Types of confidence intervals used for prediction

The following are the types of confidence intervals used for predictions in regression and other linear models:

Prediction interval: Provides a range of likely values for a single response.
Confidence interval of the prediction: Provides a range of likely values for the mean response.

For example, you developed a regression model for the number of calls a calling center receives per day. The number varies greatly depending on factors such as day of the week, month of the year, market conditions, and economic factors. You feel confident that the model accurately fits the data. Therefore, you conclude that it is acceptable to use the model to predict the number of callers per day in order to schedule the appropriate number of customer service agents.

For each day's prediction, you specify the values for all the predictors and set the confidence level at 95%. The result is a 95% prediction interval of [230, 270]. You can be 95% confident that this range includes the value of the new observation. Furthermore, the 95% confidence interval of the prediction is [240, 260]. You can be 95% confident that this range includes the mean response for all days that are identical to these predictor values.

The prediction interval is always wider than the confidence interval because of the added uncertainty involved in predicting a single response versus the mean response.