The University of Southampton
University of Southampton Institutional Repository

A study of partial F tests for multiple linear regression models

Liu, Wei and Jamshidian, Mortaza (2007) A study of partial F tests for multiple linear regression models , Southampton, GB University of Southampton 23pp. (S3RI Methodology Working Papers, M07/03).

Record type: Monograph (Working Paper)


Partial F tests play a central role in model selections in multiple linear regression models. This paper studies the partial F tests from the view point of simultaneous confidence bands. It first shows that there is a simultaneous confidence band associated naturally with a partial F test. This confidence band provides more information than the partial F test and the partial F test can be regarded as a side product of the confidence band. This view point of confidence bands also leads to insights of the major weakness of the partial F tests, that is, a partial F test requires implicitly the linear regression model holds over the entire range of the covariates in concern. Improved tests are proposed and they are induced by simultaneous confidence bands over restricted regions of the covariates. Power comparisons between the partial F tests and the new tests have been carried out to assess when the new tests are more or less powerful than the partial F tests. Computer programmes have been developed for easy implements of these new confidence band based inferential methods. An illustrative example is provided.

PDF 44609-01.pdf - Other
Download (250kB)

More information

Published date: 28 February 2007


Local EPrints ID: 44609
PURE UUID: e2ad46ac-ff64-4307-af4f-2890ba771eba
ORCID for Wei Liu: ORCID iD

Catalogue record

Date deposited: 28 Feb 2007
Last modified: 17 Jul 2017 15:14

Export record


Author: Wei Liu ORCID iD
Author: Mortaza Jamshidian

University divisions

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton:

ePrints Soton supports OAI 2.0 with a base URL of

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.