We can implement a bootstrap analysis by performing this command many times, recording all of the corresponding estimates for \(\alpha\), and computing the resulting standard deviation. However, the boot() function automates this approach. Below we produce R = 1,000 bootstrap estimates for \(\alpha\).

> boot(Portfolio, alpha.fn, R = 1000)

ORDINARY NONPARAMETRIC BOOTSTRAP

Call:
boot(data = Portfolio, statistic = alpha.fn, R = 1000)

Bootstrap Statistics :
     original       bias    std. error
t1* 0.5758321 -0.001695873  0.09366347

The final output shows that using the original data, \(\hat\alpha = 0.576\), and that the bootstrap estimate for \(SE(\hat\alpha)\) is 0.0937.

Try to create 10 bootstrap estimates for your own and store them in bootstrap:

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Assume that:

• The ISLR2 and boot libraries have been loaded
• The Portfolio dataset has been loaded and attached