## Abstract

Consider an adjoined n x p matrix Z = (Y:X) relating to the regression of a dependent variable Y on a set of predictors X. It is shown that the Moore-Penrose inverse of Z contains a useful summary of information about multiple regressions between any column of Z and all other columns, as well as a set of case diagnostics that may be used to identify outliers and influential points. Z and the inverse are dual, so that Z is itself a diagnostic indicator of multiple regressions in the inverse. It is shown how the inverse may be used as a case diagnostic for both leverage and outlyingness, and also provides information about the dependence of subset regressions on particular cases.

Original language | English (US) |
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Pages (from-to) | 403-425 |

Number of pages | 23 |

Journal | Linear Algebra and Its Applications |

Volume | 127 |

Issue number | C |

DOIs | |

State | Published - 1990 |