Title

Construction of a conservative confidence region from projections of an exact confidence region in multiple linear regression

Keywords

Bonferroni; Scheffe; Working-Hotelling

Abstract

The problem of constructing a confidence region for simultaneously estimating p, p ≥ 2, linear regression parameters for which confidence statements can be made on the individual parameters is revisited. Here, an intercept may be included among the p parameters. The technique is due to Working and Hotelling (1929) and Scheffe (1959) and uses the p separate projections of the exact (1 – α)100% confidence ellipsoid (ellipse if p = 2) to give confidence intervals for each regression parameter. The Cartesian product of these p confidence intervals gives a p-dimensional rectangle that contains the confidence ellipsoid and hence has a joint confidence coefficient of at least (1 – α). A simple calculus proof is given to determine these projections. The projection procedure is compared with the Bonferroni procedure for this case. © 1994 Taylor & Francis Group, LLC.

Publication Date

1-1-1994

Publication Title

American Statistician

Volume

48

Issue

2

Number of Pages

120-124

Document Type

Article

Identifier

scopus

Personal Identifier

scopus

DOI Link

https://doi.org/10.1080/00031305.1994.10476038

Socpus ID

21344483887 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/21344483887

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