# 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

***

#### 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
```

***

#### 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

***

### 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!