Calculate a prediction interval for a single new observation.
A prediction interval adds the variability of individual observations to the uncertainty in the fitted line, which is the extra 1 inside the square root. It is therefore always wider than a confidence band. For large samples the prediction interval approaches ±1.96 residual standard errors and never narrows further, no matter how much data is collected.
Prediction Interval
SE(prediction) = s √(1 + 1/n + (x − x̄)² ÷ Σ(x − x̄)²)
SE(prediction) = s √(1 + 1/n + (x − x̄)² ÷ Σ(x − x̄)²) A prediction interval adds the variability of individual observations to the uncertainty in the fitted line, which is the extra 1 inside the square root. It is therefore always wider than a confidence band.
For large samples the prediction interval approaches ±1.96 residual standard errors and never narrows further, no matter how much data is collected.
This calculator takes 5 inputs: Predicted value, Residual standard error, Sample size, Distance of x from its mean, Sum of squared deviations of x. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.