How do interaction terms in multiple regression change how I interpret coefficients?

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AcadiFi · Accepted Answer

Interaction terms change the interpretation fundamentally: a coefficient on a main effect no longer represents the total effect of that variable because part of the effect now runs through the interaction. You have to read them jointly.

Suppose Torrini Apparel models monthly revenue (in thousands USD) as: Revenue = 120 + 8.4 × Marketing + 25 × RegionEast + 3.1 × (Marketing × RegionEast) + error. Marketing is in thousands; RegionEast is a dummy (1 if East, 0 otherwise).

For stores in the West (RegionEast = 0), the model simplifies to: Revenue = 120 + 8.4 × Marketing. Each additional $1,000 in marketing spend adds $8,400 in revenue.

For stores in the East (RegionEast = 1), it becomes: Revenue = (120 + 25) + (8.4 + 3.1) × Marketing = 145 + 11.5 × Marketing. Marketing is more productive in the East: every $1,000 adds $11,500 instead of $8,400.

The main effect of marketing (8.4) is NOT 'the average effect of marketing across regions.' It's specifically the effect when RegionEast = 0. The total marketing effect in the East is the main effect PLUS the interaction coefficient: 8.4 + 3.1 = 11.5.

Common mistakes: interpreting the main effect as an overall average, or testing whether marketing matters by looking only at the 8.4 coefficient's t-stat. If you want the overall marketing effect, either remove the interaction, center the moderator, or test the linear combination of coefficients jointly.

How do interaction terms in multiple regression change how I interpret coefficients?

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