Regression

Regression models are widely used for addressing scientific questions of interest regarding the associations among a set of variables. In particular, linear regression models describe how part of the natural individual-to-individual variation in a continuous response variable can be explained by one or more explanatory variables. In this article we provide a general overview of regression concepts, emphasizing the two most common goals of regression analysis: explanation and prediction. We discuss various aspects of interpretation of regression coefficients. We also consider the notions of confounding and interaction within regression analyses. Finally, we consider important generalizations of linear regression to handle the case where the response variable is binary (logistic regression) and also settings with correlated responses (e.g., repeated measurements on individuals over time). We conclude by discussing how linear and logistic regression are special cases of a broad and useful collection of regression models known as generalized linear models.