Calculated Results
Prediction Interval Plot
Residuals versus Fitted
Residual Distribution
Normal Q-Q Plot
Actual versus Predicted
Interval Width
Coverage Status
Prediction Results Table
Model Summary
Formula Used
A linear-model prediction interval adds observation uncertainty to mean-response uncertainty. Wider intervals indicate greater expected variation around a future observation.
Prediction interval: ŷ₀ ± t(α/2, n − p) × s × √[1 + x₀ᵀ(XᵀX)⁻¹x₀] Mean-response confidence interval: ŷ₀ ± t(α/2, n − p) × s × √[x₀ᵀ(XᵀX)⁻¹x₀]
Quantile, conformal, and bootstrap methods replace strict parametric assumptions. Their bounds come from empirical errors or repeated fitted samples.
How to Use
- Paste a dataset or upload a CSV file.
- Select the predictor shown on the horizontal axis.
- Choose a regression model and training settings.
- Select an interval method and confidence level.
- Adjust the prediction range and chart appearance.
- Press Calculate and Plot to review results.
- Inspect diagnostics before accepting uncertainty estimates.
- Export the chart, table, or PDF report.
Example Data
| Advertising | Price Index | Sales |
|---|---|---|
| 10 | 1.00 | 22.4 |
| 20 | 1.05 | 31.8 |
| 30 | 0.98 | 42.1 |
| 40 | 1.08 | 49.7 |
| 50 | 1.12 | 61.5 |
Frequently Asked Questions
What is a prediction interval?
It estimates a range for a future observation. It includes model uncertainty and observation noise.
How does it differ from a confidence interval?
A confidence interval estimates the mean response. A prediction interval targets an individual future outcome.
Why are prediction intervals wider?
They include irreducible observation variability. Confidence intervals usually include only uncertainty in the fitted mean.
Which interval method should I choose?
Use parametric intervals for well-behaved regression errors. Use conformal or bootstrap methods when assumptions appear doubtful.
What does empirical coverage mean?
Coverage is the percentage of observed targets inside calculated bounds. It helps evaluate interval calibration.
Can I use multiple predictors?
Yes. Place the target in the final column. Choose one predictor for the horizontal display axis.
Can the calculator extrapolate?
Yes, but extrapolated predictions receive a warning. Results outside observed ranges can be unreliable.
What causes very wide intervals?
Small samples, noisy residuals, extrapolation, and unstable models increase uncertainty. High confidence levels also widen bounds.
Are random forest intervals exact?
No. The calculator uses empirical residual or bootstrap approximations. Interpret them as practical uncertainty estimates.
Generated page timestamp: 2026-08-10T14:18:17+00:00