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

The use of regression analysis is common in research. This article presents an introductory section that explains basic terms and concepts such as independent and dependent variables (IVs and DVs), covariates and confounds, zero-order correlations and multiple correlations, variance explained by variables and shared variance, bivariate and multivariable linear regression, line of least squares and residuals, unadjusted and adjusted analyses, unstandardized (b) and standardized (β) coefficients, adjusted R², interaction terms, and others. Next, this article presents a more advanced section with the help of 3 examples; the raw data files for these examples are included in supplementary materials, and readers are encouraged to download the data files and run the regressions on their own in order to better follow what is explained in the text (this, however, is not mandatory, and readers who do not do so can also follow the discussions in the text). The 3 examples illustrate many points. When important covariates are not included in regressions, the included IVs explain a smaller proportion of the variance in the DV, and the relationships between the included IVs and the DV may not be correctly understood. Including interaction terms between IVs can improve the explanatory value of the model whether the IVs are intercorrelated or not. When IVs are intercorrelated (such as when one is a confound), although their net effect in multivariable regression may explain a greater proportion of the variance in the DV, their individual b and β coefficients decrease in proportion to the shared variance that is removed. Thus, variables that were found statistically significant in unadjusted analyses may lose statistical significance in fully adjusted analyses. Readers may find it useful to keep these points in mind when running regressions on their data or when reading studies that present their results through regressions.