StatReason

Regression Prediction Interval Calculator

Predict a single new outcome from your regression line, with an interval that reflects the uncertainty of that one specific prediction.

What this answers

This calculator answers "if I observe one new individual case at this specific x value, what range is that single new outcome likely to fall in?" A prediction interval is always wider than a confidence interval for the mean response at the same x value, since predicting one new individual observation carries both the uncertainty in estimating the average response and the natural variability of any individual case around that average.

How it is calculated

The predicted y comes directly from the fitted regression line. The prediction interval's width uses the residual standard error, adjusted by both the sample size and how far your chosen x value sits from the average x in your original data, using a t distribution with n minus 2 degrees of freedom. Predicting at an x value outside the range of your original data is flagged directly, since that is extrapolation, not interpolation.

Worked example

For a near-linear dataset (x from 1 to 5, y approximately 2 plus 3 times x with small deviations) predicted at x=3.5: the predicted y sits close to the fitted line's value there, with an interval noticeably wider than the corresponding mean-response confidence interval would be, reflecting the added uncertainty of a single new observation.

Assumption audit

Calculated from your data: the fitted line, the residual standard error, and whether your requested x value falls inside or outside your observed data range.
Evidence to review: check that the linear model actually fits your data well before trusting this interval; a poor-fitting line produces a prediction interval built on a wrong assumption about the relationship's shape.
You must verify: that predicting at your chosen x value is a sensible use of this model, especially if it falls outside your original data's range, where the linear relationship you fit is not confirmed to still hold.

Common mistakes

A frequent mistake is confusing this interval with the mean-response confidence interval; the two answer different questions and the prediction interval is always the wider of the two, since it must also cover an individual case's natural scatter around the line, not just uncertainty in the line's location. Another is ignoring the extrapolation warning because the predicted value "looks reasonable"; a linear fit can look fine near your data and still be wrong just past its edge, especially if the true relationship curves. A third is applying this interval when the residual spread clearly grows or shrinks across the x range, since the calculation assumes constant residual variance throughout.

Limitations

This interval assumes the same linear relationship and constant residual variance observed in your original data continues to hold at the new x value, an assumption that becomes progressively less certain the further that x value sits from your observed data.