Calculate a confidence band around a fitted regression line.
The confidence band is narrowest at the mean of x and widens toward the extremes, producing the characteristic bow-tie shape. It describes uncertainty in the fitted line, not in individual observations. Confusing a confidence band with a prediction interval understates the spread of actual observations substantially.
Confidence Band
SE(fit) = s √(1/n + (x − x̄)² ÷ Σ(x − x̄)²)
SE(fit) = s √(1/n + (x − x̄)² ÷ Σ(x − x̄)²) The confidence band is narrowest at the mean of x and widens toward the extremes, producing the characteristic bow-tie shape. It describes uncertainty in the fitted line, not in individual observations.
Confusing a confidence band with a prediction interval understates the spread of actual observations substantially.
This calculator takes 5 inputs: Predicted value at this x, 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.