Prediction Interval Calculator

Calculate a prediction interval for a new observation in simple linear regression from the standard error and sample size.

Lower Prediction Limit

39.591

Prediction Margin10.409

Lower Prediction Limit vs Predicted Value (y-hat)

सूत्र देखें →

सूत्र

## 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.

हल किया गया उदाहरण

Predicted value 50, Se = 5, n = 30, 95% confidence (t = 2.048).

  1. 01sqrt(1 + 1/30) = sqrt(1.0333) = 1.0165
  2. 02Margin = 2.048 × 5 × 1.0165 = 10.41
  3. 03PI: 50 ± 10.41 = (39.59, 60.41)