Coefficient of Determination (R²)

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Measure the goodness-of-fit for your regression model.

Data Points

Actual Observation Set (y)

Predicted/Model Set (ŷ)

Datasets must be of equal length and contain at least 2 points.

Goodness of Fit

Coefficient (R²)0.9950Strong Correlation

Explained Variance99.5%Accounted for by model

Residual Error0.5%Unexplained variance

Data Points (n)5

Residual Stat5.00Sum of Squares Residual

About this calculator

Overview

The coefficient of determination, denoted R², is a statistical measure that represents the proportion of the variance for a dependent variable that's explained by an independent variable or variables in a regression model. It is the most common metric for gauging the goodness-of-fit in linear regressions.

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Pro Tips

R² only measures linear relationships. Your data could have a perfect curved relationship and still have an R² of 0.
Always look at both R² and the residual plots to understand model performance fully.
The difference (1 - R²) represents the residual error or variance that the model failed to capture.

Fun Facts

"An R² of 0.85 means that 85% of the movement in the actual data is accounted for by your model."
"A negative R² actually means your model is worse than simply guessing the average value every time."
"Suspiciously high R² values (above 0.99) often indicate data leakage or overfitting in machine learning."

Formula: R² = 1 - (SSres / SStot)