Model Fit Results
These results appear above the form after calculation.
Interpretation
Dataset Summary
Calculator Inputs
Enter actual values, predicted values, and model settings. The form uses three columns on large screens, two on medium screens, and one on small screens.
Plotly Graph
A best fit view helps reveal alignment and residual spread.
Calculated Data Table
| Row | Actual | Predicted | Residual | Residual Squared |
|---|---|---|---|---|
| Run the calculator to populate this table. | ||||
Example Data Table
This sample dataset is also available through the example button in the calculator.
| Row | Actual | Predicted |
|---|---|---|
| 1 | 120 | 118 |
| 2 | 128 | 130 |
| 3 | 135 | 133 |
| 4 | 142 | 144 |
| 5 | 150 | 149 |
| 6 | 158 | 160 |
| 7 | 165 | 166 |
| 8 | 173 | 171 |
| 9 | 181 | 183 |
| 10 | 189 | 187 |
| 11 | 196 | 198 |
| 12 | 205 | 203 |
Formula Used
For multiple regression with an intercept, the coefficient of determination measures how much variance in the dependent variable is explained by the model.
Residual = Actual - Predicted
SSE = Σ(Actual - Predicted)²
SST = Σ(Actual - Mean Actual)²
R² = 1 - (SSE / SST)
Adjusted R² = 1 - [(1 - R²) × (n - 1) / (n - p - 1)]
Multiple R = √R²
RMSE = √[Σ(Residual²) / n]
MAE = Σ|Residual| / n
F = (R² / p) ÷ [(1 - R²) / (n - p - 1)]
Here, n is the sample size and p is the number of predictors. Adjusted R squared and the F statistic require a valid sample size larger than p + 1.
How to Use This Calculator
- Enter a model name and dependent variable label.
- Type the number of predictors used in your regression.
- Paste the actual dependent variable values in the first box.
- Paste the predicted values in the second box.
- Choose the number of decimal places for displayed results.
- Click the calculation button to generate the metrics.
- Review the result block above the form and inspect the chart.
- Download the summary in CSV or PDF format if needed.
Frequently Asked Questions
1. What does multiple R squared measure?
It measures the share of variance in the dependent variable explained by the regression model. Higher values indicate predictions that track the observed data more closely.
2. Why is adjusted R squared useful?
Adjusted R squared penalizes unnecessary predictors. It helps compare models more fairly when the predictor count differs, especially in feature-rich data science workflows.
3. Can R squared ever be negative?
Yes. It can become negative when the prediction set performs worse than simply using the mean of the actual values as a baseline.
4. What is the difference between R squared and multiple R?
R squared is the explained variance proportion. Multiple R is the square root of R squared and represents the overall correlation strength between actual and predicted values.
5. Why do I need the number of predictors?
The predictor count is required for adjusted R squared and the model F statistic. Without it, those statistics cannot reflect model complexity correctly.
6. What inputs should I paste into the text boxes?
Paste matched lists of actual and predicted values from the same observations. Every actual value must correspond to its predicted value in the same position.
7. Does a high R squared always mean a good model?
No. A high value may still hide overfitting, unstable coefficients, poor generalization, or biased residual patterns. Always review errors and validation performance too.
8. When should I export the results?
Export results when documenting model quality, sharing a quick audit, or preserving a fitted dataset summary for presentations, reports, or team review.