Question

An interaction term is the multiplication of two or more explanatory variables

true or false

Answer 1

TRUE

explanation ----

Consider this model:

Y=β₀+β₁X₁+β₂X₂+ε.

Now, the marginal effect of X₁on Y(Y's derivative w.r.t X₁) is simply β₁. I can replace β₁ with anything, that will be X₁ 's effect (assuming it doesn't contain X₁):

Y=β₀+(<what we write here will be X₁ 's effect>)X₁+β₂X₂+ε

In the first case, we wrote β₁, which is a constant, so the effect of X₁is independent of X₂ That's why there is no interaction. We want to introduce an interaction, i.e., that X₁ 's effect depends on X₂? Let's write something there which depends on X₂ ​​​​​​?  For simplicity, be linear here as well, i.e., assume that the dependence itself is also linear:

Y=β₀+(β₁+ɣ₁₂X₂)X₁+β₂X₂+ε..

That is, the effect of X₁ will be β₁+ɣ₁₂X₂ so we have the interaction as we aimed for: the effect of X₁ depends on the value of X₂. (In this simplest case, linearly.)

Now we expand it:

β₀+β₁X₁+ɣ₁₂X₂X₁+β₂X₂+ε

and voilá, we have the product.

interaction term is the multiplication of two or more explanatory variables.