LaTeX
RMSE=\sqrt{\frac{1}{n}\sum_{i=1}^{n}(y_i-\hat y_i)^2}Variables
- y_i: observed value
- ŷ_i: prediction
- n: count
How to use this formula
Returns the square root of mean squared error in the response variable’s units.
Important notes
- RMSE is sensitive to large errors.
- Compare models on the same response scale and dataset.
Quick example
If MSE=9, RMSE=3.
Applicability, worked calculation, and verification
Assumptions and domain checks
- RMSE is sensitive to large errors.
- For the Root Mean Squared Error, every denominator must be nonzero, and the numerator and denominator must remain correctly grouped.
- For a real-valued result, each even-root radicand must be nonnegative unless complex values are intended.
- For the Root Mean Squared Error, the index variable, lower bound, upper bound, and any empty-sum or empty-product convention must be clear.
Worked example
If MSE=9, RMSE=3.
Common mistakes
- When copying Root Mean Squared Error, keep the complete numerator and denominator grouped; a missing brace or parenthesis changes the result.
- For the Root Mean Squared Error, do not interpret a descriptive statistic as a causal or population conclusion without the sampling and model assumptions.
Continue the workflow
Use Root Mean Squared Error in your own work
- Check the domainMatch the variables and assumptions to the problem before substituting values.
- Copy the exact notationPreserve grouping, signs, and exponents in
RMSE=\sqrt{\frac{1}{n}\sum_{i=1}^{n}(y_i-\hat y_i)^2}. - Edit or convertOpen the expression in the LaTeX editor, then export it for your document or web page.
Review and verification
Last reviewed: 2026-07-23
Automated quality check: Kept noindex until the missing evidence is supplied.
Formula references
- Introductory Statistics 2eOpenStax, Rice University — Reviewed probability and statistics definitions, notation, and formulas.
Frequently asked questions
What is the Root Mean Squared Error used for?
Returns the square root of mean squared error in the response variable’s units.
Can I copy this formula as LaTeX?
Yes. Copy RMSE=\sqrt{\frac{1}{n}\sum_{i=1}^{n}(y_i-\hat y_i)^2} or open it in the LaTeX editor.
What should I check before using it?
Confirm that each variable, unit, domain restriction, and assumption matches the problem.