Chapter:5 - Resampling Methods, q6

library(ISLR)

(a)

set.seed(1)
glm.model = glm(default~income+balance,data=Default,family=binomial)
summary(glm.model)

Call:
glm(formula = default ~ income + balance, family = binomial, 
    data = Default)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-2.4725  -0.1444  -0.0574  -0.0211   3.7245  

Coefficients:
              Estimate Std. Error z value Pr(>|z|)    
(Intercept) -1.154e+01  4.348e-01 -26.545  < 2e-16 ***
income       2.081e-05  4.985e-06   4.174 2.99e-05 ***
balance      5.647e-03  2.274e-04  24.836  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 2920.6  on 9999  degrees of freedom
Residual deviance: 1579.0  on 9997  degrees of freedom
AIC: 1585

Number of Fisher Scoring iterations: 8

(b)

set.seed(1)
boot.fn = function(data, index){
    glm.model = glm(default~income+balance,data=data,family=binomial,subset=index)
    return(coef(glm.model))
}

(c)

library(boot)
boot(data=Default, statistic=boot.fn, R=50)

ORDINARY NONPARAMETRIC BOOTSTRAP


Call:
boot(data = Default, statistic = boot.fn, R = 50)


Bootstrap Statistics :
         original        bias     std. error
t1* -1.154047e+01  1.181200e-01 4.202402e-01
t2*  2.080898e-05 -5.466926e-08 4.542214e-06
t3*  5.647103e-03 -6.974834e-05 2.282819e-04

(d)

We get almost similar standard error estimates for the coefficients