Interaction Terms
When the effect of salary depends on position
The additive model forces both groups to have the same slope. But is that a reasonable assumption?
Right now the model assumes that an extra €1M in salary has the same effect on market value for both goalkeepers and outfield players.
But what if the salary effect is different for each group? Maybe an extra €1M matters more for outfield players than for goalkeepers. The additive model can't capture that — we need a way to let the slope vary by group.
An interaction term lets the slope differ between groups. We multiply salary × position.
We add a new variable: salary × outfield. This is zero for all goalkeepers, and equals the salary for outfield players.
| Salary | Outfield | Salary × Outfield |
|---|---|---|
| 5 | 0 | 0 |
| 5 | 1 | 5 |
| 10 | 0 | 0 |
| 10 | 1 | 10 |
For goalkeepers (outfield = 0), the interaction term is always zero — it vanishes from the equation. For outfield players, it adds an extra salary effect on top of b₁.
Now each group gets its own slope and intercept.
b₃ tells us how much steeper the salary effect is for outfield players compared to goalkeepers.
For each extra €1M in salary, outfield players gain 1.66 M€ more in market value than goalkeepers.
Compare: parallel vs non-parallel.