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I want to see if my logic is correct. Say that I have 250 data samples and for each of the sample I run a simple OLS $y=\beta x$. I then have 250 $\beta$. Now my objective is to see if, on average, these $\beta$ are statistically significant. I can't simply take the average of the T-Statistics coming from my 250 OLS regression. What I had in mind (and I believe this is the common practice) is to bootstrap a distribution using my sample estimates of $\beta$. Hence, if I bootstrap $n$ distributions and get the 95% confidence interval around the mean of my $n$ distributions, is it acceptable for me to see if each of the estimated $\beta$ (from my 250 OLS regression) fall outside of this confidence interval and claim for instance that 80% of my estimated $\beta$ are statistically significant?

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    $\begingroup$ What is the sample size of the data for each sample? Why not pool the data and get $\beta$ on the combined sample if each of the samples is representative? $\endgroup$ Jan 18, 2015 at 7:00
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    $\begingroup$ Each of my sample is a time-series of 23,000+ observations hence I want to run a regression for each of my sample. They cannot be combined. $\endgroup$
    – CharlesM
    Jan 18, 2015 at 7:11
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    $\begingroup$ Ok. I would say that in that case replacing the asymptotic distribution with the bootstrap distribution of your regression coefficients is not going to change much (if you are worried about size and power of the t-test). You might as well show the asymptotic confidence interval for each estimate. $\endgroup$ Jan 18, 2015 at 7:15

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