Kostenloser Prediction Interval Rechner
Berechnen Sie prediction intervals for new observations in linear regression. Account for both model und individual uncertainty.
Lower Prediction Limit
39.591
Lower Prediction Limit vs Predicted Value (y-hat)
Formel
## 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.
Lösungsbeispiel
Predicted value 50, Se = 5, n = 30, 95% confidence (t = 2.048).
- 01sqrt(1 + 1/30) = sqrt(1.0333) = 1.0165
- 02Margin = 2.048 × 5 × 1.0165 = 10.41
- 03PI: 50 ± 10.41 = (39.59, 60.41)
Häufig Gestellte Fragen
How is a prediction interval different from a confidence interval?
A confidence interval estimates where the mean response lies (narrows with more data). A prediction interval estimates where a single new observation will fall (never narrows below Se even with infinite data).
Why is the prediction interval wider far from x-bar?
The full formula includes a term (x0 - x-bar)²/Sxx that increases as you move away from the center of the data. This reflects greater uncertainty in the regression line position at extreme x values.
Can I use prediction intervals for extrapolation?
Technically you can calculate them, but they become unreliable outside the range of observed x values. The linear relationship may not hold, and the intervals will be overly optimistic about prediction accuracy.
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