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In multiple regression, I've seen the following phenomena, but I am wondering if there's a formal terminology for each of these:

(1) A regressor, when added, flips the coefficient sign of some other regressor

(2) A regressor, when added, reduces the magnitude of the coefficient of another regressor to zero

(3) A regressor, when added, increases the magnitude of the coefficient of another regressor from zero or negligible number to a more significant value

Based on Suppression effect in regression: definition and visual explanation/depiction, it appears (3) is known as "suppression." What about the first two? Have I missed any others?

24n8
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  • Multicollinearity: https://en.wikipedia.org/wiki/Multicollinearity#Consequences – Sergio Apr 21 '21 at 19:10
  • @Sergio But this post isn't about multicollinearity. You can have these phenomena outside of the presence of multicollinearity – 24n8 Apr 21 '21 at 19:11
  • The first one sounds like Simpson’s paradox: https://en.m.wikipedia.org/wiki/Simpson%27s_paradox. – Dave Apr 22 '21 at 00:46

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This may reflect bias possibly caused by an excluded variable. If an excluded variable influences Y and is correlated with an X in the model this can bias the slope of that X (including flipping the sign I assume). I think this is called excluded variable bias. You should be careful with assuming, however, there is a formal terminology in statistics. Different authors use different words for the same thing. Or the same words for different things. Gelman found I think nine different uses of the term random effects, and hierarchical regression can mean multilevel models or forms of regression that has nothing to do with that approach. It is one of the frustrating elements of statistics to me

user54285
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