Ejercicio 1. Bootstrap

library(boot)

ocupacion <- c(78, 82, 75, 80, 85, 88, 92, 90, 86, 84, 80, 83)

bootstrap_media <- function(data, indices) {
  return(mean(data[indices]))  
}
set.seed(616)  
bootstrap_result <- boot(data = ocupacion, statistic = bootstrap_media, R = 1000)

print(bootstrap_result)

## 
## ORDINARY NONPARAMETRIC BOOTSTRAP
## 
## 
## Call:
## boot(data = ocupacion, statistic = bootstrap_media, R = 1000)
## 
## 
## Bootstrap Statistics :
##     original     bias    std. error
## t1* 83.58333 0.07033333    1.358444

intervalo_confianza <- boot.ci(bootstrap_result, type = "perc")
print(intervalo_confianza)

## BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
## Based on 1000 bootstrap replicates
## 
## CALL : 
## boot.ci(boot.out = bootstrap_result, type = "perc")
## 
## Intervals : 
## Level     Percentile     
## 95%   (81.00, 86.42 )  
## Calculations and Intervals on Original Scale

hist(bootstrap_result$t, main = "Distribución Bootstrap (1000 repeticiones)",
     xlab = "Ocupación Remuestreada", col = "lightblue", border = "black")

set.seed(616)  
bootstrap_result2 <- boot(data = ocupacion, statistic = bootstrap_media, R = 100000)

print(bootstrap_result2)

## 
## ORDINARY NONPARAMETRIC BOOTSTRAP
## 
## 
## Call:
## boot(data = ocupacion, statistic = bootstrap_media, R = 1e+05)
## 
## 
## Bootstrap Statistics :
##     original       bias    std. error
## t1* 83.58333 -0.003584167    1.374485

intervalo_confianza2 <- boot.ci(bootstrap_result2, type = "perc")
print(intervalo_confianza2)

## BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
## Based on 100000 bootstrap replicates
## 
## CALL : 
## boot.ci(boot.out = bootstrap_result2, type = "perc")
## 
## Intervals : 
## Level     Percentile     
## 95%   (80.92, 86.25 )  
## Calculations and Intervals on Original Scale

ocupacion2 <- c(78, 82, 75, 80, 85, 88, 92, 90, 86, 84, 80, 73)

set.seed(616)  
bootstrap_result3 <- boot(data = ocupacion2, statistic = bootstrap_media, R = 1000)

print(bootstrap_result3)

## 
## ORDINARY NONPARAMETRIC BOOTSTRAP
## 
## 
## Call:
## boot(data = ocupacion2, statistic = bootstrap_media, R = 1000)
## 
## 
## Bootstrap Statistics :
##     original  bias    std. error
## t1*    82.75  0.0545    1.605597

intervalo_confianza3 <- boot.ci(bootstrap_result3, type = "perc")
print(intervalo_confianza3)

## BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
## Based on 1000 bootstrap replicates
## 
## CALL : 
## boot.ci(boot.out = bootstrap_result3, type = "perc")
## 
## Intervals : 
## Level     Percentile     
## 95%   (79.67, 86.00 )  
## Calculations and Intervals on Original Scale

hist(bootstrap_result3$t, main = "Distribución Bootstrap (Diciembre = 73%)",
     xlab = "Ocupación Remuestreada", col = "salmon", border = "black")