# Mechanics of CQR

In the previous section, we observed that ICP generates prediction intervals of uniform width. Consequently, it doesn’t adjust adaptively to heteroscedastic data, where the variability of the response variable isn’t constant across different regions of the data.

In many cases, not only it is crucial to ensure valid coverage in final samples but it is also beneficial to generate the most concise prediction intervals for each point within the input space. This helps maintain the informativeness of these intervals. When dealing with heteroscedastic data, the model should be capable of adjusting the length of prediction intervals to match the local variability associated with each point in the feature space.

CQR (developed by Yaniv Romano, Evan Patterson, and Emmanuel Candes and published in the paper *Conformalized Quantile Regression* (https://arxiv.org/abs/1905.03222)) is one of the most popular and widely adopted conformal prediction models. It was...