Free 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
Lower Prediction Limit vs Predicted Value (y-hat)
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.
Example Calculation
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)
Frequently Asked Questions
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