Suppose that after going apple picking you have 12 apples left over. You decide to conduct an experiment to investigate how quickly they will rot under certain conditions. You place six apples in a cool spot in your basement, and leave the other six on the window sill in the kitchen. Every week, you estimate the percentage of the surface area of the apple that is rotten or moldy.
Consider the following models:
$$ rot = \beta_0 + \beta_1 \cdot t + \beta_2 \cdot temp \,, $$
$$ rot = \beta_0 + \beta_1 \cdot t + \beta_2 \cdot temp + \beta_3 \cdot temp \cdot t \,, $$
where \(t\) is time, measured in weeks, and \(temp\) is a binary variable indicating either cool or warm.
If you decide to keep the interaction term present in the second model, you are implicitly assuming that: