# Bootstrap intervals for predictions, how to interpret it?

I want to come up with a way to get how confident I am in my predictions. I am not using a Bayesian model so I was thinking a bootstrap confidence interval would be good:

I would re-sample my original training set, train on it and predict. And repeat that n number of times. I would then gather the n predictions and I could get some bootstrap intervals on my prediction.

The way that I interpret that would be: the larger the interval, the more sensitive my prediction is to the variation in the training data, which would in turn mean that I am fairly uncertain about my prediction. The smaller the interval would mean the opposite.

The questions are:

1) Is this a sensible thing to do to start with? 2) Is there any other interpretation that could be made? In this case, it is not true that for a 95% interval say, I would expect my interval to contain the truth 95% of the time, correct?

Thank you!

2. For a quick interpretation, I like the one provided by Davison: Assuming $T$ is an estimator of a parameter $\psi$ based on a random sample $Y_1, . . . , Y_n$, $V_T^{0.5}$ is the standard error of $T$, $n \rightarrow \infty$ and $\zeta_\alpha$ is the $\alpha$-th quantile of a standard normal distribution function, the interval with endpoints: $T − \zeta_{1−\alpha} V_T^{0.5}, T + \zeta_{\alpha} V_T^{0.5}$ contains $\psi_0$, the true but unknown value of $\psi$, with probability approximately $(1 − 2\alpha)$. (See A.C. Davison "Statistical models", Chapt. 3 for more.)