Dear Samiksha S. V. ,

RMSE is the mean of the residuals (that has been squared in order to account for negative values) and to obtain its CI you need to use the distribution of residuals.

You can get the residuals by subtracting the modelled values from the actual values. You can then calculate the mean of the squared residual and the square root of that mean should yield the RMSE. On this basis you can proceed to calculate the sd of residuals.

I assume that the population variance of residuals is not known and thus your formula for calculating the CI would look like this mean + t * sd/sqrt(df), where t is the upper (1-C)/2 critical value for the t distribution with n-1 degrees of freedom, t(n-1).

So you have to look up your t-value, and include all other values in he formuly and you are done.

If you want to I can provide you with example code in R

Best

Sven

Dear Samiksha S.V.,

First of all, RMSE is an estimate of actual standard deviation or dispersion Sigma. And you want to estimate confidence interval of Sigma, not RMSE.

Now, MSE is square of RMSE. And estimate of Sigma-Squared. Multiply MSE by number of samples n. You get SE. If you divide SE by Sigma-Squared, the ratio theoretically follows Chi-square distribution with n-1 df. 95% confidence interval for SE/Sigma-square is (Chi-square with df at 0.025, Chi-square with df at 0.975). You can find that interval from Chi-square table. You know SE. Therefore, confidence interval for Sigma-square becomes (SE/Chi-square with df at 0.975, SE/Chi-square with df at 0.025).

All the best

Somenath

Here is a chapter you might find helpful.

• https://learn.lboro.ac.uk/archive/olmp/olmp_resources/pages/workbooks_1_50_jan2008/Workbook40/40_2_intvl_est_var.pdf

PS- The other "workbooks" can be found here:

• https://learn.lboro.ac.uk/archive/olmp/olmp_resources/pages/wbooks_fulllist.html

So, are you calculating RSME based on, say, a linear model, where you are comparing the predicted values to actual values?

My temptation is to always think about using bootstrapping to determine confidence intervals. I wonder how that approach would compare to those mentioned above.

Thank you everyone for the detailed responses. All information will be surely helpful for me.

.F.