Multiple linear regression generalizes straight line regression to allow multiple explanatory (or predictor) variables, in this chapter under the normal errors assumption. The focus may be on accurate prediction. Or it may, alternatively or additionally, be on the regression coefficients themselves. Simplistic interpretations of coefficients can be grossly misleading. Later chapters elaborate on the ideas and methods developed in this chapter, applying them in new contexts. The attaching of causal interpretations to model coefficients must be justified both by reference to subject area knowledge and by careful checks to ensure that they are not artefacts of the correlation structure. There is attention to regression diagnostics, to assessment, and comparison of models. Variable selection strategies can readily over-fit. Hence the importance of training/test approaches and cross-validation. The potential is demonstrated for errors in x to seriously bias regression coefficients. Strong multicollinearity leads to large variance inflation factors.

Multilevel multicomponent complex adaptive systems are not reducible to the sum of the causal effects of independent variables. Causal inference, which has a privileged place in contemporary IR (and many other social sciences) cannot address systems effects, which arise from interdependent elements and operations (not the impact of independent variables on dependent variables). Systems effects explanations explain why by showing how. They identify mechanisms and processes of causation. They thus are able to establish causal efficacy; that is, show how processes produce – actually cause – outcomes (rather than merely identify some elements that are part of an unspecified causal process). Such an understanding leads us away from a “laws and theories” conception of science, which remains popular in Physics and Chemistry, towards a “models and mechanisms” understanding, which predominates in the life sciences (which, on their face, seem a much better model for the social sciences).

This and the following four chapters address the systemic/structural theory of Kenneth N. Waltz. Despite extensive criticisms of its details, Waltz’s account of the nature of system, structures, and systemic/structural theory continues to predominate in contemporary IR. This chapter shows that, despite its systemic starting point, Waltzian structural theory is thoroughly analytic. Waltz replaced components arranged and operating as parts of a structured whole with a reified structure that exerts causal effects on units that interact with one another and with the structure. The resulting one-sided explanation of the actions of “units” by “the system” reduces systems to mere environments of autonomous actors (whose activities are not constituted, generated, or structured by being parts of a system but are simply constrained by external “system-level” forces).