This article studies robustification strategies for the linear model in the presence of outliers. The advantages of an internal analysis of the robustness of least squares for a given sample are pointed out. The application of this methodology is illustrated bThis article studies robustification strategies for the linear model in the presence of outliers. The advantages of an internal analysis of the robustness of least squares for a given sample are pointed out. The application of this methodology is illustrated by building an explicit model of the determinants of rental housing values in the Madrid Metropolitan Area.[+][-]