Calculator Inputs
Formula Used
Weighted MSE: Weighted MSE = Σ(weightᵢ × errorᵢ²) / Σ(weightᵢ)
RMSE: RMSE = √MSE
R²: R² = 1 − SSE / SST
How to Use
- Choose manual entry, pasted data, or CSV upload.
- Enter matching actual and predicted observation lists.
- Add weights when some observations require greater importance.
- Select missing-data, normalisation, and outlier options.
- Choose decimal precision and optional percentage error.
- Submit the form and inspect every calculated metric.
- Copy results or export detailed CSV and PDF files.
Worked Example
| Actual | Predicted | Residual | Squared Error |
|---|---|---|---|
| 3 | 2.8 | 0.2 | 0.04 |
| 5 | 5.4 | -0.4 | 0.16 |
| 7 | 6.5 | 0.5 | 0.25 |
| 9 | 9.3 | -0.3 | 0.09 |
The squared errors total 0.54 across four observations. Dividing by four produces an MSE of 0.135. Lower values indicate predictions staying closer to targets.
Frequently Asked Questions
What does MSE measure?
MSE measures average squared differences between predictions and targets. Squaring makes larger errors influence the result more strongly. It remains sensitive to outliers and target scaling.
Is a lower MSE always better?
Lower MSE usually indicates closer predictions on identical data. However, scale and baseline performance still require careful comparison. Context determines whether the final value is acceptable.
Why does MSE use squared units?
Each residual is squared before values are averaged. Therefore, the result uses squared target measurement units. RMSE restores the original target unit for interpretation.
How does weighted MSE work?
Weighted MSE multiplies each squared error by importance. The weighted total is divided by total weight. Larger weights make selected observations affect results more.
Can MSE compare different datasets?
Direct comparison can mislead when target scales differ. Normalised metrics provide more consistent cross-dataset comparisons. Always report the chosen normalisation method clearly.
What happens with missing values?
The calculator offers rejection, removal, zero, or mean replacement. Each method changes the retained data and final result. Choose handling rules before comparing competing machine learning models.
How are zero actual values handled?
Zero actual values remain valid for ordinary MSE. They cannot support percentage errors because division fails. The calculator excludes them only from optional MSPE.
What does a negative R² mean?
A negative R² indicates predictions underperform the mean baseline. This can happen with weak or badly fitted models. Review features, validation, leakage, and target preparation carefully.
Should outliers be removed?
Outliers should not be removed without domain justification. They may represent errors or important rare cases. Compare retained and filtered results before deciding.