<p>Prediction intervals (PIs) are a practical tool for uncertainty quantification in regression, but comparatively little work has addressed fully incremental PI generation for data streams. In streaming settings, data arrive continuously, each instance is typically processed once, and concept drift can quickly invalidate a previously well-calibrated interval. These properties make many batch PI methods and window-based adaptations difficult to apply efficiently. This paper studies Adaptive Prediction Interval (AdaPI), an online post-calibration framework that adjusts interval width according to observed coverage. We instantiate the framework with a fully incremental variant of Mean and Variance Estimation (MVE) and investigate three adaptive scaling functions. We also adopt an evaluation perspective that jointly considers coverage accuracy and interval width. Experiments on a collection of real-world and synthetic regression streams show that AdaPI can often move coverage closer to the desired confidence level while maintaining competitive interval width; under the default 95% confidence setting and coverage-heavy CING weighting, the linear variant frequently gives the strongest empirical coverage–width trade-off among the three adaptive strategies.</p>