Calculator Inputs
Example Data Table
This sample shows paired values and residuals, plus the computed score for the same rows.
| # | y_true | y_pred | residual |
|---|---|---|---|
| 1 | 3 | 2.8 | 0.2 |
| 2 | 2.5 | 2.7 | -0.2 |
| 3 | 4.2 | 4 | 0.2 |
| 4 | 5.1 | 5.3 | -0.2 |
| 5 | 6 | 5.8 | 0.2 |
| 6 | 5.7 | 5.6 | 0.1 |
Formula Used
Explained Variance Score measures how much variance in y_true is captured by predictions.
Variance uses population variance (ddof = 0). If Var(y_true) is zero, the score is 1 when predictions match exactly, otherwise 0.
How to Use
- Choose Paste values or Upload CSV.
- Provide paired numeric values for y_true and y_pred.
- Optionally provide sample_weight to weight each row.
- Click Submit to calculate the score and error metrics.
- Review the residual preview to spot outliers or bias.
- Use Download CSV or Download PDF to export results.
What the Score Represents
Explained variance score compares the variance of residuals to the variance of observed targets. It answers a stability question: do prediction errors fluctuate less than the targets themselves? A score of 1 means residual variance is zero. A score near 0 means residual variance matches the target variance. Negative values indicate residuals vary more than targets, often from a poor model, wrong features, or leakage.
Why Variance Beats Absolute Error
Mean absolute error and RMSE summarize average magnitude, but they ignore how errors spread across the range. Explained variance reacts when a model captures swings and seasonality, even if a small bias remains. This makes it useful for monitoring regression systems where volatility matters, such as demand planning, energy forecasting, or latency prediction. Pair it with MAE or RMSE to detect both dispersion and scale.
Interpreting Values in Practice
For many real datasets, values between 0.6 and 0.9 suggest the model explains most variability, but that is not a universal threshold. Always compare against baselines: a constant mean predictor often yields a score near 0. Cross validation helps, because a single split can inflate variance estimates. If your target variance is tiny, small residual changes can swing the score.
Effects of Sample Weighting
Weights let you emphasize critical segments, like high revenue customers or peak hours. In this calculator, weighting affects both target variance and residual variance, so the ratio stays consistent with the business objective. Use non-negative weights and avoid all zero totals. If you up weight rare events, expect the score to move toward how well the model captures those events, not the average case.
Reporting and Model Governance
Treat explained variance score as one KPI in a monitoring panel. Track it by time window and by segment, alongside drift indicators and error percentiles. When the score drops, inspect residual plots, outliers, and feature availability. Export CSV or PDF reports for audits, and record the exact input window, preprocessing choices, and any weights used. For regulated environments, keep target definition, units, and data lineage documented. Recompute the score after model updates, and validate it on backtests before promoting changes to production.
FAQs
1) What data do I need to calculate the score?
Provide paired numeric y_true and y_pred values with the same length. You may paste lists or upload a CSV with y_true and y_pred columns. Optional sample_weight values must be non-negative and match the row count.
2) Can the explained variance score be negative?
Yes. Negative scores occur when residual variance exceeds the variance of y_true. This can happen with an underfit model, a bad feature set, a shifted target definition, or mismatched preprocessing between training and scoring.
3) How is this different from R²?
R² compares residual sum of squares to total sum of squares around the mean. Explained variance compares variances directly. They often move together, but they can differ when bias or weighting changes the mean and dispersion relationship.
4) When should I use sample weights?
Use weights when some rows should influence evaluation more, such as high-value customers, peak periods, or rare events. Weighting makes the score reflect performance on prioritized segments, not just the average pattern.
5) What happens if the target variance is zero?
If all y_true values are identical, Var(y_true)=0. The score becomes 1 only when every prediction matches exactly; otherwise it returns 0. In that scenario, consider reviewing whether the target definition is meaningful.
6) How many observations are recommended?
Use as many paired rows as you can validate. Very small samples make variance estimates unstable. Start with at least 30-50 rows for quick checks, and hundreds or more for reliable monitoring and comparisons.