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I am wondering because I'm doing a Poisson regression, and using the confint function in R to generate confidence intervals for my beta's, results in different intervals than when I would calculate them manually using: Lower bound = beta_hat - 1.96*sigma_beta/sqrt(n) and Upper bound = beta_hat + 1.96*sigma_beta/sqrt(n).

If the beta's were normally distributed, then using the confint function or the manual calculation has to yield the same result?

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