# Is there a way to add sample confidence interval to regression?

I have the following situation. We want to measure if animal weight has an influence on their home range size (measured as an area).

However, there is inherent error measuring an animal home range. The method we're using output the home range value plus a 95% confidence interval.

Is there a way to incorporate this confidence interval in the regression of home range and mass?

I am aware that you can add weight to samples but I'm not sure if there is a better way.

• Have you looked at Errors-In-Variables models? If I am understanding you correctly, confidence intervals wouldn't do what you are intending them to do. Maybe you should explain the calculation method that you are using to find the home range in the first place. Commented Jul 29, 2020 at 20:42
• @Dave An EIV model deals with errors in the explanatory variables. This problem appears to be of the form $Y_i=x_i\beta+\epsilon_i$ where $$\operatorname{Var}(\epsilon)=\sigma^2\mathbb{I}_n+\operatorname{Diag}(\sigma_1^2,\sigma_2^2,\ldots,\sigma_n^2)$$ and the response measurement errors $\sigma_i^2$ are specified (they do not need to be estimated).
– whuber
Commented Jul 29, 2020 at 20:51
• @whuber, ah, I misunderstood the question. Commented Jul 29, 2020 at 20:53
• @whuber is correct, there is an error associated in measuring the $Y_i$, which has been estimated. I found a similar question, and they seem to be suggesting adding weights to the explanatory variable proportional to the inverse of the variance $w_i = 1/\sigma_i^2$ Commented Jul 30, 2020 at 22:07
• Unfortunately that doesn't work. It's wrong because the weights don't accommodate the contribution of the unknown value $\sigma^2,$ which often is substantial.
– whuber
Commented Jul 31, 2020 at 15:52