Normal probability plots with confidence for the residuals in linear regression

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.

KEYWORDS:

• Graphical tests
• Linear regression model
• Normal distribution
• Normal probability plot
• Power
• Residuals
• Simultaneous inference

MATHEMATICS SUBJECT CLASSIFICATION:

• 62F03

Additional information

Funding

The authors sincerely thank all the referees, associate editor and editor for constructive comments. This research was supported by The Thailand Research Fund (TRF) and Office of the Higher Education Commission (OHEC), Ministry of Education, Thailand, under the grant MRG5980068.