Regression models where the dependent variable is censored (limited) are usually considered in statistical analysis. Particularly, the case of a truncation to the left of zero and a normality assumption for the error terms is studied in detail by [1] in the well known Tobit model. In the present article, this typical censored regression model is extended by considering a partial linear model with errors belonging to the class of scale mixture of normal distributions. We achieve a fully Bayesian inference by adopting a Metropolis algorithm within a Gibbs sampler. The likelihood function isutilized to compute not only some Bayesian model selection measures but also to develop Bayesian case-deletion influencediagnostics based on the q-divergence measures. We evaluate the performances of the proposed methods with simulated data. In addition, we present an application in order to know what type of variables affect the income of housewives. © 2012 American Institute of Physics.