Data diagnostics in subset selection of regression

In multivariate linear regression, subset selection relies on models and relates closely to mfluence data. In this paper, the relation between subset selection and data based on C_p-criterion is studied from the model perturbation. Using the concepts of differential geometry, three measures——velocity, acceleration and curvature are proposed to assess the influence of data on subset selection and to detect the influence data. A numerical example is given showing that the influence measures are effective.