The least trimmed squares (LTS) estimator is a robust regression estimator, which is known to be robust to bad leverage and many other types of outliers. Implementation of LTS requires choosing the number of 'good' observations, which is generally unknown. In this paper, we propose consistent estimators for the proportion of 'good' observations. The starting point is that when the number of 'good' observations is known, the LTS estimator is maximum likelihood in the semi-parametric LTS model where 'good' observations are normal and 'outliers' are more extreme than 'good' observations. When the number of 'good' observations is unknown, the proposed estimator must select one model among many non-nested semi-parametric models. We also show that the LTS estimator evaluated at the estimated proportion of 'good' observations leads to standard, nuisance-parameter free inference.