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... • . . . the statement “yi causes yj” is just shorthand for the more precise, but longwinded, statement, “yi contains useful information for predicting yj (in the linear least squares sense), over and above the past histories of the other variables in the system.” To save space, we simply say that yi ...
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Interaction (statistics)



In statistics, an interaction may arise when considering the relationship among three or more variables, and describes a situation in which the simultaneous influence of two variables on a third is not additive. Most commonly, interactions are considered in the context of regression analyses.The presence of interactions can have important implications for the interpretation of statistical models. If two variables of interest interact, the relationship between each of the interacting variables and a third ""dependent variable"" depends on the value of the other interacting variable. In practice, this makes it more difficult to predict the consequences of changing the value of a variable, particularly if the variables it interacts with are hard to measure or difficult to control.The notion of ""interaction"" is closely related to that of ""moderation"" that is common in social and health science research: the interaction between an explanatory variable and an environmental variable suggests that the effect of the explanatory variable has been moderated or modified by the environmental variable.
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