R-squared

R-squared measures what proportion of variation in the dependent variable the regression model explains, on a scale from 0 to 1.

Also known asR2 · coefficient of determination

ByHoang TruongUpdated June 30, 2026

FrameworkOrdinary least squares (OLS)

See it move

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A split bar shows total variation (SST) of 400 units divided into two portions: 300 explained by the regression model and a residual (SSR) of 100 that the model leaves unexplained. A note at the base states R² = 1 − SSR/SST = 1 − 100/400 = 0.75, meaning the model accounts for 75 per cent of the variation in the outcome variable, and adds that including further regressors can only raise R², never reduce it.

Where it fits

SubjectData Analysis & StatisticsCoreTopicSimple Linear Regression & OLSCore

The formula

LaTeX

R^2 = 1 - \frac{SSR}{SST}

Variables

$R^{2}$: Coefficient of determination
$S S R$: Sum of squared residuals (unexplained variation)
$S S T$: Total sum of squares (total variation in Y)

Ranges from 0 (model explains nothing) to 1 (model explains all variation).

Check yourself

PracticeCORE

A simple regression of monthly ice-cream sales on average temperature produces an R² of 0.81. Which statement correctly interprets this result?

Select an answer to check your understanding.