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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References
Box GEP, Hunter JS, Hunter WC (2005) Statistics for experimenters II. Wiley, New York
Braun WJ (2014) MPV: data sets from montgomery, Peck and Vining’s Book. R package version 1.35
Galpin JS, Hawkins DM (1984) The use of recursive residuals in checking model fit in linear regression. Am Stat 38:94–105
Meloche J (1991) Estimation of a symmetric density. Can J Stat 19:151–164
Rousseeuw PJ, Croux C (1993) Alternatives to the median absolute deviation. J Am Stat Assoc 88:1273–1283
R Development Core Team (2013) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0, http://www.R-project.org/
Theil H (1965) The analysis of disturbances in regression analysis. J Am Stat Assoc 60:1067–1079
Wood S (2006) Generalized additive models: an introduction with R. Chapman and Hall, Boca Raton
Zhang P (1992) Inference after variable selection in linear regression models. Biometrika 79:741–746
Zou H, Hastie T (2005) Regularization and variable selection via the elastic net. J R Stat Soc B 67:301–320
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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Appendices
Appendix 1
Standard regression summary information for the jojoba oil example follows.
Appendix 2
Code for the simulated data example of Sect. 3 is provided here.
The regression summary for this simulated dataset is obtained as follows.
Appendix 3
The regression summary for the NFL dataset is obtained as follows.
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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