Question 1

Load the dataset.

Create a bootstrap object for 1000 resamples.

Calculate the correlation statistic for each sample.

library(UsingR)
library(boot)
# Load the dataset
data = father.son
# Create a boot object
boot_obj = boot(data, corr, R=1000)
# Plot the output of the bootstrap method
plot(boot_obj)

Question 2

# Printing out the summary of the bootstrap object which contains standard error
print(boot_obj)
## 
## ORDINARY NONPARAMETRIC BOOTSTRAP
## 
## 
## Call:
## boot(data = data, statistic = corr, R = 1000)
## 
## 
## Bootstrap Statistics :
##     original      bias    std. error
## t1* 0.498953 0.002260723  0.01268245

Standard error = 0.0127

Question 3

# Calculate 95% confidence limitis for teh bootstrap object
boot_obj_conf_int = boot.ci(boot_obj, conf = 0.95, type = 'norm')
print(boot_obj_conf_int)
## BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
## Based on 1000 bootstrap replicates
## 
## CALL : 
## boot.ci(boot.out = boot_obj, conf = 0.95, type = "norm")
## 
## Intervals : 
## Level      Normal        
## 95%   ( 0.4718,  0.5215 )  
## Calculations and Intervals on Original Scale