[Paper Review] Dummy variables and their interactions in regression analysis: examples from research on body mass index

Manfred te Grotenhuis, P.E. Thijs|arXiv (Cornell University)|Nov 18, 2015

Obesity, Physical Activity, Diet5 references18 citations

TL;DR

This paper provides a practical, non-technical guide to using dummy variables and their interactions in regression analysis, using body mass index (BMI) data to illustrate how to model differences by gender and education level. It demonstrates correct coding, interpretation, and statistical inference for nominal and ordinal predictors, with applied examples, SPSS syntax, and data available online, making it ideal for students and researchers new to regression modeling with categorical variables.

ABSTRACT

This paper is especially written for students and demonstrates the correct use of nominal and ordinal scaled variables in regression analysis by means of so-called dummy variables. We start out with examples of body mass index (BMI) differences between males and females, and between low, middle, and high educated people. We extend our examples with several explanatory (dummy) variables and the interactions between dummy variables. Readers learn how to use dummy variables and their interactions and how to interpret the statistical results. We included data, SPSS syntax, and additional information on a website (http://www.ru.nl/sociology/mt/bmi/downloads/) that goes with this text. No mathematical knowledge is required.

Motivation & Objective

• To teach students and researchers how to correctly apply dummy variables in regression analysis for nominal and ordinal variables.
• To demonstrate the interpretation of regression coefficients when using dummy variables and their interactions.
• To provide accessible, applied examples using real BMI data to illustrate gender and education-level differences in body mass index.
• To offer SPSS syntax and supplementary materials to support hands-on learning and replication of results.
• To clarify common misconceptions in coding and interpreting categorical predictors in regression models.

Proposed method

• Use of dummy coding to represent nominal and ordinal variables (e.g., gender, education level) in linear regression.
• Incorporation of interaction terms between dummy variables to assess conditional effects (e.g., gender differences by education level).
• Application of ordinary least squares (OLS) regression to model BMI as a function of categorical predictors and their interactions.
• Step-by-step explanation of how regression coefficients correspond to group means and differences in the context of dummy variable coding.
• Use of SPSS syntax to implement models and generate output, with detailed interpretation of regression tables and effect sizes.
• Inclusion of supplementary data and syntax on a dedicated website to enable replication and practical learning.

Experimental results

Research questions

• RQ1 How do male and female BMI levels differ when controlling for education level?
• RQ2 How do BMI levels vary across low, middle, and high education groups?
• RQ3 What is the nature of the interaction between gender and education level in predicting BMI?
• RQ4 How should regression coefficients be interpreted when using dummy variables and their interactions?
• RQ5 What are the correct coding and interpretation practices for categorical variables in regression analysis?

Key findings

• Males consistently show higher BMI than females in the dataset, with a statistically significant difference in the regression model.
• Individuals with higher education levels tend to have lower BMI compared to those with lower education, with a significant trend across the three education groups.
• The interaction between gender and education level reveals that the gender difference in BMI is more pronounced in the low-education group, suggesting a conditional effect.
• Proper dummy variable coding ensures that regression coefficients represent meaningful contrasts between reference and comparison groups.
• The inclusion of interaction terms allows for the detection of subgroup differences that would be missed by main effects alone.
• The SPSS syntax and data provided enable accurate replication of all models and facilitate learning through practical application.