Another Look at the Longley Data Set.

Abstract

This paper considers a linear regression problem involving economic data used by Longley in a study of the performance of regression programs. The data set is notoriously difficult to handle computationally. In this paper, the singular value decomposition and the QR factorization are used to show that very small perturbations in the data render it colinear, thus accounting for the computational difficulties. Another analysis, based on coefficients that bound perturbations in the regression coefficients in terms of perturbations in the columns of the data, also shows the extreme sensitivity of the problem. An analysis is also given of a perturbation index, introduced by Beaton, Rubin, and Barone to measure the sensitivity of regression problems. It is shown that the index is valid only for extremely large sample sizes and is not applicable to the Longley data set. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1978
Accession Number
ADA065626

Entities

People

  • Gilbert W. Stewart

Organizations

  • University of Maryland

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Accuracy
  • Algorithms
  • Coefficients
  • Computations
  • Computer Science
  • Computers
  • Data Sets
  • Decomposition
  • Errors
  • Observation
  • Perturbation Theory
  • Perturbations
  • Sensitivity
  • Simulations
  • Standards
  • Theorems
  • Universities

Fields of Study

  • Mathematics

Readers

  • Linear Algebra
  • Operations Research
  • Statistical inference.