A **quantile regression** is a type of [[Regression|regression]] that, instead of using the mean of the response variable (as per, for example, the least squares method would do), uses a given percentile to fit. That way, the prediction is **biased by design**: if $q=20\%$, then 80% of the samples are expected to fall above its value. Quantile regressions are useful in econometrics and other predictions to define upper or lower bounds, and to be used as intervals. ## Loss function ![[Quantile Loss|Quantile Loss]]