios/Modulo 4/Actividad Análisis /TransactionsSummary2018.csv")

Juntar Bases de Datos y Filtrar

bd <- merge(bd1, bd2, by="ClaimID" , all=TRUE)

#Eliminar columas X
bdlimpia <- bd%>% select (- (X: X.22)) 

bdcabeza <- filter(bdlimpia, BodyPartRegion %in% c("Head"))
count(bdcabeza, BodyPartRegion, sort=TRUE)
##   BodyPartRegion     n
## 1           Head 12832
summary(bdcabeza)
##     ClaimID           TotalPaid         TotalReserves     TotalRecovery     
##  Min.   :  777635   Min.   :      0.0   Min.   :      0   Min.   :    0.00  
##  1st Qu.:  808894   1st Qu.:     36.2   1st Qu.:      0   1st Qu.:    0.00  
##  Median :  842276   Median :    157.6   Median :      0   Median :    0.00  
##  Mean   :10578303   Mean   :   3238.6   Mean   :   1230   Mean   :   59.17  
##  3rd Qu.:22721561   3rd Qu.:    501.0   3rd Qu.:      0   3rd Qu.:    0.00  
##  Max.   :62203645   Max.   :1353862.0   Max.   :1303215   Max.   :90357.52  
##                                                                             
##  IndemnityPaid      OtherPaid         ClaimStatus        IncidentDate      
##  Min.   :     0   Min.   :      0.0   Length:12832       Length:12832      
##  1st Qu.:     0   1st Qu.:     36.2   Class :character   Class :character  
##  Median :     0   Median :    156.0   Mode  :character   Mode  :character  
##  Mean   :  1415   Mean   :   1823.8                                        
##  3rd Qu.:     0   3rd Qu.:    484.0                                        
##  Max.   :450680   Max.   :1156503.6                                        
##                                                                            
##  IncidentDescription ReturnToWorkDate   AverageWeeklyWage  ClaimantOpenedDate
##  Length:12832        Length:12832       Length:12832       Length:12832      
##  Class :character    Class :character   Class :character   Class :character  
##  Mode  :character    Mode  :character   Mode  :character   Mode  :character  
##                                                                              
##                                                                              
##                                                                              
##                                                                              
##  ClaimantClosedDate EmployerNotificationDate ReceivedDate      
##  Length:12832       Length:12832             Length:12832      
##  Class :character   Class :character         Class :character  
##  Mode  :character   Mode  :character         Mode  :character  
##                                                                
##                                                                
##                                                                
##                                                                
##     IsDenied      ClaimantAge_at_DOI    Gender          ClaimantType      
##  Min.   :0.0000   Length:12832       Length:12832       Length:12832      
##  1st Qu.:0.0000   Class :character   Class :character   Class :character  
##  Median :0.0000   Mode  :character   Mode  :character   Mode  :character  
##  Mean   :0.0272                                                           
##  3rd Qu.:0.0000                                                           
##  Max.   :1.0000                                                           
##                                                                           
##  InjuryNature       BodyPartRegion       BodyPart         BillReviewALE     
##  Length:12832       Length:12832       Length:12832       Min.   : -456.00  
##  Class :character   Class :character   Class :character   1st Qu.:   16.00  
##  Mode  :character   Mode  :character   Mode  :character   Median :   24.00  
##                                                           Mean   :  177.61  
##                                                           3rd Qu.:   68.47  
##                                                           Max.   :16208.91  
##                                                           NA's   :10458     
##     Hospital        PhysicianOutpatient       Rx           
##  Min.   :-12570.4   Min.   :  -549.5    Min.   :     0.00  
##  1st Qu.:   205.3   1st Qu.:   109.0    1st Qu.:    22.50  
##  Median :   569.6   Median :   215.7    Median :    58.95  
##  Mean   :  4007.1   Mean   :  1595.5    Mean   :  1605.50  
##  3rd Qu.:  2124.9   3rd Qu.:   681.9    3rd Qu.:   185.10  
##  Max.   :194966.4   Max.   :310220.3    Max.   :210564.39  
##  NA's   :10878      NA's   :8003        NA's   :11076
glimpse(bdcabeza)
## Rows: 12,832
## Columns: 26
## $ ClaimID                  <int> 777635, 777647, 777649, 777650, 777677, 77768…
## $ TotalPaid                <dbl> 66.68, 60.01, 439.71, 45.99, 682.68, 58.93, 3…
## $ TotalReserves            <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
## $ TotalRecovery            <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
## $ IndemnityPaid            <dbl> 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.0…
## $ OtherPaid                <dbl> 66.68, 60.01, 439.71, 45.99, 682.68, 58.93, 3…
## $ ClaimStatus              <chr> "C", "C", "C", "C", "C", "C", "C", "C", "C", …
## $ IncidentDate             <chr> "01/07/99", "02/07/99", "02/07/99", "02/07/99…
## $ IncidentDescription      <chr> "EE. Alleges cleaning restroom in ninth floor…
## $ ReturnToWorkDate         <chr> "#VALUE!", "#VALUE!", "#VALUE!", "#VALUE!", "…
## $ AverageWeeklyWage        <chr> "NULL", "NULL", "NULL", "NULL", "NULL", "NULL…
## $ ClaimantOpenedDate       <chr> "16/07/99", "16/07/99", "19/07/99", "14/07/99…
## $ ClaimantClosedDate       <chr> "31/03/05", "31/03/05", "31/03/05", "31/03/05…
## $ EmployerNotificationDate <chr> "01/07/99", "02/07/99", "02/07/99", "02/07/99…
## $ ReceivedDate             <chr> "15/07/99", "15/07/99", "19/07/99", "14/07/99…
## $ IsDenied                 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
## $ ClaimantAge_at_DOI       <chr> "43", "NULL", "NULL", "NULL", "NULL", "NULL",…
## $ Gender                   <chr> "Female", "Male", "Male", "Female", "Female",…
## $ ClaimantType             <chr> "Medical Only", "Medical Only", "Medical Only…
## $ InjuryNature             <chr> "Poisoning?Chemical (Other Than Metals)", "Co…
## $ BodyPartRegion           <chr> "Head", "Head", "Head", "Head", "Head", "Head…
## $ BodyPart                 <chr> "Eyes", "Eyes", "Eyes", "Eyes", "Eyes", "Mult…
## $ BillReviewALE            <dbl> NA, NA, NA, 264, NA, NA, NA, NA, NA, NA, NA, …
## $ Hospital                 <dbl> NA, NA, NA, 730.14, NA, NA, 214.79, 189.05, N…
## $ PhysicianOutpatient      <dbl> NA, NA, NA, 3493.30, 0.00, 327.64, 361.98, 28…
## $ Rx                       <dbl> NA, NA, 15.16, 417.90, NA, NA, 19.99, NA, NA,…
Observaciones
  1. Total Paid, Indemity Paid, Other Paid, BillReviewALE, PhysicianOutPatient, Hospital, ClaimantAge_at_DOI tienen números negativos.
  2. Hay muchos NA’s.
  3. Las variables de fecha están en carácter

Cambiar a Fechas

bdcabeza$ClaimantOpenedDate <- as.Date(bdcabeza$ClaimantOpenedDate, format ="%d/%m/%y")
bdcabeza$ClaimantClosedDate <- as.Date(bdcabeza$ClaimantClosedDate, format ="%d/%m/%y")
bdcabeza$IncidentDate <- as.Date(bdcabeza$IncidentDate, format ="%d/%m/%y")
bdcabeza$EmployerNotificationDate <- as.Date(bdcabeza$EmployerNotificationDate, format ="%d/%m/%y")
bdcabeza$ReceivedDate <- as.Date(bdcabeza$ReceivedDate, format ="%d/%m/%y")
summary(bdcabeza)
##     ClaimID           TotalPaid         TotalReserves     TotalRecovery     
##  Min.   :  777635   Min.   :      0.0   Min.   :      0   Min.   :    0.00  
##  1st Qu.:  808894   1st Qu.:     36.2   1st Qu.:      0   1st Qu.:    0.00  
##  Median :  842276   Median :    157.6   Median :      0   Median :    0.00  
##  Mean   :10578303   Mean   :   3238.6   Mean   :   1230   Mean   :   59.17  
##  3rd Qu.:22721561   3rd Qu.:    501.0   3rd Qu.:      0   3rd Qu.:    0.00  
##  Max.   :62203645   Max.   :1353862.0   Max.   :1303215   Max.   :90357.52  
##                                                                             
##  IndemnityPaid      OtherPaid         ClaimStatus         IncidentDate       
##  Min.   :     0   Min.   :      0.0   Length:12832       Min.   :1976-10-29  
##  1st Qu.:     0   1st Qu.:     36.2   Class :character   1st Qu.:2000-06-20  
##  Median :     0   Median :    156.0   Mode  :character   Median :2005-01-19  
##  Mean   :  1415   Mean   :   1823.8                      Mean   :2005-03-21  
##  3rd Qu.:     0   3rd Qu.:    484.0                      3rd Qu.:2010-04-12  
##  Max.   :450680   Max.   :1156503.6                      Max.   :2014-06-26  
##                                                                              
##  IncidentDescription ReturnToWorkDate   AverageWeeklyWage  ClaimantOpenedDate  
##  Length:12832        Length:12832       Length:12832       Min.   :1986-09-03  
##  Class :character    Class :character   Class :character   1st Qu.:2000-07-20  
##  Mode  :character    Mode  :character   Mode  :character   Median :2005-02-25  
##                                                            Mean   :2005-04-28  
##                                                            3rd Qu.:2010-04-28  
##                                                            Max.   :2014-06-30  
##                                                                                
##  ClaimantClosedDate   EmployerNotificationDate  ReceivedDate       
##  Min.   :2000-03-08   Min.   :1976-10-30       Min.   :1986-09-03  
##  1st Qu.:2005-03-31   1st Qu.:2000-05-15       1st Qu.:2000-07-25  
##  Median :2007-04-12   Median :2005-03-31       Median :2005-02-22  
##  Mean   :2008-01-25   Mean   :2005-04-28       Mean   :2005-04-28  
##  3rd Qu.:2010-09-20   3rd Qu.:2010-09-18       3rd Qu.:2010-05-06  
##  Max.   :2014-06-30   Max.   :2014-06-26       Max.   :2033-09-18  
##  NA's   :369          NA's   :1184                                 
##     IsDenied      ClaimantAge_at_DOI    Gender          ClaimantType      
##  Min.   :0.0000   Length:12832       Length:12832       Length:12832      
##  1st Qu.:0.0000   Class :character   Class :character   Class :character  
##  Median :0.0000   Mode  :character   Mode  :character   Mode  :character  
##  Mean   :0.0272                                                           
##  3rd Qu.:0.0000                                                           
##  Max.   :1.0000                                                           
##                                                                           
##  InjuryNature       BodyPartRegion       BodyPart         BillReviewALE     
##  Length:12832       Length:12832       Length:12832       Min.   : -456.00  
##  Class :character   Class :character   Class :character   1st Qu.:   16.00  
##  Mode  :character   Mode  :character   Mode  :character   Median :   24.00  
##                                                           Mean   :  177.61  
##                                                           3rd Qu.:   68.47  
##                                                           Max.   :16208.91  
##                                                           NA's   :10458     
##     Hospital        PhysicianOutpatient       Rx           
##  Min.   :-12570.4   Min.   :  -549.5    Min.   :     0.00  
##  1st Qu.:   205.3   1st Qu.:   109.0    1st Qu.:    22.50  
##  Median :   569.6   Median :   215.7    Median :    58.95  
##  Mean   :  4007.1   Mean   :  1595.5    Mean   :  1605.50  
##  3rd Qu.:  2124.9   3rd Qu.:   681.9    3rd Qu.:   185.10  
##  Max.   :194966.4   Max.   :310220.3    Max.   :210564.39  
##  NA's   :10878      NA's   :8003        NA's   :11076

Cambiar a Numérico

bdcabeza$TotalPaid <- as.numeric(bdcabeza$TotalPaid)
bdcabeza$TotalReserves <- as.numeric(bdcabeza$TotalReserves)
bdcabeza$TotalRecovery <- as.numeric(bdcabeza$TotalRecovery)
glimpse(bdcabeza)
## Rows: 12,832
## Columns: 26
## $ ClaimID                  <int> 777635, 777647, 777649, 777650, 777677, 77768…
## $ TotalPaid                <dbl> 66.68, 60.01, 439.71, 45.99, 682.68, 58.93, 3…
## $ TotalReserves            <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
## $ TotalRecovery            <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
## $ IndemnityPaid            <dbl> 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.00, 0.0…
## $ OtherPaid                <dbl> 66.68, 60.01, 439.71, 45.99, 682.68, 58.93, 3…
## $ ClaimStatus              <chr> "C", "C", "C", "C", "C", "C", "C", "C", "C", …
## $ IncidentDate             <date> 1999-07-01, 1999-07-02, 1999-07-02, 1999-07-…
## $ IncidentDescription      <chr> "EE. Alleges cleaning restroom in ninth floor…
## $ ReturnToWorkDate         <chr> "#VALUE!", "#VALUE!", "#VALUE!", "#VALUE!", "…
## $ AverageWeeklyWage        <chr> "NULL", "NULL", "NULL", "NULL", "NULL", "NULL…
## $ ClaimantOpenedDate       <date> 1999-07-16, 1999-07-16, 1999-07-19, 1999-07-…
## $ ClaimantClosedDate       <date> 2005-03-31, 2005-03-31, 2005-03-31, 2005-03-…
## $ EmployerNotificationDate <date> 1999-07-01, 1999-07-02, 1999-07-02, 1999-07-…
## $ ReceivedDate             <date> 1999-07-15, 1999-07-15, 1999-07-19, 1999-07-…
## $ IsDenied                 <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
## $ ClaimantAge_at_DOI       <chr> "43", "NULL", "NULL", "NULL", "NULL", "NULL",…
## $ Gender                   <chr> "Female", "Male", "Male", "Female", "Female",…
## $ ClaimantType             <chr> "Medical Only", "Medical Only", "Medical Only…
## $ InjuryNature             <chr> "Poisoning?Chemical (Other Than Metals)", "Co…
## $ BodyPartRegion           <chr> "Head", "Head", "Head", "Head", "Head", "Head…
## $ BodyPart                 <chr> "Eyes", "Eyes", "Eyes", "Eyes", "Eyes", "Mult…
## $ BillReviewALE            <dbl> NA, NA, NA, 264, NA, NA, NA, NA, NA, NA, NA, …
## $ Hospital                 <dbl> NA, NA, NA, 730.14, NA, NA, 214.79, 189.05, N…
## $ PhysicianOutpatient      <dbl> NA, NA, NA, 3493.30, 0.00, 327.64, 361.98, 28…
## $ Rx                       <dbl> NA, NA, 15.16, 417.90, NA, NA, 19.99, NA, NA,…

Costo Total & Fechas

bdcabeza$Total_Incurred_Cost <- bdcabeza$TotalReserves + bdcabeza$TotalPaid - bdcabeza$TotalRecovery
bdcabeza$TP <- difftime(bdcabeza$ClaimantClosedDate, bdcabeza$ClaimantOpenedDate, units ="days")
bdcabeza$TP <- as.numeric(bdcabeza$TP)
summary(bdcabeza)
##     ClaimID           TotalPaid         TotalReserves     TotalRecovery     
##  Min.   :  777635   Min.   :      0.0   Min.   :      0   Min.   :    0.00  
##  1st Qu.:  808894   1st Qu.:     36.2   1st Qu.:      0   1st Qu.:    0.00  
##  Median :  842276   Median :    157.6   Median :      0   Median :    0.00  
##  Mean   :10578303   Mean   :   3238.6   Mean   :   1230   Mean   :   59.17  
##  3rd Qu.:22721561   3rd Qu.:    501.0   3rd Qu.:      0   3rd Qu.:    0.00  
##  Max.   :62203645   Max.   :1353862.0   Max.   :1303215   Max.   :90357.52  
##                                                                             
##  IndemnityPaid      OtherPaid         ClaimStatus         IncidentDate       
##  Min.   :     0   Min.   :      0.0   Length:12832       Min.   :1976-10-29  
##  1st Qu.:     0   1st Qu.:     36.2   Class :character   1st Qu.:2000-06-20  
##  Median :     0   Median :    156.0   Mode  :character   Median :2005-01-19  
##  Mean   :  1415   Mean   :   1823.8                      Mean   :2005-03-21  
##  3rd Qu.:     0   3rd Qu.:    484.0                      3rd Qu.:2010-04-12  
##  Max.   :450680   Max.   :1156503.6                      Max.   :2014-06-26  
##                                                                              
##  IncidentDescription ReturnToWorkDate   AverageWeeklyWage  ClaimantOpenedDate  
##  Length:12832        Length:12832       Length:12832       Min.   :1986-09-03  
##  Class :character    Class :character   Class :character   1st Qu.:2000-07-20  
##  Mode  :character    Mode  :character   Mode  :character   Median :2005-02-25  
##                                                            Mean   :2005-04-28  
##                                                            3rd Qu.:2010-04-28  
##                                                            Max.   :2014-06-30  
##                                                                                
##  ClaimantClosedDate   EmployerNotificationDate  ReceivedDate       
##  Min.   :2000-03-08   Min.   :1976-10-30       Min.   :1986-09-03  
##  1st Qu.:2005-03-31   1st Qu.:2000-05-15       1st Qu.:2000-07-25  
##  Median :2007-04-12   Median :2005-03-31       Median :2005-02-22  
##  Mean   :2008-01-25   Mean   :2005-04-28       Mean   :2005-04-28  
##  3rd Qu.:2010-09-20   3rd Qu.:2010-09-18       3rd Qu.:2010-05-06  
##  Max.   :2014-06-30   Max.   :2014-06-26       Max.   :2033-09-18  
##  NA's   :369          NA's   :1184                                 
##     IsDenied      ClaimantAge_at_DOI    Gender          ClaimantType      
##  Min.   :0.0000   Length:12832       Length:12832       Length:12832      
##  1st Qu.:0.0000   Class :character   Class :character   Class :character  
##  Median :0.0000   Mode  :character   Mode  :character   Mode  :character  
##  Mean   :0.0272                                                           
##  3rd Qu.:0.0000                                                           
##  Max.   :1.0000                                                           
##                                                                           
##  InjuryNature       BodyPartRegion       BodyPart         BillReviewALE     
##  Length:12832       Length:12832       Length:12832       Min.   : -456.00  
##  Class :character   Class :character   Class :character   1st Qu.:   16.00  
##  Mode  :character   Mode  :character   Mode  :character   Median :   24.00  
##                                                           Mean   :  177.61  
##                                                           3rd Qu.:   68.47  
##                                                           Max.   :16208.91  
##                                                           NA's   :10458     
##     Hospital        PhysicianOutpatient       Rx            Total_Incurred_Cost
##  Min.   :-12570.4   Min.   :  -549.5    Min.   :     0.00   Min.   :  -1521.2  
##  1st Qu.:   205.3   1st Qu.:   109.0    1st Qu.:    22.50   1st Qu.:     38.0  
##  Median :   569.6   Median :   215.7    Median :    58.95   Median :    160.2  
##  Mean   :  4007.1   Mean   :  1595.5    Mean   :  1605.50   Mean   :   4409.7  
##  3rd Qu.:  2124.9   3rd Qu.:   681.9    3rd Qu.:   185.10   3rd Qu.:    526.7  
##  Max.   :194966.4   Max.   :310220.3    Max.   :210564.39   Max.   :1869254.9  
##  NA's   :10878      NA's   :8003        NA's   :11076                          
##        TP        
##  Min.   :   0.0  
##  1st Qu.: 114.5  
##  Median : 684.0  
##  Mean   :1081.9  
##  3rd Qu.:1811.0  
##  Max.   :6544.0  
##  NA's   :369

Clusters

bdclusters <- select(bdcabeza, ClaimID, Total_Incurred_Cost, TP)
rownames(bdclusters) <- bdclusters$ClaimID
bdclusters <- subset(bdclusters, select= -c(ClaimID))

Eliminar NA’s

sum(is.na(bdclusters))
## [1] 369
sapply(bdclusters, function(x) sum(is.na(x)))
## Total_Incurred_Cost                  TP 
##                   0                 369
bdclusters <- na.omit(bdclusters)
sapply(bdclusters, function(x) sum(is.na(x)))
## Total_Incurred_Cost                  TP 
##                   0                   0

Eliminar outliers

bdclusters <- bdclusters[bdclusters$Total_Incurred_Cost > 0,]
boxplot(bdclusters$TP, horizontal = TRUE)

boxplot(bdclusters$Total_Incurred_Cost, horizontal = TRUE)

bdclusters <- bdclusters[bdclusters$TP < 5000,]
bdclusters <- bdclusters[bdclusters$Total_Incurred_Cost < 500000,]
boxplot(bdclusters$TP, horizontal = TRUE)

boxplot(bdclusters$Total_Incurred_Cost, horizontal = TRUE)

IQR

Columna Tiempo de Procesamiento

IQR_TP <- IQR(bdclusters$TP)
IQR_TP
## [1] 1587
summary(bdclusters)
##  Total_Incurred_Cost       TP      
##  Min.   :     1.4    Min.   :   3  
##  1st Qu.:   111.2    1st Qu.: 137  
##  Median :   233.7    Median : 687  
##  Mean   :  2359.8    Mean   :1041  
##  3rd Qu.:   694.0    3rd Qu.:1724  
##  Max.   :386860.2    Max.   :4639
LI_TP <- 137 - 1.5*IQR_TP
LI_TP
## [1] -2243.5
LS_TP <- 1724 + 1.5*IQR_TP
LS_TP
## [1] 4104.5
bdclusters <- bdclusters[bdclusters$TP < 4104.5,]
summary(bdclusters)
##  Total_Incurred_Cost       TP        
##  Min.   :     1.8    Min.   :   3.0  
##  1st Qu.:   111.7    1st Qu.: 135.0  
##  Median :   234.0    Median : 668.5  
##  Mean   :  2350.1    Mean   :1016.0  
##  3rd Qu.:   694.9    3rd Qu.:1696.0  
##  Max.   :386860.2    Max.   :4088.0

Columna Costo Total

IQR_TP2 <- IQR(bdclusters$Total_Incurred_Cost)
IQR_TP2
## [1] 583.2225
summary(bdclusters)
##  Total_Incurred_Cost       TP        
##  Min.   :     1.8    Min.   :   3.0  
##  1st Qu.:   111.7    1st Qu.: 135.0  
##  Median :   234.0    Median : 668.5  
##  Mean   :  2350.1    Mean   :1016.0  
##  3rd Qu.:   694.9    3rd Qu.:1696.0  
##  Max.   :386860.2    Max.   :4088.0
LI_TP2 <- 137 - 1.5*IQR_TP2
LI_TP2
## [1] -737.8338
LS_TP2 <- 1724 + 1.5*IQR_TP2
LS_TP2
## [1] 2598.834
bdclusters <- bdclusters[bdclusters$Total_Incurred_Cost < 2598.834,]
summary(bdclusters)
##  Total_Incurred_Cost       TP      
##  Min.   :   1.8      Min.   :   3  
##  1st Qu.: 102.0      1st Qu.: 129  
##  Median : 202.3      Median : 664  
##  Mean   : 407.0      Mean   :1020  
##  3rd Qu.: 466.1      3rd Qu.:1722  
##  Max.   :2597.7      Max.   :4088

Determinar el número de grupos

grupos <- 10

Realizar la clasificación y asignación de grupos

segmentos <- kmeans(bdclusters, grupos)
asignacion <- cbind(bdclusters, clauster=segmentos$cluster)
print(asignacion)
##          Total_Incurred_Cost   TP clauster
## 777635                 66.68 2085        9
## 777647                 60.01 2085        9
## 777649                439.71 2082        9
## 777650                 45.99 2087        9
## 777677                682.68 2024        9
## 777680                 58.93 2093        9
## 777685                371.57 2082        9
## 777697                 36.36 2089        9
## 777702                160.00 2075        9
## 777712                111.99 2058        9
## 777727                 66.68 2092        9
## 777739                202.24 2061        9
## 777740                130.78 2064        9
## 777751                190.06 2814        8
## 777756                 56.68 2080        9
## 777757                234.93 2079        9
## 777758                265.95 2079        9
## 777761                 91.97 2074        9
## 777764                303.05 2010        9
## 777767                162.35 2074        9
## 777770                109.69 3073        8
## 777774                182.00 3057        8
## 777784                124.76 2087        9
## 777839                131.76 2087        9
## 777844                311.55 2087        9
## 777897                 55.00 3009        8
## 777922                 95.28 2015        9
## 777958                 65.00 2079        9
## 777969                 50.01 2275        9
## 777991                161.27 2011        9
## 777993               1087.44 2078        1
## 777999                139.95 2073        9
## 778002                141.68 2071        9
## 778017               1181.51 2071        1
## 778024                850.89 2072        9
## 778034               1583.66 2058       10
## 778055                 30.00 2058        9
## 778060                 51.50 3359        8
## 778068                 96.00 2061        9
## 778074                121.61 2058        9
## 778079                166.02 2073        9
## 778081                 25.00 2071        9
## 778086                185.51 2039        9
## 778096                 76.86 2072        9
## 778130                363.55 2053        9
## 778149                198.66 2066        9
## 778150                383.71 2067        9
## 778151                 55.00 2067        9
## 778154               1920.55 2058       10
## 778159                 45.00 2058        9
## 778176                 59.70 2058        9
## 778184                153.14 2101        9
## 778196                 67.43 2057        9
## 778203                117.51 2057        9
## 778220                 88.29 2037        9
## 778224                387.07 2065        9
## 778234                 77.17 3053        8
## 778235                311.92 2058        9
## 778245                177.41 2066        9
## 778264                 86.66 1780        6
## 778292                665.32 2043        9
## 778293                821.51 2585        1
## 778299                314.08 2053        9
## 778309                137.10 2025        9
## 778315                176.27 2058        9
## 778316                245.59 2058        9
## 778318                 69.26 2060        9
## 778330                238.00 2040        9
## 778336                311.50 2061        9
## 778348                102.89 2046        9
## 778365                128.24 2015        9
## 778379                852.13 2046        9
## 778382                422.03 2040        9
## 778399                120.00 2025        9
## 778407                806.69 1771        4
## 778408                240.45 2038        9
## 778413                180.00 2870        8
## 778462                111.30 2038        9
## 778505                269.95 2051        9
## 778508                 68.23 2023        9
## 778510                 95.00 2004        9
## 778518                836.87 2050        9
## 778520                 47.53 2050        9
## 778534                815.37 2050        9
## 778554                102.36 1661        6
## 778558                131.62 2038        9
## 778563                 68.76 2011        9
## 778568                163.45 2030        9
## 778575                 71.27 2038        9
## 778587                 51.50 2823        8
## 778590                261.25 2038        9
## 778633                 62.24 2017        9
## 778634                142.95 2017        9
## 778649                326.49 2018        9
## 778653                145.20 2177        9
## 778657                605.83 2039        9
## 778666                 36.21 2015        9
## 778667                178.79 2036        9
## 778675                382.50 1834        6
## 778677                163.00 2017        9
## 778682                154.26 2039        9
## 778683                 56.68 2017        9
## 778688                167.72 1997        9
## 778692                206.10 2070        9
## 778697                 72.65 2019        9
## 778704                 35.98 2012        9
## 778713                136.49 2025        9
## 778715                159.20 2036        9
## 778735                 61.35 2015        9
## 778762                 66.92 2026        9
## 778769                382.09 1988        9
## 778804                 80.45 2030        9
## 778814                 58.41 1576        6
## 778845                253.35 1995        9
## 778866                 80.57 2026        9
## 778883                139.22 2016        9
## 778913                 60.01 2004        9
## 778917                155.75 2011        9
## 778922                467.50 1812        6
## 778928                134.04 2005        9
## 778938               1295.00 2018        1
## 778944                 92.72 2019        9
## 778945               1032.22 2019        1
## 778949                 79.50 2012        9
## 778952                 67.30 1497        6
## 779005                 38.37 2178        9
## 779031                145.66 2008        9
## 779036                247.45 2005        9
## 779040                173.49 2012        9
## 779075                  9.50 2005        9
## 779094                387.30 2010        9
## 779096                328.49 3072        8
## 779103                116.09 1997        9
## 779113                 13.09 2009        9
## 779124               1693.13 2005       10
## 779132                334.36 2011        9
## 779135                 24.67 1974        9
## 779136                232.77 1977        9
## 779138                239.87 1918        9
## 779203                389.30 1703        6
## 779204               1131.26 1968        1
## 779230                211.55 1991        9
## 779231                 41.00 2001        9
## 779235                346.86 1997        9
## 779254                 86.22 1946        9
## 779263                 60.00 1973        9
## 779319                251.75 1997        9
## 779338                852.67 1998        9
## 779346                177.55 1967        9
## 779352                 87.15 1998        9
## 779361                365.28 1989        9
## 779368                225.00 1967        9
## 779377                483.87 3176        8
## 779388                 56.68 1990        9
## 779394                 36.21 1996        9
## 779401                427.50 1966        9
## 779433                141.03 3230        8
## 779441                 50.01 1984        9
## 779466                187.37 1959        9
## 779472                337.25 1988        9
## 779477                 33.31 1976        9
## 779493                227.93 1989        9
## 779530               1848.80 1966       10
## 779535                168.84 1982        9
## 779562               1525.67 1837       10
## 779580                251.93 1967        9
## 779586                214.81 1962        9
## 779611                 38.00 1980        9
## 779612                160.94 1905        6
## 779625                 36.21 1976        9
## 779638                365.21 1977        9
## 779649                217.65 1877        6
## 779655                183.14 1919        9
## 779674                173.62 1976        9
## 779677                 51.16 3058        8
## 779685                138.02 1975        9
## 779690                 72.40 1970        9
## 779737                111.97 1932        9
## 779742                143.80 1945        9
## 779743                 40.28 1946        9
## 779795                212.09 1941        9
## 779802                240.00 1942        9
## 779811                 65.00 1956        9
## 779832                 96.41 1963        9
## 779835                138.52 1962        9
## 779851               1154.00 1940        1
## 779853                113.12 1935        9
## 779854                 14.09 1954        9
## 779895                108.00 1925        9
## 779928                405.92 1947        9
## 779950                 69.88 1959        9
## 780005                167.47 1954        9
## 780010                 51.16 1941        9
## 780022                245.29 1890        6
## 780036                 37.26 1949        9
## 780037               2476.03 1949       10
## 780042                 89.50 1948        9
## 780058                 97.11 1947        9
## 780109                168.41 1945        9
## 780110               1397.40 1945       10
## 780118                330.85 1946        9
## 780121                105.12 1919        9
## 780141                252.47 2201        9
## 780155                474.32 1941        9
## 780156                155.04 1941        9
## 780178                 86.00 1932        9
## 780181                 58.26 1926        9
## 780182                213.66 1942        9
## 780193               1290.05 3146        1
## 780195                331.42 1918        9
## 780219                796.48 2256        1
## 780231                 67.04 3125        8
## 780247                 55.00 3086        8
## 780251                221.15 1935        9
## 780253                250.12 1885        6
## 780270                205.12 1904        6
## 780276                811.75 1931        9
## 780283               1160.51 1913        1
## 780311                 88.29 1857        6
## 780332                948.89 1913        4
## 780342                213.46 1919        9
## 780353                183.24 2661        8
## 780395                188.00 1912        9
## 780405               1533.64 1918       10
## 780418                 38.50 1920        9
## 780428               2511.31 1918       10
## 780429                 69.00 1918        9
## 780435                344.00 1904        6
## 780452                 41.00 1918        9
## 780471                117.03 1850        6
## 780473                126.05 1918        9
## 780498                246.41 1854        6
## 780501                545.00 1861        6
## 780506               1328.82 1920       10
## 780564                 14.52 1627        6
## 780595                111.51 1822        6
## 780601                174.46 1865        6
## 780603                 91.97 1907        9
## 780621                138.56 2395        9
## 780629                128.81 1638        6
## 780646                116.62 1846        6
## 780649                127.29 1882        6
## 780661                146.00 1904        6
## 780670                 49.22 1872        6
## 780694                 49.84 1879        6
## 780706                154.62 1900        6
## 780710                441.67 1897        6
## 780735                187.14 2338        9
## 780761                175.00 1889        6
## 780767                394.03 1872        6
## 780802                179.32 1891        6
## 780810                346.61 1850        6
## 780819               1613.00 1858       10
## 780833                 25.00 2051        9
## 780840                429.50 1878        6
## 780841                308.51 1878        6
## 780876                611.21 1885        6
## 780909               1569.60 1875       10
## 780919                271.36 1889        6
## 780921                514.37 1890        6
## 780937               2161.93 1864       10
## 780940                260.07 1875        6
## 780945                611.00 2142        9
## 780965                127.91 1877        6
## 780976                847.00 1868        4
## 780982                193.10 1837        6
## 780994                700.85 1851        6
## 781001               1288.96 2515        1
## 781034                256.79 1872        6
## 781046                105.97 1850        6
## 781057               1006.90 2284        1
## 781064                268.06 1868        6
## 781076                 83.35 1877        6
## 781094                 41.00 1949        9
## 781117                182.88 1876        6
## 781157                275.08 1879        6
## 781173                 82.51 2368        9
## 781174                151.45 1826        6
## 781184                 50.00 1869        6
## 781190                100.00 1872        6
## 781207                202.07 1871        6
## 781212                474.05 3147        8
## 781213                 84.00 1874        6
## 781219               2561.09 1807       10
## 781243                464.00 2700        8
## 781258                710.62 1862        6
## 781259                149.57 1872        6
## 781262                 60.47 3132        8
## 781289                176.51 3081        8
## 781291                345.42 3002        8
## 781298                104.09 1861        6
## 781320                 98.70 1865        6
## 781325                181.44 1864        6
## 781330                 13.00 1868        6
## 781340                111.98 2422        9
## 781347                164.59 1728        6
## 781366                109.64 1850        6
## 781367                521.51 1849        6
## 781394                150.60 1861        6
## 781430                748.88 1829        6
## 781441                 66.38 2086        9
## 781455                155.00 1848        6
## 781459                201.65 1857        6
## 781461                  9.00 1862        6
## 781486                376.59 1840        6
## 781489                105.23 1851        6
## 781540                115.42 1854        6
## 781566                 41.90 1206        7
## 781575                 76.05 1854        6
## 781576                 35.00 1854        6
## 781594                 18.10 1829        6
## 781596                340.04 1854        6
## 781602                 71.47 1015        7
## 781609                173.96 1834        6
## 781611                 36.21 1843        6
## 781614                 14.09 1837        6
## 781625                 79.80 1836        6
## 781636                120.00 1836        6
## 781642                 53.31 1844        6
## 781654                152.80 1682        6
## 781655                135.08 1798        6
## 781662                 94.72 1847        6
## 781667                 59.40 1844        6
## 781672                281.51 1836        6
## 781673                116.21 1836        6
## 781687                 86.90 1842        6
## 781690                776.90 1848        6
## 781707                287.21 1841        6
## 781731                242.02 1802        6
## 781737                340.06 1836        6
## 781744               1355.77 1785       10
## 781750                 47.35 1819        6
## 781755                227.79 1842        6
## 781769                143.10 1835        6
## 781778                134.15 1785        6
## 781785                 61.40 1835        6
## 781787                135.95 2873        8
## 781811                 68.26 1835        6
## 781817                139.17 1835        6
## 781822                131.97 1829        6
## 781823                221.54 1835        6
## 781831                514.55 3137        8
## 781876                231.47 1829        6
## 781877                270.99 2626        9
## 781885                261.36 1834        6
## 781905                148.27 1834        6
## 781937                 96.21 1799        6
## 781941                157.59 1808        6
## 781952                 92.50 1820        6
## 781964                759.79 2691        1
## 781969                254.23 1737        6
## 781972                116.68 1829        6
## 781984                233.76 1800        6
## 781990                742.80 1829        6
## 781999                 66.40 1791        6
## 782021                103.08 1791        6
## 782022                128.51 1791        6
## 782036                 60.00 1791        6
## 782038                174.60 1801        6
## 782046                183.70 1820        6
## 782052                184.54 1822        6
## 782056                 51.16 1973        9
## 782061                 47.00 1387        6
## 782075                 51.16 2879        8
## 782089                288.00 2327        9
## 782106                278.56 1812        6
## 782108                227.28 1794        6
## 782112                242.00 1809        6
## 782158                 78.42 1816        6
## 782160                 50.01 2778        8
## 782169                 72.65 1759        6
## 782176                 87.46 2813        8
## 782204                 97.60 2324        9
## 782231                460.23 1808        6
## 782243                108.42 1791        6
## 782244                199.22 1799        6
## 782250                415.72 1802        6
## 782271                170.00 1808        6
## 782272                377.94 1809        6
## 782292                174.18 1809        6
## 782317                478.93 1799        6
## 782342                118.25 1800        6
## 782386               1230.30 2129        1
## 782420                458.71 1800        6
## 782421                789.93 1785        4
## 782438                303.17 1799        6
## 782470                186.88 1793        6
## 782475               1200.61 1764        4
## 782476                 55.00 1599        6
## 782480                890.64 1798        4
## 782491                122.55 1787        6
## 782526                154.79 1785        6
## 782579                 78.63 1701        6
## 782580                280.38 1931        9
## 782582                 51.16 1785        6
## 782609                572.56 1778        6
## 782634                447.38 1773        6
## 782638                416.44 1777        6
## 782644               1959.69 1773       10
## 782646                339.15 1779        6
## 782649                631.46 2196        9
## 782655                220.58 1791        6
## 782657                454.23 1764        6
## 782659                 63.55 1757        6
## 782672                240.69 1774        6
## 782679                 68.58 1777        6
## 782713                 96.68 1774        6
## 782727                 78.17 1765        6
## 782738                139.44 2072        9
## 782743                182.07 1764        6
## 782773                102.89 1950        9
## 782777                170.71 2774        8
## 782779                122.15 1773        6
## 782781                 51.51 3070        8
## 782795                 46.56 1730        6
## 782812                  6.50 1885        6
## 782824                  5.70 1779        6
## 782840               2400.46 2478       10
## 782849                 88.10 1770        6
## 782855                168.26 1774        6
## 782865                 64.01 1753        6
## 782869               1374.68 1760       10
## 782888                 29.86 1778        6
## 782898                687.35 1772        6
## 782911                164.98 1750        6
## 782913                182.85 1750        6
## 782915                285.33 1764        6
## 782916                284.25 1764        6
## 782940                 32.59 1721        6
## 782973                 18.10 1791        6
## 782975                 81.60 1743        6
## 782977                 98.25 1764        6
## 782982                 68.98 1759        6
## 783003                128.18 1763        6
## 783008                100.00 1739        6
## 783025                681.00 1728        6
## 783041                362.00 1764        6
## 783048                134.97 1759        6
## 783053                124.93 1758        6
## 783054                472.34 1755        6
## 783059                445.63 1666        6
## 783066                318.64 1760        6
## 783067               1424.18 1764       10
## 783098                183.09 1763        6
## 783110                345.21 1758        6
## 783113                 87.15 1736        6
## 783153                194.24 2199        9
## 783169                 61.36 1742        6
## 783200                 53.31 1756        6
## 783207                576.57 1743        6
## 783219                703.40 1716        6
## 783269                266.72 1742        6
## 783273                128.53 2158        9
## 783284                121.93 1528        6
## 783289                 66.05 1744        6
## 783290               1330.05 1743       10
## 783297                429.34 1750        6
## 783301                 66.68 1737        6
## 783307                111.99 1751        6
## 783320               1593.67 1743       10
## 783335                166.57 1302        6
## 783356                333.61 1652        6
## 783367                 86.22 1736        6
## 783397                657.98 2876        8
## 783399                 50.32 1513        6
## 783406                290.23 1686        6
## 783408                 98.35 2839        8
## 783413               1361.56 2157        1
## 783423                117.28 1736        6
## 783424               1764.84 2624        1
## 783439                264.62 1732        6
## 783447                 59.00 1708        6
## 783451                122.00 1739        6
## 783456                518.00 2869        8
## 783460                 41.90 1668        6
## 783473               1562.78 1623       10
## 783495                965.71 1739        4
## 783556                 59.50 1736        6
## 783609                115.99 1730        6
## 783613                960.50 3083        1
## 783619                 84.75 1728        6
## 783626                200.59 2027        9
## 783644                 58.63 1722        6
## 783674                  6.50 1729        6
## 783690                298.87 1728        6
## 783694                553.83 1728        6
## 783702                206.40 1721        6
## 783716                252.47 1728        6
## 783736                181.27 1735        6
## 783741                582.12 1722        6
## 783762                 45.00 1724        6
## 783767                165.00 1716        6
## 783768                402.82 1716        6
## 783778                 55.20 1710        6
## 783791                399.84 3057        8
## 783803                 70.00 1715        6
## 783807                223.78 2590        9
## 783821                154.38 1804        6
## 783823                 61.35 1722        6
## 783827                 76.19 1718        6
## 783834                218.94 1709        6
## 783836                159.18 1715        6
## 783841                207.17 1686        6
## 783848                140.00 1721        6
## 783871                127.92 1721        6
## 783879                142.62 2756        8
## 783881                184.12 1710        6
## 783886                 95.92 1541        6
## 783902                116.13 2289        9
## 783920                 68.98 2318        9
## 783930                 49.22 1715        6
## 783932                145.37 1715        6
## 783946               1411.07 1710       10
## 783947                 67.50 1714        6
## 783963                156.34 1930        9
## 783973                215.87 2058        9
## 783980                342.80 1700        6
## 783990                 50.01 1368        6
## 783996                 51.16 1708        6
## 784015                255.22 1690        6
## 784023                616.78 1679        6
## 784024                367.58 1683        6
## 784027                843.07 1702        4
## 784041                238.42 1577        6
## 784044                133.36 3023        8
## 784045                162.21 1694        6
## 784050               2011.08 2165       10
## 784052               1278.85 1704        4
## 784077                223.97 1709        6
## 784084                108.42 1651        6
## 784090                 61.75 2268        9
## 784096                 10.00 1708        6
## 784120                 33.62 1704        6
## 784129                364.47 1683        6
## 784139                 38.00 1707        6
## 784157                101.67 2008        9
## 784158                121.00 1704        6
## 784166                255.00 1631        6
## 784168                 66.68 1682        6
## 784192                 29.00 1689        6
## 784217               1560.84 1703       10
## 784222               1177.90 1702        4
## 784230                103.49 1668        6
## 784233                132.81 1660        6
## 784245                212.75 1675        6
## 784262               1040.11 1683        4
## 784291                119.80 1690        6
## 784312                123.53 1700        6
## 784313                 49.00 1696        6
## 784317                149.41 1697        6
## 784320                617.02 1695        6
## 784322                103.57 1690        6
## 784334                 69.33 1696        6
## 784340                116.68 1724        6
## 784351                 96.27 1696        6
## 784354                548.84 2461        9
## 784366                262.45 1695        6
## 784367                879.77 1696        4
## 784370                 92.90 1696        6
## 784388                251.29 1672        6
## 784395                116.33 1693        6
## 784400                223.45 1694        6
## 784431                 71.13 1638        6
## 784448                 76.46 1679        6
## 784452                 60.01 1687        6
## 784499                665.55 1688        6
## 784505                247.65 1679        6
## 784512                 35.44 1680        6
## 784530               1325.98 2667        1
## 784536                 86.15 1687        6
## 784548                 80.33 1581        6
## 784551                684.51 1687        6
## 784560                497.55 1686        6
## 784568                 40.00 1673        6
## 784594                819.20 1680        4
## 784601                229.59 2514        9
## 784613                195.53 1680        6
## 784625                116.44 1682        6
## 784657                184.94 1675        6
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## 59369229              206.06   35        5
## 59370475               97.53   28        5
## 59373713               94.93  130        5
## 59376658              149.52  113        5
## 59378771             1307.12   96        3
## 59379259              209.31   87        5
## 59380440              417.91  129        5
## 59380570             1021.45  124        3
## 59380571             1149.88  126        3
## 59421393              125.12   36        5
## 59422667              992.16   39        3
## 59477160               94.93  115        5
## 59477530              759.92   62        3
## 59480690              138.49  103        5
## 59639569              307.46   98        5
## 59639579             1164.05  102        3
## 59665103             2011.43   79        2
## 59665104              272.23  115        5
## 59665105              275.60  108        5
## 59669034              107.06  101        5
## 59671896              525.80  122        5
## 59676210             1021.00   15        3
## 59676836             1701.99  102        2
## 59676841              251.45   88        5
## 59676849              911.28  127        3
## 59677526             1122.45   63        3
## 59958679             1804.93   86        2
## 59958681              367.00   66        5
## 60084394              312.95   52        5
## 60091387             1861.27   93        2
## 60092759              210.93   31        5
## 60096229              494.00   93        5
## 60097149             1264.24  123        3
## 60103531               20.00   56        5
## 60104133              433.34  121        5
## 60112007              385.02   91        5
## 60133993              128.39   81        5
## 60136734               94.47   31        5
## 60142842              366.07   66        5
## 60401867              157.62   88        5
## 60412561             1376.75   94        3
## 60412814              282.57   55        5
## 60580863              190.80   78        5
## 60583173             1289.29   68        3
## 60584889              229.93   50        5
## 60595115               38.36   96        5
## 60599143              369.43   73        5
## 60600982              304.02   82        5
## 60601331              143.09   82        5
## 60721067              250.25   55        5
## 60757821              365.93   70        5
## 60758831              127.81   25        5
## 60769712              107.07   92        5
## 60771748              124.23   97        5
## 60781423              233.76   29        5
## 60782721              116.26   95        5
## 60787427              349.29   90        5
## 60818919              167.44   90        5
## 60828221              824.46   29        3
## 60833755              616.74   57        3
## 60833758              123.33   82        5
## 60839166              247.65   41        5
## 60839167              458.11   80        5
## 60868387              391.00   36        5
## 60876827              197.00   53        5
## 60876830               33.46   69        5
## 60877201               74.76   29        5
## 60877266               74.76   29        5
## 60879070              264.40   66        5
## 60956281              655.76   43        3
## 61016656               74.76   67        5
## 61076705              118.84   26        5
## 61076709             2171.04   61        2
## 61076710              893.85   65        3
## 61102926               26.41   41        5
## 61112891              777.33   42        3
## 61113119              303.42   29        5
## 61115134              436.89   29        5
## 61186664             2103.20   38        2
## 61206643              794.29   46        3
## 61251276              396.91   30        5
## 61289152              197.95   43        5
## 61407328             1075.25   34        3
## 61574924              460.35   17        5

Gráficar Resultados

fviz_cluster(segmentos, data=bdclusters)

Optimizar la cantidad de grupos

set.seed(123)
optimizacion <- clusGap(bdclusters, FUN=kmeans, nstart=1, K.max = 10)
## Warning: did not converge in 10 iterations
plot(optimizacion, xlab="Número de clusters K")

El punto más arriba indica la cantidad de grupos óptimos.

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