Linear Regression Prediction Interval

Produce an immediate interval around your regression forecast. Supply the predicted value, residual standard error, sample size, and leverage terms to bracket where the next observation should land.

Value from your regression equation at x₀.
Standard error of estimate (same units as y).
Number of paired observations in the regression.
Independent variable value for the prediction.
Optional. Defaults to 0 if centred.
Optional. Defaults to 1; use the sample standard deviation.
Optional. Defaults to 95 % prediction confidence.

Examples

  • Sales forecast with ŷ = 56, residual SE 2.1, n = 36, x₀ = 15, x̄ = 11, sₓ = 3.4 at 95 % ⇒ Prediction interval: 51.59 to 60.41
  • Temperature regression with ŷ = 22.6, SE 1.8, n = 60, x₀ = 30, x̄ = 27, sₓ = 5.1 at 90 % ⇒ Prediction interval: 19.56 to 25.64

FAQ

Do I need slope and intercept as inputs?

No. Enter the point estimate ŷ produced by your model at the desired x₀ and the calculator handles the rest.

What if my x-values are already standardised?

Leave the mean at 0 and the standard deviation at 1 so leverage is computed against the scaled features.

How accurate is the t-critical approximation?

For df ≥ 5 the approximation is within a few thousandths of tables, which is sufficient for applied forecasting.

Additional Information

  • The leverage term ( (x₀ − x̄)² / ((n−1)·sₓ²) ) widens the interval when you extrapolate beyond the centre of your data.
  • Student’s t is approximated from the normal quantile with higher-order corrections, keeping accuracy for typical sample sizes.
  • Prediction intervals cover individual future observations, so they are wider than confidence intervals for the mean response.

Related calculators