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If I want to test the accuracy of a predicted coefficient based on my data set $N$, then I create a bootstrap sample by sampling from by data set with replacement $N$ times, and then refit my model and calculate the estimate once again.

Why do we sample WITH replacement?

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    $\begingroup$ If you did not use replacement, then every bootstrap sample would be the same as your original sample, since we bootstrap a sample the size of our real N. $\endgroup$
    – Mark White
    May 16, 2017 at 20:09
  • $\begingroup$ When you bootstrap you are sampling from the original sample N times and so as Mark White said if you do this without replacement you will just get a permutation of the original sample. $\endgroup$
    – Michael R. Chernick
    May 16, 2017 at 20:25

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