Prediction Interval Calculator

Calculate a prediction interval for a single new observation.

About Prediction Interval Calculator

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.

Formula

Prediction Interval

SE(prediction) = s √(1 + 1/n + (x − x̄)² ÷ Σ(x − x̄)²)

extra 1: Accounts for the scatter of individual observations about the line

Worked example

With the default values below, Prediction Interval Calculator returns Half-Width of the Prediction Interval of 23.90835. Change any input above and every figure here is recalculated in your browser.

Inputs used

Predicted value: 150
Residual standard errorminimum 0: 12
Sample sizeminimum 3: 80
Distance of x from its mean: 5
Sum of squared deviations of xminimum 0: 1,200

Results

Half-Width of the Prediction Interval: 23.90835
Lower Prediction Bound: 126.0917
Upper Prediction Bound: 173.9083
Standard Error of Prediction: 12.19836
Width Relative to the Confidence Band: 5.5678

Step by step

1Values used
2Prediction Interval
3Half-Width of the Prediction Interval= 23.90835
4Lower Prediction Bound= 126.0917
5Upper Prediction Bound= 173.9083
6Standard Error of Prediction= 12.19836
7Width Relative to the Confidence Band= 5.5678

Assumptions and limits

The result is derived only from the 5 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 5 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is Prediction Interval calculated?

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.

Why does Prediction Interval matter?

For large samples the prediction interval approaches ±1.96 residual standard errors and never narrows further, no matter how much data is collected.

What values do I need to enter?

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.