In an interaction model, the relationship between $E ( y )$ and $x _ { 1 }$ is linear for each fixed value of $x _ { 2 }$ but the slopes of the lines relating $E ( y )$ and $x _ { 1 }$ may be different for two different fixed values of $x _ { 2 }$.

Question

Quizplus · Accepted Answer

In an interaction model, the effect of one explanatory variable ($x_1$) on the expected value of the outcome variable ($E(y)$) depends on the level of another explanatory variable ($x_2$). This means that while the relationship between $E(y)$ and $x_1$ remains linear for any fixed value of $x_2$, the slope of this relationship (i.e., how much $E(y)$ changes with a one-unit change in $x_1$) can vary depending on the value of $x_2$, indicating an interaction between $x_1$ and $x_2$.

In an Interaction Model, the Relationship Between E(y)E ( y )E(y)

In an Interaction Model, the Relationship Between $E ( y )$