LaTeX
R^2=1-\frac{SS_{res}}{SS_{tot}}Variables
- SS_res: residual sum of squares
- SS_tot: total sum of squares
- R²: coefficient of determination
How to use this formula
Measures the fraction of response variation explained by a regression model relative to a constant-mean baseline.
Important notes
- R² does not establish causation or model adequacy.
- Out-of-sample R² can be negative.
Quick example
Perfect in-sample predictions give SS_res=0 and R²=1.
Applicability, worked calculation, and verification
Assumptions and domain checks
- R² does not establish causation or model adequacy.
- For the Coefficient of Determination, every denominator must be nonzero, and the numerator and denominator must remain correctly grouped.
- For the Coefficient of Determination, identify whether each quantity is a sample statistic, population parameter, estimator, or model value, and check the method assumptions.
Worked example
Perfect in-sample predictions give SS_res=0 and R²=1.
Common mistakes
- When copying Coefficient of Determination, keep the complete numerator and denominator grouped; a missing brace or parenthesis changes the result.
- For the Coefficient of Determination, do not interpret a descriptive statistic as a causal or population conclusion without the sampling and model assumptions.
Continue the workflow
Use Coefficient of Determination 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
R^2=1-\frac{SS_{res}}{SS_{tot}}. - 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 Coefficient of Determination used for?
Measures the fraction of response variation explained by a regression model relative to a constant-mean baseline.
Can I copy this formula as LaTeX?
Yes. Copy R^2=1-\frac{SS_{res}}{SS_{tot}} 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.