Slope modified confidence bands for a simple linear regression model
Slope modified confidence bands for a simple linear regression model
Considerable attention has been directed in the statistical literature towards the construction of confidence bands for a simple linear regression model. These confidence bands allow the experimenter to make inferences about the model over a particular region of interest. However, in practice an experimenter will usually first check the significance of the regression line before proceeding with any further inferences such as those provided by the confidence bands. From a theoretical point of view, this raises the question of what the conditional confidence level of the confidence bands might be, and from a practical point of view it is unsatisfactory if the confidence bands contain lines that are inconsistent with the directional decision on the slope. In this paper it is shown how confidence bands can be modified to alleviate these two problems.
simple linear regression, confidence bands, acceptance sets, directional decisions
186-192
Hayter, A.J.
55bd07a5-db1d-4d3d-8c87-b307485420d9
Wynn, H.P.
849f3bf7-a005-4361-a9ec-f3a28b75d398
Liu, W.
b64150aa-d935-4209-804d-24c1b97e024a
April 2006
Hayter, A.J.
55bd07a5-db1d-4d3d-8c87-b307485420d9
Wynn, H.P.
849f3bf7-a005-4361-a9ec-f3a28b75d398
Liu, W.
b64150aa-d935-4209-804d-24c1b97e024a
Hayter, A.J., Wynn, H.P. and Liu, W.
(2006)
Slope modified confidence bands for a simple linear regression model.
Statistical Methodology, 3 (2), .
(doi:10.1016/j.stamet.2005.09.008).
Abstract
Considerable attention has been directed in the statistical literature towards the construction of confidence bands for a simple linear regression model. These confidence bands allow the experimenter to make inferences about the model over a particular region of interest. However, in practice an experimenter will usually first check the significance of the regression line before proceeding with any further inferences such as those provided by the confidence bands. From a theoretical point of view, this raises the question of what the conditional confidence level of the confidence bands might be, and from a practical point of view it is unsatisfactory if the confidence bands contain lines that are inconsistent with the directional decision on the slope. In this paper it is shown how confidence bands can be modified to alleviate these two problems.
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Submitted date: 25 May 2005
Published date: April 2006
Keywords:
simple linear regression, confidence bands, acceptance sets, directional decisions
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Local EPrints ID: 55147
URI: http://eprints.soton.ac.uk/id/eprint/55147
ISSN: 1572-3127
PURE UUID: 7a0a8803-7cc4-4153-a014-2cf55e8d0360
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Date deposited: 05 Aug 2008
Last modified: 16 Mar 2024 02:42
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Author:
A.J. Hayter
Author:
H.P. Wynn
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