Suppose that I have N different businesses running during the summer. Let us further suppose that I estimate (using regression) the income for each business with a 95% confidence interval. I then sum up the income estimates for the N businesses to get an estimate for the total income of the N businesses over the entire season. What is the confidence interval now for the total income estimate for the entire season? Would it be correct to say that it's still a 95% confidence interval? If not, what is the correct way to compute the new confidence interval? Thank you for your help!
2026-04-08 04:08:02.1775621282
confidence intervals additive?
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No, confidence intervals are not additive.
If you can assume all the businesses are independent, then you can add up the variances of each of the component businesses to get the variance of the total revenue. Then you can construct the confidence interval for the total.