A study of partial F tests for multiple linear regression models
A study of partial F tests for multiple linear regression models
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.
University of Southampton
Liu, Wei
b64150aa-d935-4209-804d-24c1b97e024a
Jamshidian, Mortaza
7603871f-ac81-48e5-9c95-743cf0334557
28 February 2007
Liu, Wei
b64150aa-d935-4209-804d-24c1b97e024a
Jamshidian, Mortaza
7603871f-ac81-48e5-9c95-743cf0334557
Liu, Wei and Jamshidian, Mortaza
(2007)
A study of partial F tests for multiple linear regression models
(S3RI Methodology Working Papers, M07/03)
Southampton, GB.
University of Southampton
23pp.
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Monograph
(Working Paper)
Abstract
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.
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Published date: 28 February 2007
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Local EPrints ID: 44609
URI: http://eprints.soton.ac.uk/id/eprint/44609
PURE UUID: e2ad46ac-ff64-4307-af4f-2890ba771eba
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Date deposited: 28 Feb 2007
Last modified: 16 Mar 2024 02:42
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Author:
Mortaza Jamshidian
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