Regression: Understanding What Covariates and Confounds Do in Adjusted Analyses.

Area of Science:

• Statistical modeling
• Quantitative research methods
• Data analysis

Background:

• Regression analysis is widely used across scientific disciplines.
• Accurate interpretation of regression results is essential for valid research conclusions.
• Many researchers require a clear understanding of regression principles and potential pitfalls.

Purpose of the Study:

• To provide an accessible introduction to fundamental regression analysis concepts.
• To illustrate advanced regression principles using practical examples.
• To enhance researchers' ability to correctly interpret regression outputs.

Main Methods:

• Explanation of core regression terms: independent and dependent variables, covariates, confounds, correlations, variance, bivariate and multivariable linear regression.
• Detailed discussion of regression components: least squares, residuals, unadjusted and adjusted analyses, coefficients (b and β), adjusted R², and interaction terms.
• Illustrative examples with downloadable raw data to demonstrate key regression concepts and interpretation.

Main Results:

• Omitting key covariates reduces the variance explained by independent variables and can distort their relationships with the dependent variable.
• Incorporating interaction terms can enhance a regression model's explanatory power, regardless of independent variable intercorrelation.
• Intercorrelated independent variables, including confounds, reduce individual coefficient estimates proportionally to shared variance, potentially impacting statistical significance.

Conclusions:

• Properly accounting for covariates and confounds is vital for accurate regression modeling.
• Interaction terms offer a valuable method for improving model fit and understanding complex relationships.
• Researchers must be aware of how variable intercorrelation affects coefficient interpretation in multivariable regression analyses.