Normal probability plots with confidence for the residuals in linear regression
Normal probability plots with confidence for the residuals in linear regression
Normal probability plots for a simple random sample and normal probability plots for residuals from linear regression are not treated differently in statistical text books. In the statistical literature, 1 − α simultaneous probability intervals for augmenting a normal probability plot for a simple random sample are available. The first purpose of this article is to demonstrate that the tests associated with the 1 − α simultaneous probability intervals for a simple random sample may have a size substantially different from α when applied to the residuals from linear regression. This leads to the second purpose of this article: construction of four normal probability plot-based tests for residuals, which have size α exactly. We then compare the powers of these four graphical tests and a non-graphical test for residuals in order to assess the power performances of the graphical tests and to identify the ones that have better power. Finally, an example is provided to illustrate the methods.
Graphical tests, Linear regression model, Normal distribution, Normal probability plot, Power, Residuals, Simultaneous inference
367-379
Chantarangsi, W.
3928c6c8-cab9-46d4-bb05-2ae8853aed2a
Liu, W.
b64150aa-d935-4209-804d-24c1b97e024a
Bretz, F.
51270819-e491-4a72-a410-679d86231e64
Kiatsupaibul, S.
b072063d-4be1-4ca0-8d4f-27740f0fa651
Hayter, A.J.
55bd07a5-db1d-4d3d-8c87-b307485420d9
7 February 2018
Chantarangsi, W.
3928c6c8-cab9-46d4-bb05-2ae8853aed2a
Liu, W.
b64150aa-d935-4209-804d-24c1b97e024a
Bretz, F.
51270819-e491-4a72-a410-679d86231e64
Kiatsupaibul, S.
b072063d-4be1-4ca0-8d4f-27740f0fa651
Hayter, A.J.
55bd07a5-db1d-4d3d-8c87-b307485420d9
Chantarangsi, W., Liu, W., Bretz, F., Kiatsupaibul, S. and Hayter, A.J.
(2018)
Normal probability plots with confidence for the residuals in linear regression.
Communications in Statistics: Simulation and Computation, 47 (2), .
(doi:10.1080/03610918.2016.1165840).
Abstract
Normal probability plots for a simple random sample and normal probability plots for residuals from linear regression are not treated differently in statistical text books. In the statistical literature, 1 − α simultaneous probability intervals for augmenting a normal probability plot for a simple random sample are available. The first purpose of this article is to demonstrate that the tests associated with the 1 − α simultaneous probability intervals for a simple random sample may have a size substantially different from α when applied to the residuals from linear regression. This leads to the second purpose of this article: construction of four normal probability plot-based tests for residuals, which have size α exactly. We then compare the powers of these four graphical tests and a non-graphical test for residuals in order to assess the power performances of the graphical tests and to identify the ones that have better power. Finally, an example is provided to illustrate the methods.
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More information
Accepted/In Press date: 9 March 2016
e-pub ahead of print date: 25 December 2017
Published date: 7 February 2018
Keywords:
Graphical tests, Linear regression model, Normal distribution, Normal probability plot, Power, Residuals, Simultaneous inference
Identifiers
Local EPrints ID: 419180
URI: http://eprints.soton.ac.uk/id/eprint/419180
ISSN: 0361-0918
PURE UUID: 93b108f5-01f6-44fb-9f60-3765caaac672
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Date deposited: 06 Apr 2018 16:30
Last modified: 18 Mar 2024 02:38
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Contributors
Author:
W. Chantarangsi
Author:
F. Bretz
Author:
S. Kiatsupaibul
Author:
A.J. Hayter
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