Calculator Inputs
Use direct mode when you already know explained, unexplained, or total variation. Use dataset mode when you have observed and predicted values.
Example Data Table
This example shows observed and predicted values that can be pasted directly into dataset mode.
| Index | Observed | Predicted | Residual |
|---|---|---|---|
| 1 | 18 | 17 | 1 |
| 2 | 22 | 21 | 1 |
| 3 | 25 | 24 | 1 |
| 4 | 29 | 30 | -1 |
| 5 | 31 | 30 | 1 |
| 6 | 35 | 34 | 1 |
Formula Used
SST = Σ (yi − ȳ)2
SSE = Σ (yi − ŷi)2
Explained Variation = SST − SSE
Explained % = (Explained Variation ÷ Total Variation) × 100
Unexplained % = (Unexplained Variation ÷ Total Variation) × 100
R² = 1 − (SSE ÷ SST)
Adjusted R² = 1 − (1 − R²) × (n − 1) ÷ (n − p − 1)
In direct mode, the calculator uses your variation totals directly. In dataset mode, it builds totals from observed and predicted values.
How to Use This Calculator
- Choose Direct variation inputs if you already know explained, unexplained, or total variation.
- Choose Observed and predicted dataset if you want the calculator to derive total variation from raw values.
- Enter the predictor count if you want adjusted R², MSE, RMSE, and F-statistic.
- Set the number of decimal places for cleaner output.
- Click the calculation button to display results above the form.
- Review the summary, results table, and chart.
- Use the CSV or PDF buttons to export the results.
FAQs
1) What does percentage of total variation mean?
It shows how much of the total spread in data is explained by a model or selected component. In many regression settings, it matches R² multiplied by 100.
2) When should I use direct mode?
Use direct mode when your report, ANOVA table, or model summary already gives explained, unexplained, or total variation. It is the fastest way to convert variation values into percentages.
3) When should I use dataset mode?
Use dataset mode when you have observed values and matching predicted values. The calculator will compute total variation, residual variation, R², adjusted R², and several supporting fit statistics automatically.
4) Why can explained percentage become negative?
In dataset mode, a negative explained percentage means the predictions perform worse than simply using the observed mean as a baseline. This signals a poor model fit or incorrect predicted values.
5) How to calculate total variation distance?
Use 0.5 × Σ|pi − qi| for two probability distributions. Add the absolute probability differences across outcomes, then divide by two. That measure differs from explained variation in regression.
6) What is adjusted R² used for?
Adjusted R² penalizes unnecessary predictors. It is useful when comparing models with different numbers of variables because it rewards stronger fit only when added predictors improve the model meaningfully.
7) What happens if total variation equals zero?
If total variation is zero, the observed values do not vary around their mean. In that case, explained and unexplained percentages are not meaningful because the denominator becomes zero.
8) Why download CSV or PDF results?
CSV files help with spreadsheets and quick audits. PDF files are better for sharing clean summaries, preserving formatting, and attaching calculation reports to assignments, project notes, or documentation.