What does it imply if a prediction interval is wider than a confidence interval?

A prediction interval being wider than a confidence interval is a reflection of the distinct purposes these intervals serve within statistical analysis.

The confidence interval estimates the range within which a population parameter, such as the mean, is likely to fall based on sample data. It accounts for the uncertainty related to estimating this parameter, focusing solely on the variability of the sample around the true population mean.

In contrast, the prediction interval is designed to capture the range within which future individual observations are expected to fall. This interval accounts for both the uncertainty associated with estimating the mean (like the confidence interval) and the inherent variability of individual observations around that mean. Because of this additional layer of variance—specifically, the natural fluctuations that can occur in individual values—the prediction interval will almost always be wider than the confidence interval, reflecting the greater uncertainty when predicting individual outcomes rather than estimating a population parameter.

In summary, a wider prediction interval signals that it incorporates both the expected mean and the variability of future data points, thereby providing a more comprehensive representation of uncertainty in predictions.