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Visualization of evidence in regression with the QR decomposition

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Abstract

Graphical ANOVA is a simple and effective tool for visualizing evidence of differences between treatment means for data coming from factorial experiments. The purpose of the present article is to propose an analogous method for the visualization of the significance of regression, using the QR decomposition. Two graphical tests are proposed and compared with the classical \(F\) test, by simulation. It is found that when the number of candidate predictors is small relative to the sample size, the classical test has slightly higher power than the graphical tests. When the number of predictors is large, the graphical tests remain powerful. while the classical \(F\) test exhibits poor power properties.

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Acknowledgments

The author thanks the Associate Editor and three anonymous referees for helpful comments on an earlier draft of this paper. All computations were carried out using R Development Core Team (2013).

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Authors and Affiliations

  1. Department of Statistics, University of British Columbia, Kelowna, BC, V1V 1V7, Canada

    W. John Braun

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  1. W. John Braun
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Correspondence to W. John Braun.

Appendices

Appendix 1

Standard regression summary information for the jojoba oil example follows.

figure b

Appendix 2

Code for the simulated data example of Sect. 3 is provided here.

figure c

The regression summary for this simulated dataset is obtained as follows.

figure d

Appendix 3

The regression summary for the NFL dataset is obtained as follows.

figure e

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Braun, W.J. Visualization of evidence in regression with the QR decomposition. Comput Stat 30, 907–927 (2015). https://doi.org/10.1007/s00180-015-0558-x

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  • DOI: https://doi.org/10.1007/s00180-015-0558-x

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