We consider the effects induced by truncation in multivariate Gaussian models, with special attention to the modification produced on the concentration matrix and, therefore, on the linear regression coefficients. Truncation mechanisms on some of the variables, which may or may not be observed, have an important role in construction of selection type models. The derivations allow (a) to recover exhisting results in a unified framework and (b) to provide some insights on the distortion induced in linear regression coefficients by the selection mechanism. In some cases, this bias can also be consistently estimated from the observed data. Connections to the Extended Skew Normal distributions are also provided and used to construct models for binary response models with selection.