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Understanding statistical principles in linear and logistic regression

Alice M Richardson, Grace Joshy and Catherine A D'Este
Med J Aust 2018; 208 (8): . || doi: 10.5694/mja17.00222
Published online: 7 May 2018

A previous article in this series assessed the association between two variables.1 Here, we introduce the concept of multivariable regression.2-4 A regression model establishes the relationship between one or more exposure, or explanatory, variables (such as height, weight and sex) and an outcome (such as body mass index or smoking status). The resulting model describes the nature of the relationship between explanatory variables and outcome, and can be used to predict an unknown outcome value based on given values of the explanatory variables. The term “multivariate” indicates more than one outcome being analysed concurrently, and “multivariable” indicates more than one explanatory variable being analysed. This article concentrates on one outcome and multiple explanatory variables.


  • National Centre for Epidemiology and Population Health, Australian National University, Canberra, ACT


Correspondence: Alice.Richardson@anu.edu.au

Series Editors

John R Attia 

Michael P Jones


Competing interests:

No relevant disclosures.

  • 1. Jones MP, Walker MM, Attia JR. Understanding statistical principles in correlation, causation and moderation in human disease. Med J Aust 2017; 207: 104-106. <MJA full text>
  • 2. Altman DG. Practical statistics for medical research. London: Chapman & Hall/CRC, 2006.
  • 3. Armitage P, Berry G, Matthews JNS. Statistical methods in medical research. 4th ed. Malden, MA: Blackwell Science, 2002.
  • 4. Clayton D, Hills M. Statistical models in epidemiology. Oxford: Oxford University Press, 1993.
  • 5. Kirkwood BR, Sterne JAC. Essential medical statistics. Malden, MA: Blackwell Science, 2003.
  • 6. Attia JR, Jones MP, Hure A. Deconfounding confounding part 1: traditional explanations. Med J Aust 2017; 206: 244-245. <MJA full text>
  • 7. Attia JR, Oldmeadow C, Holliday EG, Jones MP. Deconfounding confounding part 2: using directed acyclic graphs (DAGs). Med J Aust 2017; 206: 480-483. <MJA full text>
  • 8. Hosmer DW, Lemeshow S. Applied logistic regression. 2nd ed. New York: Wiley, 2000.

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