Prediction Interval Calculator — Formula
## Prediction Interval for New Observation
A prediction interval estimates the range where a single new observation is likely to fall, accounting for both estimation uncertainty and individual variability.
### Simplified Formula (at x-bar)
**PI = y-hat ± t × Se × sqrt(1 + 1/n)**
Prediction intervals are always wider than confidence intervals for the mean because they must account for individual observation scatter. The full formula also includes a term for distance from x-bar.
A prediction interval estimates the range where a single new observation is likely to fall, accounting for both estimation uncertainty and individual variability.
### Simplified Formula (at x-bar)
**PI = y-hat ± t × Se × sqrt(1 + 1/n)**
Prediction intervals are always wider than confidence intervals for the mean because they must account for individual observation scatter. The full formula also includes a term for distance from x-bar.
Exemplo Resolvido
Predicted value 50, Se = 5, n = 30, 95% confidence (t = 2.048).
- sqrt(1 + 1/30) = sqrt(1.0333) = 1.0165
- Margin = 2.048 × 5 × 1.0165 = 10.41
- PI: 50 ± 10.41 = (39.59, 60.41)