Regression Analysis


Regression analysis describes the average association of a focal outcome variable with one or more predictor variables. Even though relatively few modern analyses stop with the most basic type of regression analysis, its foundational concepts and techniques lie at the core of advanced modeling strategies. This entry explains these fundamental ideas and approaches based on a linear regression estimated with the ordinary least squares approach, setting the stage for other entries that examine their extensions to advanced models. The entry begins by discussing why regression modeling is so useful, commenting on the historical origins of the approach. Then, key components of linear regression models are presented along with how these components are estimated and interpreted. Bivariate models, with one predictor variable, are discussed first. Then, multiple regression models, which have two or more predictors, are covered. Final sections consider the ways in which regression modeling can be extended and its assumptions tested and related. Throughout, examples are provided that demonstrate how regression models have been used in a wide array of applications from popular media to industry to scholarly journals. Regression analysis is a useful tool not only for highly sophisticated and seemingly esoteric academic applications but also for basic descriptions of data covering many societal contexts. Across applications, however, the strengths and limitations of regression modeling approaches should be kept front and center. Balancing the two is emphasized throughout the entry.

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