LaTeX
MSE=\frac{1}{n}\sum_{i=1}^{n}(y_i-\hat y_i)^2Variables
- y_i: observed value
- ŷ_i: prediction
- n: observation count
How to use this formula
Averages squared prediction errors.
Important notes
- Squaring gives large errors greater weight.
- Training and test MSE answer different questions.
Quick example
Errors 1, −1, and 2 give MSE=(1+1+4)/3=2.
Applicability, worked calculation, and verification
Assumptions and domain checks
- Squaring gives large errors greater weight.
- For the Mean Squared Error, every denominator must be nonzero, and the numerator and denominator must remain correctly grouped.
- For the Mean Squared Error, the index variable, lower bound, upper bound, and any empty-sum or empty-product convention must be clear.
- For the Mean Squared Error, identify whether each quantity is a sample statistic, population parameter, estimator, or model value, and check the method assumptions.
Worked example
Errors 1, −1, and 2 give MSE=(1+1+4)/3=2.
Common mistakes
- When copying Mean Squared Error, keep the complete numerator and denominator grouped; a missing brace or parenthesis changes the result.
- For the 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 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
MSE=\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 Mean Squared Error used for?
Averages squared prediction errors.
Can I copy this formula as LaTeX?
Yes. Copy MSE=\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.