Curve Testing Interface

Discovering Optimal Saturation Curves for Your Marketing Variables

What is Curve Testing?

Purpose: Find optimal saturation curve parameters (Alpha, Power) that best explain the relationship between marketing spend and outcomes

Method: Systematically test multiple curve configurations, evaluate statistical fit, identify the transformation that maximizes model R²

Output: Ranked list of curve options with statistical metrics and visualizations

Accessing Curve Testing

Navigation: Main Menu → Variable Workshop → Curve Testing

Requirements:

• At least one model in Model Library

• Numeric marketing variables in dataset

• Professional or Enterprise subscription

Interface Overview

1. Model Selection

Select which model to use for testing curves. The curve transformation will be tested by adding it to this model temporarily.

Best Practice: Use your most complete model (includes all key variables) for most reliable curve testing.

2. Formula Selection

Choose between two formula options:

CDR (Constant Diminishing Returns):

• 3 parameters: Alpha, Beta, Gamma

• More flexible but slower

• Better for complex saturation patterns

ATAN (Arctangent):

• 2 parameters: Alpha, Power

• Simpler and faster

• Sufficient for most channels

• Recommended default

3. Curve Type Selection

Choose the expected curve shape:

S-Shape (ICP):

• For channels with threshold effects

• Slow start → rapid growth → saturation

• Use for: Brand TV, new product launches, viral campaigns

Concave (ADBUG):

• For immediate diminishing returns

• Best prospects first, continuous decline

• Use for: Paid search, email, retargeting, promotions

4. Variable Selection

Table View: Shows all numeric variables with:

• Variable name

• Type (NUMERIC)

• Group category

Selection: Click checkbox to select ONE variable to test

Search: Use search box to filter variables by name

Best Practice: Test curves on media/marketing spend variables, not control variables or KPIs

Running Curve Tests

Test Execution

1. Select model

2. Choose formula (ATAN recommended)

3. Select curve type (ICP or ADBUG)

4. Select ONE variable

5. Click "Test Curves" button

What Happens During Testing

For ATAN Formula:

S-Shape (ICP):

• Tests Alpha: 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0

• Tests Power: 1.6, 1.8, 2.0

• Total: 30 curve combinations tested

Concave (ADBUG):

• Tests Alpha: 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0

• Tests Power: 1.0 (fixed)

• Total: 10 curve combinations tested

For each combination:

1. Transforms the variable using curve parameters

2. Adds transformed variable to model

3. Re-runs regression

4. Calculates statistical metrics

5. Removes transformed variable (doesn't save yet)

Understanding Results

Results Table

After testing completes, results appear sorted by R² Increase (best fit first):

Columns:

Curve Name: Shows the transformation applied (e.g., "TV_Spend|ICP_ATAN a0.5_power1.8")

Alpha: Inflection point parameter value tested

Power: Shape parameter value tested

Coefficient: The β coefficient for this transformed variable in the regression

T-Stat: T-statistic measuring coefficient reliability

P-Value: Statistical significance (lower is better, < 0.05 is significant)

R² Increase: How much this curve improved model fit vs. untransformed variable

Interpreting Results

Good Result Indicators:

✅ High R² Increase: Curve improves model fit substantially ✅ Low P-Value: < 0.05 (significant), ideally < 0.01 ✅ Positive Coefficient: More spend → more sales (as expected) ✅ High T-Stat: Absolute value > 2.0 indicates reliability ✅ Business Logic: Parameters align with channel behavior

Warning Signs:

⚠️ Negative Coefficient: More spend → less sales (counterintuitive) ⚠️ High P-Value: > 0.05 (not statistically significant) ⚠️ Minimal R² Increase: < 0.01 (curve adds little value) ⚠️ Illogical Parameters: e.g., TV with alpha=0.1 (implies tiny audience)

Sorting Results

Click column headers to sort by different metrics:

• R² Increase: Default sort, shows best statistical fit first

• P-Value: Shows most significant curves first

• Alpha: Groups by inflection point

• Power: Groups by shape parameter

Visualizing Curves

Generating Charts

1. Select curves to visualize (checkbox selection)

2. Click "Generate Chart" button

3. Interactive chart displays showing curve shapes

Select All Checkbox: Quickly select/deselect all curves for visualization

Chart Features

X-Axis: Original variable values (spend) Y-Axis: Transformed values (0 to 1 scale)

Multiple Curves: Can overlay multiple curves to compare shapes visually

Interactive: Hover over curves to see exact values at any point

What to Look For in Charts

For S-Shape (ICP):

• Look for clear inflection point (where curve accelerates)

• Check if threshold aligns with business expectations

• Verify saturation level makes sense

For Concave (ADBUG):

• Look for smooth diminishing returns

• Check if saturation speed aligns with audience size

• Verify no unexpected inflection points

Adding Curves to Your Model

Creating Curve Variables

Once you've identified winning curves:

1. Select curves to keep (checkbox selection)

2. Click "Add to Model" or "Create Variables" button

3. Curves are permanently added as new variables

Variable Creation: Each selected curve becomes a new column in your dataset with the naming format: OriginalVariable|CurveType_ATAN aX.X_powerY.Y

Model Update: Variables are added to the model's available variable list (not automatically included in regression - you control that)

Using Curve Variables in Models

After creating curve variables:

1. Go to Model Builder

2. Find your curve variable in the variable list

3. Add it to your model (replaces or supplements original variable)

4. Run model to see final results

Best Practice: Remove the original untransformed variable when adding curve version to avoid multicollinearity

Testing Multiple Variables

Sequential Testing

Test curves for multiple variables one at a time:

1. Test Variable 1 (e.g., TV_Spend)

2. Review results, add winning curve

3. Test Variable 2 (e.g., Digital_Spend)

4. Review results, add winning curve

5. Continue for all media variables

Why sequential? Testing one variable at a time gives clearest signal about which curve fits that specific variable best.

Building Comprehensive Saturated Models

Typical workflow:

1. Test all media variables individually

2. Add winning curves for each

3. Build final model with all curve variables

4. Run diagnostics to validate overall model quality

Best Practices

Variable Selection

✅ Test curves on: Media spend, impressions, GRPs, clicks ❌ Don't test on: Price, temperature, GDP, seasonality, KPIs

Curve Type Selection

Start with ADBUG (concave) if:

• Performance marketing channels

• Audience sorting expected

• Frequency fatigue likely

Start with ICP (S-shape) if:

• Brand/awareness campaigns

• Threshold effects expected

• Need frequency for impact

Not sure? Test both and compare results

Formula Selection

Use ATAN as default:

• Faster testing

• Sufficient for most channels

• Easier interpretation

Switch to CDR only if:

• ATAN shows poor fit

• Complex saturation pattern suspected

• Have large dataset to support 3 parameters

Interpreting Results

Don't just pick highest R²:

• Verify business logic makes sense

• Check statistical significance (p-value)

• Review coefficient sign (should be positive)

• Visualize curve shape

Red flags requiring investigation:

• Negative coefficients

• P-value > 0.05

• Extreme parameter values (alpha < 0.1 or > 0.95)

Common Issues

No Curves Show Improvement

Possible reasons:

• Variable already shows linear relationship (no saturation)

• Variable is external factor, not marketing spend

• Model already includes curve version

• Dataset too small for reliable curve detection

Solutions:

• Check if variable is appropriate for curves

• Try different curve type (ICP vs ADBUG)

• Verify sufficient data range and variation

All Curves Show Similar Results

Possible reasons:

• Variable has limited range (not enough variation)

• Saturation effects are subtle

• Model has other issues (multicollinearity, missing variables)

Solutions:

• Check variable statistics (min, max, variance)

• Review model diagnostics before curve testing

• Consider if curve is actually needed

Curve Results Seem Illogical

Possible reasons:

• Wrong curve type selected (ICP vs ADBUG)

• Multicollinearity with other variables

• Model specification issues

Solutions:

• Test opposite curve type

• Review VIF statistics in model diagnostics

• Simplify model before curve testing

Key Takeaways

• Test curves on media/marketing variables systematically

• ATAN formula recommended for speed and simplicity

• Choose ICP (S-shape) or ADBUG (concave) based on channel behavior

• Review statistical fit AND business logic before selecting curves

• Visualize curves to verify shape makes sense

• Add winning curves as new variables, then use in models