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
Select model
Choose formula (ATAN recommended)
Select curve type (ICP or ADBUG)
Select ONE variable
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:
Transforms the variable using curve parameters
Adds transformed variable to model
Re-runs regression
Calculates statistical metrics
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
Select curves to visualize (checkbox selection)
Click "Generate Chart" button
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:
Select curves to keep (checkbox selection)
Click "Add to Model" or "Create Variables" button
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:
Go to Model Builder
Find your curve variable in the variable list
Add it to your model (replaces or supplements original variable)
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:
Test Variable 1 (e.g., TV_Spend)
Review results, add winning curve
Test Variable 2 (e.g., Digital_Spend)
Review results, add winning curve
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:
Test all media variables individually
Add winning curves for each
Build final model with all curve variables
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
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