Tobit regression – also known as censored regression – refers to the regression methodology when observations are truncated at a threshold value. Truncation can be applied at a lower and, optionally, at an upper threshold. Applying ordinary linear regression methodology to truncated data can lead to biased parameter estimates that give poor in-sample and out-of-sample predictions. This occurs because of the non-linear shape of observable variables due to truncation. Censored regression handles this complexity by accounting for truncation of observations and modeling the non-truncated part of data separately.