Abstract
In the previous chapters, we have focused on relationships between only two variables at a time. Most relationships that we are interested in social science research are more complicated, however, than can be understood with only bivariate analyses. In some cases, the relationship between two variables depends entirely on a third variable, and so a bivariate analysis can be misleading. In some cases, the relationship between two variables depends on, or operates through, additional variables. In this chapter, we will discuss multiple regression. In multiple regression analysis, a single outcome variable is modeled as a linear combination of as many additional variables as desired. Multiple regression is sometimes used simply to understand factors that are relevant to predicting an outcome, but it is also used in science to help establish that the relationship between two variables is a causal one and to understand complex relationships that simply cannot be understood with bivariate analyses. In this chapter, before introducing the details of multiple regression, we will discuss causal thinking in order to lay the foundation for seeing why multivariate analyses are necessary.
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- 1.
In fact, my wife has informed me that she would never do so. We may have to talk about this, but doing so is beyond the scope of this chapter.
- 2.
Teleological arguments—arguments in which actions in nature are purposeful, with some sort of predetermined endpoint that causes actions along the way to the endpoint—have long been rejected in science.
- 3.
This can happen either because the respondent selects him/herself into a treatment vs. control group or because the experimenter does. For example, suppose an experimenter assigns sicker patients to the control group in an experiment evaluating how well a new drug works.
- 4.
Total, direct, and indirect effects do not need to be in a standardized metric. However, I use standardized coefficients here so that the relative magnitudes of the effects are more apparent.
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Lynch, S.M. (2013). Introduction to Multiple Regression. In: Using Statistics in Social Research. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8573-5_10
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