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Coefficient of Determination (R²)

Definition
AI-generated

The coefficient of determination, denoted R², is the proportion of variance in the outcome explained by a regression fit on a given sample—typically 1 minus the ratio of residual to total sum of squares for ordinary least squares.

Topics
Regression and multivariate statistics
Synonyms
R squared
Related
Liability Scale Mean Absolute Error (MAE) Mean Squared Error (MSE)

Why it matters in GWAS

R² on the observed or liability scale quantifies variance explained by polygenic predictors, PRS, or covariate sets; compare definitions across papers because case–control oversampling and scale transforms change comparability.

Example usage

"The full PRS plus PCs increased liability-scale R² by 0.04 over PCs alone in the European holdout."

Liability Scale Mean Absolute Error (MAE) Mean Squared Error (MSE) Observed Scale Polygenic Risk Score (PRS) Pseudo-R² Root Mean Squared Error (RMSE) SNP Heritability
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References

  • Nagelkerke NJD. (1991). A note on a general definition of the coefficient of determination. Biometrika.
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