Simple graphs and bounds for the elements of the hat matrix

In regression analysis, the matrix H = X (XTX)-1XT is known as the 'hat' or 'projection' matrix, among other names. It has been studied by many authors from different perspectives. The main area of study has been the type of measure best adapted to detect leverage points in linear regression. For computational reasons, these measures were originally based on the diagonal elements of the hat matrix. In the present paper, we propose a very simple procedure for identifying leverage groups. The procedure is based on upper and lower bounds for the diagonal and the off-diagonal elements of H. These upper and lower bounds can easily be shown on an index plot of the elements of H.