Prediction interval

Definition

A prediction interval provides a range of values within which a future observation is expected to fall, with a certain level of confidence. It accounts for the uncertainty in both the estimated regression line and the inherent variability in the data.

5 Must Know Facts For Your Next Test

1. A prediction interval is wider than a confidence interval for the mean response at the same level of confidence.
2. The formula for a prediction interval includes both the standard error of the regression and an additional term that accounts for individual variability.
3. As sample size increases, the width of the prediction interval decreases because estimates become more precise.
4. Prediction intervals are useful when making forecasts or predictions about individual future observations rather than estimating population parameters.
5. To calculate a prediction interval, you need an estimate of the variance of the residuals from your regression model.

Review Questions

• Why is a prediction interval typically wider than a confidence interval?
• What components are necessary for calculating a prediction interval?
• How does increasing sample size affect the width of a prediction interval?

Related terms

Confidence Interval: A range of values used to estimate a population parameter with a certain level of confidence.

Standard Error: A measure of the statistical accuracy of an estimate, equal to the standard deviation divided by the square root of the sample size.

Residuals: The differences between observed and predicted values in a regression analysis.