Skip to main content
SpringerLink
Log in
Book cover

Statistical Analysis and Data Display pp 315–344Cite as

Multiple Regression—Dummy Variables, Contrasts, and Analysis of Covariance

  • Chapter

Part of the book series: Springer Texts in Statistics ((STS))

Abstract

Any analysis of variance model (for example, anything in Chapters 6, 12, 13, or 14) can be expressed as a regression with dummy variables. The dummy variables are usually based on a set of contrasts . The algebra of individual contrast vectors is discussed in Section 6.9 Many software procedures and functions make explicit use of this form of expression. Here we explore this equivalence of different representations of the contrasts associated with a factor. The notation in Chapter 10 is that used in Sections I.4.2, 9.3, and 9.4.1.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   99.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   129.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   179.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  • A.A. Adish, S.A. Esrey, T.W. Gyorkos, J. Jean-Baptiste, A. Rojhani, Effect of consumption of food cooked in iron pots on iron status and growth of young children: a randomised trial. Lancet 353(9154), 712–716 (1999)

    Article  Google Scholar 

  • A. Agresti, Categorical Data Analysis (Wiley, New York, 1990)

    MATH  Google Scholar 

  • A. Agresti, B. Caffo, Simple and effective confidence intervals for proportions and differences of proportions result from adding two successes and two failures. Am. Stat. 54(4), 280–288 (2000)

    MathSciNet  MATH  Google Scholar 

  • Albuquerque Board of Realtors (1993). URL: http://lib.stat.cmu.edu/DASL/Stories/homeprice.html

  • American Statistical Association, Career Center (2015). URL: http://www.amstat.org/careers

  • O. Amit, R.M. Heiberger, P.W. Lane, Graphical approaches to the analysis of safety data from clinical trials. Pharm. Stat. 7(1), 20–35 (2008). URL: http://www3.interscience.wiley.com/journal/114129388/abstract

  • A.H. Anderson, E.B. Jensen, G. Schou, Two-way analysis of variance with correlated errors. Int. Stat. Rev. 49, 153–167 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  • R.L. Anderson, T.A. Bancroft, Statistical Theory in Research (McGraw-Hill, New York,1952)

    MATH  Google Scholar 

  • V.L. Anderson, R.A. McLean, Design of Experiments (Marcel Dekker, New York,1974)

    MATH  Google Scholar 

  • D.F. Andrews, A.M. Herzberg, Data: A Collection of Problems from Many Fields for the Student and Research Worker (Springer, New York,1985). URL: http://lib.stat.cmu.edu/datasets/Andrews/

  • E. Anionwu, D. Watford, M. Brozovic, B. Kirkwood, Sickle cell disease in a British urban community. Br. Med. J. 282, 283–286 (1981)

    Article  Google Scholar 

  • P.K. Asabere, F.E. Huffman, Negative and positive impacts of golf course proximity on home prices. Apprais. J. 64(4), 351–355 (1996)

    Google Scholar 

  • T. Baier, Sword (2014). URL: http://rcom.univie.ac.at

  • T. Baier, E. Neuwirth, Excel:: Com:: R. Comput. Stand. 22(1), 91–108 (2007)

    MathSciNet  Google Scholar 

  • M.K. Barnett, F.C. Mead, A 24 factorial experiment in four blocks of eight. Appl. Stat. 5, 122–131 (1956)

    Article  Google Scholar 

  • R.A. Becker, J.M. Chambers, A.R. Wilks, The S Language; A Programming Environment for Data Analysis and Graphics (Wadsworth & Brooks/Cole, Pacific Grove, 1988)

    Google Scholar 

  • R.A. Becker, W.S. Cleveland, S-PLUS Trellis Graphics User’s Manual (1996a). URL: http://www.stat.purdue.edu/~wsc/papers/trellis.user.pdf

  • Becker, R.A., W.S. Cleveland, M.-J. Shyu, S.P. Kaluzny, A tour of trellis graphics (1996b). URL: http://www2.research.att.com/areas/stat/doc/95.12.color.ps

  • Y.Y.M. Bishop, S.E. Fienberg, P.W. Holland, Discrete Multivariate Analysis (MIT, Cambridge,1975)

    MATH  Google Scholar 

  • A. Bjork, Solving least squares problems by Gram–Schmidt orthogonalization. BIT 7, 1–21 (1967)

    Article  MathSciNet  Google Scholar 

  • C.I. Bliss, Statistics in Biology (McGraw-Hill, New York, 1967)

    MATH  Google Scholar 

  • C.R. Blyth, On Simpson’s paradox and the sure-thing principle. J. Am. Stat. Assoc. 67, 364–366 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  • B.L. Bowerman, R.T. O’Connell, Linear Statistical Models (Duxbury, Belmont, 1990)

    Google Scholar 

  • G.E.P. Box, D.R. Cox, An analysis of transformations. J. R. Stat. Soc. B 26, 211–252 (1964)

    MathSciNet  MATH  Google Scholar 

  • G.E.P. Box, W.G. Hunter, J.S. Hunter, Statistics for Experimenters (Wiley, New York, 1978)

    MATH  Google Scholar 

  • G.E.P. Box, G.M. Jenkins, Time Series Analysis: Forecasting and Control, revised edn. (Holden-Day, San Francisco, 1976)

    MATH  Google Scholar 

  • R.G. Braungart, Family status, socialization and student politics: a multivariate analysis. Am. J. Sociol. 77, 108–130 (1971)

    Article  Google Scholar 

  • C. Brewer, Colorbrewer (2002). URL: http://colorbrewer.org

  • L. Brochard, J. Mancebo, M. Wysocki, F. Lofaso, G. Conti, A. Rauss, G. Simonneau, S. Benito, A. Gasparetto, F. Lemaire, D. Isabey, A. Harf, Noninvasive ventilation for acute exacerbations of chronic pulmonary disease. N. Engl. J. Med. 333(13), 817–822 (1995)

    Article  Google Scholar 

  • D.G. Brooks, S.S. Carroll, W.A. Verdini, Characterizing the domain of a regression model. Am. Stat. 42, 187–190 (1988)

    Google Scholar 

  • B.W. Brown Jr., Prediction analyses for binary data, in Biostatistics Casebook, ed. by R.G. Miller Jr., B. Efron, B.W. Brown Jr., L.E. Moses (Wiley, New York, 1980)

    Google Scholar 

  • M.B. Brown, A.B. Forsyth, Robust tests for equality of variances. J. Am. Stat. Assoc. 69, 364–367 (1974)

    Article  MATH  Google Scholar 

  • Bureau of the Census, Statistical Abstract of the United States (U.S. Department of Commerce, Washington, DC, 2001)

    Google Scholar 

  • T.T. Cai, One-sided confidence intervals in discrete distributions. J. Stat. Plan. Inference 131, 63–88 (2003). URL: http://www-stat.wharton.upenn.edu/~tcai/paper/1sidedCI.pdf

  • E. Cameron, L. Pauling, Supplemental ascorbate in the supportive treatment of cancer: re-evaluation of prolongation of survival times in terminal human cancer. Proc. Natl. Acad. Sci. USA 75, 4538–4542 (1978)

    Article  Google Scholar 

  • J.M. Chambers, W.S. Cleveland, B. Kleiner, P.A. Tukey, Graphical Methods for Data Analysis (Wadsworth, Belmont, 1983)

    MATH  Google Scholar 

  • T.F.C. Chan, G.H. Golub, R.J. LeVeque, Algorithms for computing the sample variance: analysis and recommendations.Am. Stat. 37(3), 242–247 (1983)

    MathSciNet  MATH  Google Scholar 

  • W. Chang, J. Cheng, J.J. Allaire, Y. Xie, J. McPherson, shiny: Web Application Framework for R. R Package Version 0.11.1 (2015). URL: http://CRAN.R-project.org/package=shiny

  • R. Chassell, Programming in Emacs Lisp: An Introduction. Free Software Foundation, 2nd edn. (1999) URL: https://www.gnu.org/software/emacs/manual/html_node/eintr/

  • T.W. Chin, E. Hall, C. Gravelle, J. Speers, The influence of Salk vaccination on the epidemic pattern and spread of the virus in the community. Am. J. Hyg. 73, 67–94 (1961)

    Google Scholar 

  • S. Chu, Diamond ring pricing using linear regression. J. Stat. Educ. 4 (1996). URL: http://www.amstat.org/publications/jse/v4n3/datasets.chu.html

  • W.S. Cleveland, Visualizing Data (Hobart Press, Summit, 1993)

    Google Scholar 

  • W.S. Cleveland, R. McGill, Graphical perception: theory, experimentation, and application to the development of graphical methods. J. Am. Stat. Assoc. 79, 531–554 (1984)

    Article  MathSciNet  Google Scholar 

  • W.G. Cochran, G.M. Cox, Experimental Designs, 2nd edn. (Wiley, New York, 1957)

    MATH  Google Scholar 

  • D.R. Collett, Modelling Binary Data (Chapman & Hall, London, 1991)

    Book  MATH  Google Scholar 

  • Comprehensive TE X Archiving Network CTAN (2002). URL: ftp://metalab.unc.edu/pub/packages/TeX/index.html

  • W.J. Conover, M.E. Johnson, M.M. Johnson, A comparative study of tests for homogeneity of variances, with applications to the outer continental shelf bidding data. Technometrics 23, 351–361 (1981)

    Article  Google Scholar 

  • Consumer Reports, Hot dogs, Consumer Reports (1986), pp. 366–367. URL: http://lib.stat.cmu.edu/DASL/Stories/Hotdogs.html

  • R.D. Cook, S. Weisberg, Applied Regression Including Computing and Graphics (Wiley, New York, 1999)

    Book  MATH  Google Scholar 

  • T. Cook, Convictions for Drunkenness (New Society, 1971)

    Google Scholar 

  • CRAN, Comprehensive R  Archive Network (2015). URL: http://CRAN.R-project.org

  • Cytel Software Corporation, Logxact Statistical Software: Release 5 (2004). URL: http://www.cytel.com/LogXact/logxact_brochure.pdf

  • S.R. Dalal, E.B. Fowlkes, B. Hoadley, Risk analysis of the space shuttle: pre-challenger prediction of failure. J. Am. Stat. Assoc. 84, 945–957 (1989)

    Google Scholar 

  • C. Darwin, The Effect of Cross- and Self-fertilization in the Vegetable Kingdom, 2nd edn. (John Murray, London, 1876)

    Book  Google Scholar 

  • Data Archive, J. Stat. Educ. (1997). URL: http://www.amstat.org/publications/jse/jse_data_archive.html

  • O.L. Davies, Design and Analysis of Industrial Experiments (Oliver and Boyd, London, 1954)

    Google Scholar 

  • O.L. Davies, P.L. Goldsmith (eds.), Statistical Methods in Research and Production, 4th edn. (Oliver and Boyd, London, 1972)

    Google Scholar 

  • M.M. Desu, D. Raghavarao, Nonparametric Statistical Methods for Complete and Censored Data, 1st edn. (Chapman & Hall, Boca Raton, 2003)

    MATH  Google Scholar 

  • R. Dougherty, A. Wade (2006).URL: http://vischeck.com

  • D. Edwards, J.J. Berry, The efficiency of simulation-based multiple comparisons. Biometrics 43, 913–928 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  • M.E. Ellis, K.R. Neal, A.K. Webb, Is smoking a risk factor for pneumonia for patients with chickenpox? Br. Med. J. 294, 1002 (1987)

    Article  Google Scholar 

  • J.D. Emerson, M.A. Stoto, Transforming data, in Understanding Robust and Exploratory Data Analysis, ed. by D.C. Hoaglin, F. Mosteller, J.W. Tukey (Wiley, New York, 1983)

    Google Scholar 

  • L.W. Erdman, Studies to determine if antibiosis occurs among Rhizobia: 1. Between Rhizobium meliloti and Rhizobium trifolii. J. Am. Soc. Agron. 38, 251–258 (1946)

    Google Scholar 

  • J.L. Fleiss, Statistical Methods for Rates and Proportions, 2nd edn. (Wiley, New York, 1981)

    MATH  Google Scholar 

  • Forbes Magazine (1993). URL: http://lib.stat.cmu.edu/DASL/Datafiles/ceodat.html

  • R.S. Fouts, Acquisition and testing of gestural signs in four young chimpanzees. Science 180, 978–980 (1973)

    Article  Google Scholar 

  • J. Fox, Regression Diagnostics: An Introduction (Sage, Thousand Oaks, 1991)

    Google Scholar 

  • J. Fox, The R Commander: a basic statistics graphical user interface to R. J. Stat. Softw. 14(9), 1–42 (2005). URL: http://www.jstatsoft.org/v14/i09

  • E.H. Frank Jr., with contributions from Charles Dupont, and many others, Hmisc: Harrell Miscellaneous. R Package Version 3.14-6 (2014). URL: http://CRAN.R-project.org/package=Hmisc

  • Free Software Foundation, Emacs (2015). URL: http://www.gnu.org/software/emacs/

  • R.J. Freund, R.C. Littell, SAS System for Regression (SAS Institute, Inc., Cary, 1991)

    Google Scholar 

  • J.H. Goodnight, Tests of hypotheses in fixed effects linear models. Technical Report R-101 (SAS Institute, Cary, 1978)

    Google Scholar 

  • P. Graham, ANSI Common Lisp (Prentice Hall, Upper Saddle River, 1996)

    Google Scholar 

  • M.J. Greenacre, Theory and Applications of Correspondence Analysis (Academic, New York, 1984)

    MATH  Google Scholar 

  • P. Grosjean, Ide/script editors. Annotated list with links to many editing environments for R. (2012). URL: http://www.sciviews.org/_rgui/

  • R.F. Gunst, R.L. Mason, Regression Analysis and Its Application: A Data-Oriented Approach (Marcel Dekker, New York, 1980)

    MATH  Google Scholar 

  • L.C. Hamilton, Saving water: a causal model of household conservation. Sociol. Perspect. 26(4), 355–374 (1983)

    Article  Google Scholar 

  • L.C. Hamilton, Regression with Graphics (Brooks-Cole, Belmont, 1992)

    MATH  Google Scholar 

  • D.J. Hand, F. Daly, A.D. Lunn, K.J. McConway, E. Ostrowski, A Handbook of Small Data Sets (Chapman and Hall, London, 1994)

    Book  MATH  Google Scholar 

  • D.D. Harrison, D.E. Harrison, T.J. Janik, R. Cailliet, J.R. Ferrantelli, J.W. Hass, B. Holland, Modeling of the sagittal cervical spine as a method to discriminate hypo-lordosis: results of elliptical and circular modeling in 72 asymptomatic subjects, 52 acute neck pain subjects, and 70 chronic neck pain subjects. Spine 29(22):2485–2492 (2004)

    Google Scholar 

  • D.E. Harrison, R. Cailliet, D.D. Harrison, T.J. Janik, B. Holland, Changes in sagittal lumbar configuration with a new method of extension traction combined with spinal manipulation and its clinical significance: non-randomized clinical control trial. Arch. Phys. Med. Rehabil. 83(11), 1585–1591 (2002)

    Article  Google Scholar 

  • R.M. Heavenrich, J.D. Murrell, K.H. Hellman, Light Duty Automotive Technology and Fuel Economy Trends through 1991 (U.S. Environmental Protection Agency, Ann Arbor, 1991)

    Google Scholar 

  • R.M. Heiberger, Computation for the Analysis of Designed Experiments (Wiley, New York, 1989)

    MATH  Google Scholar 

  • R.M. Heiberger, HH: Statistical Analysis and Data Display: Heiberger and Holland. Spotfire S+ Package Version 2.1-29 (2009). URL: http://csan.insightful.com/PackageDetails.aspx?Package=HH

  • R.M. Heiberger, HH: Statistical Analysis and Data Display: Heiberger and Holland. R Package Version 3.1-15 (2015). URL: http://CRAN.R-project.org/package=HH

  • R.M. Heiberger, F.E. Harrell Jr., Design of object-oriented functions in S for screen display, interface and control of other programs (SAS and LaTeX), and S programming, in Computing Science and Statistics, vol. 26 (1994), pp. 367–371. The software is available in both S-Plus and R in library(hmisc). It is included in the S-Plus distribution. It may be downloaded for R from the contrib page of the R Development Core Team (2004) website

    Google Scholar 

  • R.M. Heiberger, B. Holland, Statistical Analysis and Data Display: An Intermediate Course with Examples in S-Plus, R, and SAS, 1st edn. (Springer, New York, 2004)

    Book  MATH  Google Scholar 

  • R.M. Heiberger, B. Holland, Mean–mean multiple comparison displays for families of linear contrasts. J. Comput. Graph. Stat. 14(4), 937–955 (2006)

    Article  MathSciNet  Google Scholar 

  • R.M. Heiberger, E. Neuwirth, R through Excel: A Spreadsheet Interface for Statistics, Data Analysis, and Graphics (Springer, New York, 2009). URL: http://www.springer.com/978-1-4419-0051-7

  • R.M. Heiberger, N.B. Robbins, Design of diverging stacked bar charts for Likert scales and other applications. J. Stat. Softw. 57(5), 1–32 (2014). URL: http://www.jstatsoft.org/v57/i05/

  • R.M. Heiberger, P. Teles, Displays for direct comparison of ARIMA models. Am. Stat. 56, 131–138, 258–260 (2002)

    MathSciNet  Google Scholar 

  • R.M. Heiberger, with contributions from H. Burt, RcmdrPlugin.HH: Rcmdr Support for the HH Package. R Package Version 1.1-42 (2015). URL: http://CRAN.R-project.org/package=RcmdrPlugin.HH

  • C.R. Hicks, K.V. Turner Jr., Fundamental Concepts in Design of Experiments, 5th edn. (Oxford, New York, 1999)

    Google Scholar 

  • J.E. Higgens, G.G. Koch, Variable selection and generalized chi-square analysis of categorical data applied to a large cross-sectional occupational health survey. Int. Stat. Rev. 45, 51–62 (1977)

    Google Scholar 

  • D.C. Hoaglin, F. Mosteller, J.W. Tukey (eds.), Understanding Robust and Exploratory Data Analysis (Wiley, New York, 1983)

    MATH  Google Scholar 

  • Y. Hochberg, A sharper Bonferroni procedure for multiple tests of significance. Biometrika 75, 800–803 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  • Y. Hochberg, A.C. Tamhane, Multiple Comparison Procedures (Wiley, NewYork, 1987)

    Book  MATH  Google Scholar 

  • M. Holzer, Mild therapeutic hypothermia to improve the neurologic outcome after cardiac arrest. N. Engl. J. Med. 346(8), 549–556 (2002)

    Article  Google Scholar 

  • D.W. Hosmer, S. Lemeshow, Applied Logistic Regression, 2nd edn. (Wiley, New York, 2000)

    Book  MATH  Google Scholar 

  • J. Hsu, M. Peruggia, Graphical representations of Tukey’s multiple comparison method. J. Comput. Graph. Stat. 3, 143–161 (1994)

    Google Scholar 

  • R. Ihaka, P. Murrell, K. Hornik, J.C. Fisher, A. Zeileis, Colorspace: Color Space Manipulation. R Package Version 1.2-4 (2013). URL: http://CRAN.R-project.org/package=colorspace

  • R.L. Iman, A Data-Based Approach to Statistics (Duxbury, Belmont, 1994)

    Google Scholar 

  • Insightful Corp., S-Plus Statistical Software: Release 6.1 (2002). URL: http://www.insightful.com.

  • F. John et al., R Commander. R Package Version 2.1-6 (2015). URL: http://CRAN.R-project.org/package=Rcmdr

  • N.L. Johnson, F.C. Leone, Statistics and Experimental Design in Engineering and the Physical Sciences, vol. 2 (Wiley, New York, 1967)

    MATH  Google Scholar 

  • P.E. Johnson, Emacs has no learning curve: Emacs and ess (2015). URL: http://pj.freefaculty.org/guides/Rcourse/emacs-ess/emacs-ess.pdf

  • P.O. Johnson, F. Tsao, Factorial design and covariance in the study of individual educational development. Psychometrika 10, 133–162 (1945)

    Article  Google Scholar 

  • R.W. Johnson, Fitting percentage of body fat to simple body measurements. J. Stat. Educ. 4(1) (1996). URL: http://www.amstat.org/publications/jse/archive.htm

  • D.E. Knuth, The TE Xbook (Addison-Wesley, Reading, 1984)

    Google Scholar 

  • L. Krantz, 1999–2000 Jobs Rated Almanac: The Best and Worst Jobs—250 in All—Ranked by More Than a Dozen Vital Factors Including Salary, Stress, Benefits and More (St. Martins Press, New York, 1999). URL: http://www.hallmaps.com/almanacs_yearbooks/29.shtml

  • L. Lamport, LaTeX: A Document Preparation System: User’s Guide and Reference Manual (Addison-Wesley, Boston, 1994)

    MATH  Google Scholar 

  • M. Lavine, Problems in extrapolation illustrated with space shuttle o-ring data. J. Am. Stat. Assoc. 86, 919–921 (1991)

    Article  Google Scholar 

  • A.J. Lea, New observations on distribution of neoplasms of female breast in certain European countries. Br. Med. J. 1, 488–490 (1965)

    Article  Google Scholar 

  • E.T. Lee, Statistical Methods for Survival Data Analysis (Lifetime Learning Publications, Belmont, 1980)

    MATH  Google Scholar 

  • E. Lehmann, Nonparametrics—Statistical Methods Based on Ranks, revised first edition (Prentice Hall, New York, 1998)

    Google Scholar 

  • F. Leisch, R-core, Sweave: automatic generation of reports (2014). URL: https://stat.ethz.ch/R-manual/R-devel/library/utils/doc/Sweave.pdf

  • A.Y. Lewin, M.F. Shakun, Policy Sciences, Methodology and Cases (Pergammon, Oxford, 1976). URL: http://lib.stat.cmu.edu/DASL/Stories/airpollutionfilters.html

  • R. Likert, A technique for the measurement of attitudes. Arch. Psychol. 140(55), 1–55 (1932)

    Google Scholar 

  • R.J.A. Little, D.B. Rubin, Statistical Analysis with Missing Data, 2nd edn. (Wiley, New York, 2002)

    MATH  Google Scholar 

  • J. Longley, An appraisal of least squares programs for the electronic computer from the point of view of the user. J. Am. Stat. Assoc. 62, 819–841 (1967)

    Article  MathSciNet  Google Scholar 

  • A. Luo, T. Keyes, Second set of results in from the career track member survey, in Amstat News (American Statistical Association, Arlington, 2005), pp. 14–15

    Google Scholar 

  • M. Mächler, S. Eglen, R.M. Heiberger, K. Hornik, S.P. Luque, H. Redesting, A.J. Rossini, R. Sparapani, V. Spinu, ESS (Emacs Speaks Statistics) (2015). URL: http://ESS.R-project.org/

  • P. McCullagh, J.A. Nelder, Generalized Linear Models (Chapman and Hall, London, 1983)

    Book  MATH  Google Scholar 

  • C.R. Mehta, N.R. Patel, P. Senchaudhuri, Efficient Monte Carlo methods for conditional logistic regression. J. Am. Stat. Assoc. 95(449), 99–108 (2000)

    Article  Google Scholar 

  • W.M. Mendenhall, J.T. Parsons, S.P. Stringer, N.J. Cassissi, R.R. Million, T2 oral tongue carcinoma treated with radiotherapy: analysis of local control and complications. Radiother. Oncol. 16, 275–282 (1989)

    Article  Google Scholar 

  • D. Meyer, A. Zeileis, K. Hornik, The strucplot framework: visualizing multi-way contingency tables with vcd. J. Stat. Softw. 17(3), 1–48 (2006). URL: http://www.jstatsoft.org/v17/i03/

  • D. Meyer, A. Zeileis, K. Hornik, vcd: Visualizing Categorical Data. R Package Version 1.2-13 (2012). URL: http://CRAN.R-project.org/package=vcd

  • Microsoft, Inc., Word (2015). URL: https://products.office.com/en-us/Word

  • G.A. Milliken, D.E. Johnson, Analysis of Messy Data, vol. I (Wadsworth, Belmont, 1984)

    MATH  Google Scholar 

  • D.C. Montgomery, Design and Analysis of Experiments, 4th edn. (Wiley, New York, 1997)

    MATH  Google Scholar 

  • D.C. Montgomery, Design and Analysis of Experiments, 5th edn. (Wiley, New York, 2001)

    Google Scholar 

  • D.S. Moore, G.P. McCabe, Introduction to the Practice of Statistics (Freeman, New York, 1989)

    MATH  Google Scholar 

  • F. Mosteller, J.W. Tukey, Data Analysis and Regression (Addison-Wesley, Reading, 1977)

    Google Scholar 

  • J.D. Murray, G. Dunn, P. Williams, A. Tarnopolsky, Factors affecting the consumption of psychotropic drugs. Psychol. Med. 11, 551–560 (1981)

    Article  Google Scholar 

  • P. Murrell, R Graphics, 2nd edn. (CRC, Boca Raton, 2011). URL: http://www.taylorandfrancis.com/books/details/9781439831762/

  • R.H. Myers, Classical and Modern Regression with Applications, Chap. 5 (PWS-Kent, Boston, 1990), p. 218

    Google Scholar 

  • S.C. Narula, J.T. Wellington, Prediction, linear regression and the minimum sum of errors. Technometrics 19, 185–190 (1977)

    Article  MATH  Google Scholar 

  • U.S. Navy, Procedures and Analyses for Staffing Standards Development: Data/Regression Analysis Handbook (Navy Manpower and Material Analysis Center, San Diego, 1979)

    Google Scholar 

  • J.A. Nelder, A reformulation of linear models. J. R. Stat. Soc. 140(1), 48–77 (1977). doi:10.2307/2344517

    MathSciNet  Google Scholar 

  • J. Neter, M.H. Kutner, C.J. Nachtsheim, W. Wasserman, Applied Linear Statistical Models, 4th edn. (Irwin, Homewood, 1996)

    Google Scholar 

  • E. Neuwirth, RColorBrewer: ColorBrewer Palettes. R Package Version 1.0-5 (2011). URL: http://CRAN.R-project.org/package=RColorBrewer

  • E. Neuwirth, RExcel (2014). URL: http://rcom.univie.ac.at

  • New Zealand Ministry of Research Science and Technology, Staying in science (2006). URL: http://www.morst.govt.nz/Documents/publications/researchreports/Staying-in-Science-summary.pdf

  • D.F. Nicholls, The analysis of time series—the time domain approach. Aust. J. Stat. 21, 93–120 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  • NIST, National Institute of Standards and Technology, Statistical Engineering Division (2002). URL: http://www.itl.nist.gov/div898/software/dataplot.html/datasets.htm

  • NIST, National Institute of Standards and Technology, Data set of southern oscillations, in NIST/SEMATECH e-Handbook of Statistical Methods (2005). URL: http://www.itl.nist.gov/div898/handbook/pmc/section4/pmc4412.htm

  • Olympic Committee, Salt Lake City 2002 Winter Olympics (2001). URL: http://www.saltlake2002.com

  • R.L. Ott, An Introduction to Statistical Methods and Data Analysis, 4th edn. (Duxbury, Belmont, 1993)

    Google Scholar 

  • S.C. Pearce, The Agricultural Field Experiment (Wiley, New York, 1983)

    Google Scholar 

  • K. Penrose, A. Nelson, A. Fisher, Generalized body composition prediction equation for men using simple measurement techniques (abstract). Med. Sci. Sports Exerc. 17(2), 189 (1985)

    Google Scholar 

  • D.H. Peterson (ed.), Aspects of Climate Variability in the Pacific and the Western Americas. Number 55 in Geophysical Monograph (American Geophysical Union, Washington, DC, 1990)

    Google Scholar 

  • R.G. Peterson, Design and Analysis of Experiments (Marcel Dekker, New York/Basel, 1985)

    Google Scholar 

  • R Core Team, R: A Language and Environment for Statistical Computing (R Foundation for Statistical Computing, Vienna, 2015). URL: http://www.R-project.org/

  • R Development Core Team, R: A Language and Environment for Statistical Computing (R Foundation for Statistical Computing, Vienna, 2004). URL: http://www.R-project.org. ISBN 3-900051-00-3

  • W. Rasband, Imagej 1.46t (2015). URL: http://rsb.info.nih.gov/ij

  • N.B. Robbins, Creating More Effective Graphs (Chart House, Ramsey, 2005, reissued 2013) [Originally Wiley-Interscience]

    Google Scholar 

  • N.B. Robbins, R.M. Heiberger, E. Neuwirth, C. Ritter, Professional statistics and graphics accessible from excel, in Presented at the Joint Statistics Meetings (American Statistical Association, Washington, DC, 2009). URL: http://rcom.univie.ac.at/papers/handoutJSM2009.pdf

  • W.S. Robinson, Ecological correlations and the behavior of individuals. Am. Sociol. Rev. 15, 351–357 (1950)

    Article  Google Scholar 

  • A.J. Rossini, R.M. Heiberger, R.A. Sparapani, M. Mächler, K. Hornik, Emacs Speaks Statistics (ESS): a multiplatform, multipackage development environment for statistical analysis. J. Comput. Graph. Stat. 13(1), 247–261 (2004). URL: http://dx.doi.org/10.1198/1061860042985

  • A.J. Rossman, Televisions, physicians, and life expectancy. J. Stat. Educ. (1994). URL: http://www.amstat.org/publications/jse/archive.htm

  • RStudio, Shiny: a web application framework for r (2015). URL: http://shiny.rstudio.com

  • D. Sarkar, Lattice: Multivariate Data Visualization with R (Springer, New York, 2008). URL: http://lmdvr.r-forge.r-project.org. ISBN 978-0-387-75968-5

  • D. Sarkar, lattice: Lattice Graphics. R Package Version 0.20-29 (2014). URL: http://CRAN.R-project.org/package=lattice

  • D. Sarkar, F. Andrews, latticeExtra: Extra Graphical Utilities Based on Lattice. R Package Version 0.6-26 (2013). URL: http://CRAN.R-project.org/package=latticeExtra

  • S. Sarkar, Some probability inequalities for ordered MTP2 random variables: a proof of the Simes conjecture. Ann. Stat. 26, 494–504 (1998)

    Article  MATH  Google Scholar 

  • SAS Institute, Inc., The four types of estimable functions, in SAS/STAT User’s Guide (SAS Institute, Inc., Cary, 1999)

    Google Scholar 

  • C. Schenk, MikTeX (2001). URL: ftp://metalab.unc.edu/pub/packages/TeX/systems/win32/miktex

  • S.R. Searle, Linear Models (Wiley, New York, 1971)

    MATH  Google Scholar 

  • H.C. Selvin, Durkheim’s suicide: further thoughts on a methodological classic, in Émile Durkheim, ed. by R.A. Nisbet (Prentice Hall, Englewood Cliffs, NJ, 1965), pp. 113–136

    Google Scholar 

  • R.T. Senie, P.P. Rosen, M.L. Lesser, D.W. Kinne, Breast self-examinations and medical examination relating to breast cancer stage. Am. J. Public Health 71, 583–590 (1981)

    Article  Google Scholar 

  • N. Shaw, Manual of Meteorology, vol. 1 (Cambridge University Press, Cambridge, 1942)

    MATH  Google Scholar 

  • W.J. Shih, S. Weisberg, Assessing influence in multiple linear regression with incomplete data.Technometrics 28, 231–240 (1986)

    Google Scholar 

  • J. Simpson, A. Olsen, J.C. Eden, A Bayesian analysis of a multiplicative treatment effect in weather modification. Technometrics 17, 161–166 (1975)

    Article  Google Scholar 

  • W. Smith, L. Gonick, The Cartoon Guide to Statistics (HarperCollins, New York, 1993)

    Google Scholar 

  • G.W. Snedecor, W.G. Cochran, Statistical Methods, 7th edn. (Iowa State University Press, Ames, 1980)

    MATH  Google Scholar 

  • R.R. Sokal, F.J. Rohlf, Biometry, 2nd edn. (W.H. Freeman, New York, 1981)

    MATH  Google Scholar 

  • R.M. Stallman, Emacs (2015). URL: http://www.gnu.org/software/emacs/

  • R.G.D. Steel, J.H. Torrie, Principles and Procedures of Statistics, 1st edn. (McGraw-Hill, Auckland, 1960)

    MATH  Google Scholar 

  • P.H. Sulzberger, The effects of temperature on the strength of wood, plywood and glued joints. Technical Report (Aeronautical Research Consultative Committee, Australia, Department of Supply, 1953)

    Google Scholar 

  • N. Teasdale, C. Bard, J. LaRue, M. Fleury, On the cognitive penetrability of posture control. Exp. Aging Res. 19, 1–13 (1993)

    Article  Google Scholar 

  • The TeX Users Group (TUG), The MacTeX-2014 Distribution (2014). URL: http://tug.org/mactex/

  • TIBCO Software Inc., TIBCO Spotfire S+: Release 8.2 (2010). URL: https://edelivery.tibco.com/storefront/eval/tibco-spotfire-s-/prod10222.html

  • TIBCO Software Inc., The TIBCO Enterprise Runtime for R Engine (2014). URL: http://spotfire.tibco.com/discover-spotfire/what-does-spotfire-do/predictive-analytics/tibco-enterprise-runtime-for-r-terr

  • R. Till, Statistical Methods for the Earth Scientist (Macmillan, London, 1974)

    Book  Google Scholar 

  • E.R. Tufte, The Visual Display of Quantitative Information, 2nd edn. (Graphics Press, Cheshire, 2001)

    Google Scholar 

  • J.W. Tukey, One degree of freedom for nonadditivity. Biometrics 5(3), 232–242 (1949)

    Article  MathSciNet  Google Scholar 

  • W. Vandaele, Participation in illegitimate activities: Erlich revisited, in Deterrence and Incapacitation, ed. by A. Blumstein, J. Cohen, D. Nagin (National Academy of Sciences, Washington, DC, 1978), pp. 270–335

    Google Scholar 

  • P.K. VanVliet, J.M. Gupta, Tham-v-sodium bicarbonate in idiopathic respiratory distress syndrome. Arch. Dis. Child. 48, 249–255 (1973)

    Article  Google Scholar 

  • W.N. Venables, Exegeses on linear models, in Proceedings of the S-PLUS Users Conference, Washington, DC (1998). URL: http://www.stats.ox.ac.uk/pub/MASS3/Exegeses.pdf

  • W.N. Venables, B.D. Ripley, Modern Applied Statistics with S-PLUS, 2nd edn. (Springer, New York, 1997)

    Book  MATH  Google Scholar 

  • H. Wainer, Graphical Tales of Fate and Deception from Napoleon Bonaparte to Ross Perot (Copernicus Books, New York, 1997)

    Google Scholar 

  • W.W.S. Wei, Time Series Analysis, Univariate and Multivariate Methods (Addison-Wesley, Reading, 1990)

    MATH  Google Scholar 

  • A.M. Weindling, F.M. Bamford, R.A. Whittall, Health of juvenile delinquents. Br. Med. J. 292, 447 (1986)

    Article  Google Scholar 

  • S. Weisberg, Applied Linear Regression, 2nd edn. (Wiley, New York, 1985)

    MATH  Google Scholar 

  • I. Westbrooke, Simpson’s paradox: an example in a New Zealand survey of jury composition. Chance 11, 40–42 (1998)

    Article  Google Scholar 

  • P.H. Westfall, D. Rom, Bootstrap step-down testing with multivariate location shift data. Unpublished (1990)

    Google Scholar 

  • H. Wickham, Ggplot2: Elegant Graphics for Data Analysis (Springer, New York, 2009). URL: http://had.co.nz/ggplot2/book

  • Wikipedia, Integrated Development Environment (2015). URL: http://en.wikipedia.org/wiki/Integrated_development_environment

  • L. Wilkinson, The Grammar of Graphics (Springer, New York, 1999)

    Book  MATH  Google Scholar 

  • A.F. Williams, Teenage passengers in motor vehicle crashes: a summary of current research. Technical report (Insurance Institute for Highway Safety, Arlington, 2001)

    Google Scholar 

  • E.J. Williams, Regression Analysis (Wiley, New York, 1959)

    MATH  Google Scholar 

  • N. Woods, P. Fletcher, A. Hughes, Statistics in Language Studies (Cambridge University Press, Cambridge, 1986)

    Book  Google Scholar 

  • World Almanac and Book of Facts, World Almanac and Book of Facts, 2002 edn. (World Almanac Books, New York, 2001)

    Google Scholar 

  • E.L. Wynder, A. Naravvette, G.E. Arostegui, J.L. Llambes, Study of environmental factors in cancer of the respiratory tract in Cuba. J. Natl. Cancer Inst. 20, 665–673 (1958)

    Google Scholar 

  • Y. Xie (2015). URL: http://cran.r-project.org/web/packages/knitr/knitr.pdf

  • F. Yates, The analysis of multiple classifications with unequal numbers in the different classes. J. Am. Stat. Assoc. 29, 51–56 (1934)

    Article  MATH  Google Scholar 

  • F. Yates, The Design and Analysis of Factorial Experiments (Imperial Bureau of Soil Science, Harpenden, 1937)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Statistics, Temple University, Philadelphia, PA, USA

    Richard M. Heiberger & Burt Holland

Authors
  1. Richard M. Heiberger
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Burt Holland
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer Science+Business Media New York

About this chapter

Cite this chapter

Heiberger, R.M., Holland, B. (2015). Multiple Regression—Dummy Variables, Contrasts, and Analysis of Covariance. In: Statistical Analysis and Data Display. Springer Texts in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2122-5_10

Download citation

Publish with us

Policies and ethics

Search

Navigation