What are the indications that one should be using interaction variables in their linear regression model? I am on page 87 of ISLR 2nd edition.
What are the indications that one should be using interaction variables in their linear regression model? Basically: When do you know "ah, I should be using interaction variables"?

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*Are there any general rules or hard-and-fast rules that I should be looking out for?

*Eg. If 2 variables on a standalone basis are statistically significant, then you should look into creating an interaction variable with the both of them? Or do we just manually go through all the possible combinations of the variables, create interaction variables out of them, and see via trial and error if the interaction is significant or not? Or is it just conjectured via gut feeling, like we just "guess" that these two variables may have synergy.

Would love rules from a trusted source that detail step-by-step what is the process for selecting interaction variables (eg. start from the variables with the highest coefficient/significance and create an interaction variable from them, and then...)

The prior for any interaction is that it is likely very, perhaps vanishingly, small (see Tosh 2021). As such, you should not explore or add-in interaction terms unless you expect them, a priori, to be large or informative. Doing so creates a massive risk for false-positives. Generally, one should only add in interactions when they are well-established or when the interaction is the question of interest (one might also add in specific interaction terms as confounders when testing an interaction of interest in a regression - see Keller 2014).
