Measure how well predictions match real outcomes here. See residuals, errors, and adjusted scoring options. Download clear tables, share results, and improve models fast.
This sample shows actual values versus model predictions.
| # | Actual | Predicted |
|---|---|---|
| 1 | 120 | 118 |
| 2 | 135 | 140 |
| 3 | 150 | 147 |
| 4 | 160 | 158 |
| 5 | 175 | 180 |
The calculator computes the coefficient of determination using:
R squared summarizes how much variation in actual outcomes is captured by predictions. Values near 1 indicate small unexplained error, while values near 0 suggest weak explanatory power. Negative values can occur when predictions perform worse than using the mean of actual values. Because scale does not affect R squared, it works for comparing models on the same target variable, but it is not an absolute guarantee of usefulness. For forecasting, evaluate R squared alongside time split validation results.
This calculator uses paired actual and predicted columns to compute SSres and SStot, then applies R² = 1 − SSres/SStot. It also reports RMSE, MAE, MSE, and MAPE to quantify typical error in the original units. Pearson correlation and r² are included for quick linear association checks. A residual preview table highlights per row errors, supporting fast validation of data quality. Set decimal precision to standardize outputs across runs.
Residuals reveal patterns that R squared may hide. If residuals increase with the predicted level, error variance is not constant and predictions may need transformation or a different algorithm. Large squared errors identify influential outliers that dominate SSE and depress R squared. The bias metric (MBE) shows systematic underprediction or overprediction. Reviewing the preview rows alongside summary metrics helps separate random noise from consistent model mistakes. MAPE is skipped where actual equals zero to avoid division artifacts.
Adjusted R squared penalizes unnecessary complexity by incorporating predictors k. When you add features, ordinary R squared cannot decrease, even if the new variables add little value. Adjusted R squared can drop if the improvement in SSE is not strong enough relative to the degrees of freedom. Use it when comparing models fitted on the same dataset but with different feature counts, especially in regression pipelines, in small samples.
Before trusting a score, confirm that the actual column varies; if SStot equals zero, R squared is undefined. Ensure both columns align by observation order and time. Use CSV export to archive results for experiments, and the PDF report for sharing with stakeholders. Combine R squared with RMSE or MAE to balance relative fit and absolute accuracy. Recalculate after cleaning missing values and obvious data entry errors.
It measures the proportion of variation in actual values explained by your predictions, computed from SSres and SStot. Higher values generally indicate better fit on the provided pairs.
Yes. If your predictions are worse than using the mean of the actual values, SSres exceeds SStot and R² becomes negative. This often signals a misspecified model or misaligned data.
If all actual values are identical, total variance is zero and SStot equals 0. In that case R² cannot be computed. Review your input to ensure the target varies.
Adjusted R² accounts for the number of predictors (k) and sample size (n). It penalizes adding features that do not materially reduce error, making comparisons across models with different k more fair.
Check RMSE or MAE to understand error magnitude in the original units. R² can look strong even when errors are large for high-variance targets, so pairing metrics improves decision quality.
Provide two columns: actual first, predicted second. You may include a header row if you enable the header option. Extra columns are ignored, and non-numeric rows are skipped.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.