Inclusion and exclusion of data or parameters in the general linear model

This paper revisits the topic of how linear functions of observations having zero expectation, play an important role in our statistical understanding of the effect of addition or deletion of a set of observations in the general linear model. The effect of adding or dropping a group of parameters is also explained well in this manner. Several sets of update equations were derived by previous researchers in various special cases of the general set-up that we consider here. The results derived here bring out the common underlying principles of these update equations and help integrate these ideas. These results also provide further insights into recursive residuals, design of experiments, deletion diagnostics and selection of subset models.