Multiply Variables

Creating Interaction Terms

Multiply Variables creates interaction terms by multiplying two variables together, allowing you to test whether marketing channels work synergistically.

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What Are Interaction Terms?

Beyond Additive Effects

Standard Linear Model (Additive):

Sales = β₀ + β₁×TV + β₂×Digital

Assumes: TV and Digital effects are independent and simply add together

Interaction Model:

Sales = β₀ + β₁×TV + β₂×Digital + β₃×(TV × Digital)

Tests: Do TV and Digital work better (or worse) together than alone?

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When to Use Interaction Terms

Synergy Testing

Scenario: TV builds awareness, Digital captures intent

Hypothesis: TV + Digital together more effective than sum of each

Solution:

Create: TV_x_Digital (multiply TV_Spend × Digital_Spend)
Model: Sales ~ TV + Digital + TV_x_Digital

If β₃ > 0: Positive synergy (amplification effect) If β₃ < 0: Negative synergy (cannibalization)

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Cross-Channel Effects

Test combinations:

• TV × Radio (similar messaging across channels)

• Brand × Performance (awareness + conversion)

• Online × Offline (digital-physical synergy)

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Creating Multiplication Variables

In Variable Workshop

Step 1: Select first variable (e.g., TV_Spend)

Step 2: Choose "Multiply Variables"

Step 3: Select second variable (e.g., Digital_Spend)

Step 4: Preview multiplication result

Step 5: Name new variable: TV_x_Digital

Step 6: Create

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Interpretation

Positive Coefficient = Synergy

Example Model:

Sales = 1000 + 0.5×TV + 0.3×Digital + 0.001×(TV×Digital)

At low spend:

• TV: $10K, Digital: $5K

• Interaction: $10K × $5K × 0.001 = $50

• Minimal synergy effect

At high spend:

• TV: $50K, Digital: $30K

• Interaction: $50K × $30K × 0.001 = $1,500

• Strong synergy effect

Insight: Channels amplify each other at higher investment levels

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Negative Coefficient = Cannibalization

Example:

β₃ = -0.0005

Interpretation: Channels competing for same audience, diminishing combined effect

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Common Use Cases

Brand + Performance

Create: TV_x_Search
Test: Does brand awareness (TV) boost search conversion?

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Geographic Overlap

Create: TV_National_x_Radio_Local
Test: National + local media synergy

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Seasonal Interactions

Create: Digital_x_Holiday_Indicator
Test: Is digital more effective during holidays?

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Best Practices

✅ Use with transformed variables - Apply adstock/saturation first, then multiply

✅ Test one interaction at a time - Don't add many interactions simultaneously

✅ Require sufficient data - Interactions need more observations to estimate reliably

✅ Business hypothesis driven - Only test theoretically meaningful interactions

❌ Don't multiply everything - Most interactions are non-significant

❌ Watch for multicollinearity - Interactions correlated with main effects

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Summary

Key Points:

✖️ Multiply = Interaction term - tests synergy/cannibalization

🤝 Positive coefficient = synergy - channels amplify each other

⚔️ Negative coefficient = cannibalization - channels compete

📊 Requires more data - interactions harder to estimate than main effects

🎯 Hypothesis-driven - test specific, meaningful combinations

Powerful tool for understanding how marketing channels work together!