R-Squared and Prediction Error
Compare predictions with observations using R² and root mean squared error.
Your numbers
R-squared
R² can be negative for poor predictions. This does not adjust for fitted parameter count.
Scenario comparison
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Formula
Use R² = 1−SSE/SST and RMSE = √(SSE/n). SSE is summed squared prediction error, SST is summed squared deviation of observations from their mean, and n is count. A constant observed series has undefined explained-variation ratio.
Compare predictions with observations using R² and root mean squared error.
Worked example
- Observed values
- 2, 4, 6
- Predicted values
- 2, 3, 5
- R-squared
- 0.75
- Root mean squared error
- 0.816496580928
Scope and limitations
R² can be negative for poor predictions. This does not adjust for fitted parameter count.
Inputs are checked for missing values and allowed ranges. A result outside the finite numeric range is not displayed. Rounding affects display, while the calculation uses the model’s numeric precision.
Check your units and assumptions before relying on a result. Changing a label does not convert a currency or physical unit.
Formula version: a6b164ec3731 · Example checked: