Confounding Without Interaction?

#1
Hello,

The attached image (source:
) is clearly an example of confounding, in regards to the effect of x on y, considering the third variable, z (qualitative variable).

Here's my proposed statement: although there is confounding present, there is not interaction; the linear effect of x on y does not depend on the level of z.

Is my statement correct? I'm thinking it depends on how you formally define interaction, and my definition may not be formal enough.

Thanks,
Ben
 

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#2
Didnt watch the video but interaction is that the mutual presence of the two predictors at the same time change their effects on the outcome on additive or multiplicative scale in a synergistic or antagonistic direction. Think about risk for lung cancer and the increased risk for smokers and asbestos or radon workers. Having both, is worse than each's individual risk combined.

confounding is when you do not address a common cause of a predictor and outcome. So when it (confounder) isnt in the model there is an open backdoor path between the two variables, which bias the true effect between them.