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It is a newbie question but I am not sure that I fully understand the confidence intervals. Let's use OLS regression as an example.

My understanding is: If alpha=0.05, so it means that OLS regression may show

Coefficient  Std. err.      z    P>|z|     [90% conf. interval]

It means that there are 95% that the coefficient value is between the lowCI and high CI. That is why alpha=0.05 is more relaxed compared to alpha=0.01 (99% that the coefficient value lies between lowCI and high CI).

Is this thought correct? Apart from that, is there any universal rule to choose the value of alpha?

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Confidence intervals (CI) exist within the `frequentist' tradition of statistics/econometrics.

In the very loosest sense, frequentism takes the perspective that there is some true parameter out there.

CI's are a representation of this school of thought. CI's should be interpreted as saying that: "upon repeated random sampling from the population, we expect 95 percent of the CI's will contain the true population parameter."

Thus, upon 20 random samples from a population, we would expect 19/20 of the CI's to contain the true population parameter.

95 percent is the standard approach. 99 percent is perhaps only used under the strictest conditions.

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    $\begingroup$ (+1) you may want to mention for completeness that although 95% of the intervals generated in this way contain the true value, there is no guarantee that this particular one of the intervals that contains the true value, nor that it means that there is a 95% probability that this interval contains the true value (just as one can say up front that the probability of throwing a 6 on a fair die is 1/6, but once the throw has been made you either have a 6 or you don't) $\endgroup$ Sep 28 at 12:14

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