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.

Full text not available from this repository.

## 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: https://eprints.soton.ac.uk/id/eprint/419180

ISSN: 0361-0918

PURE UUID: 93b108f5-01f6-44fb-9f60-3765caaac672

## Catalogue record

Date deposited: 06 Apr 2018 16:30

Last modified: 14 Mar 2019 01:54

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## Contributors

Author:
W. Chantarangsi

Author:
F. Bretz

Author:
S. Kiatsupaibul

Author:
A.J. Hayter

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