Regression and Predictive Models

The workhorse of marketing analytics. Linear, logistic, tree-based, MMM as regression, feature engineering, validation, interpretation, deployment.

Why regression matters

Regression underlies most marketing analytics: MMM is regression; attribution models often use regression; LTV prediction uses regression. Understanding the basics enables interpretation of analyst outputs and recognition when methodology is misused.

Linear regression

Models continuous outcomes as linear function of predictors:

Y = β₀ + β₁X₁ + β₂X₂ + … + β_kX_k + ε

• Coefficients (β): Effect of one-unit change in X on Y, holding others constant.
• R²: Proportion of variance explained.
• Standard errors: Uncertainty in coefficient estimates.
• P-values: Probability of observing coefficient if true effect were zero.
• Assumptions: Linearity, independence, homoscedasticity, normality of residuals.

Logistic regression

For binary outcomes (converted vs not, churned vs not).

• Models log-odds as linear function of predictors.
• Output: probability between 0 and 1.
• Use cases: Conversion prediction, churn prediction, lead scoring.
• Coefficients: Effect on log-odds; exponentiate for odds ratios.

Tree-based models

• Decision trees. Interpretable but high variance.
• Random forests. Ensemble of trees; lower variance.
• Gradient boosting (XGBoost, LightGBM, CatBoost). Best-in-class predictive accuracy for tabular data.
• Trade-offs: Predictive power vs interpretability; tree models often outperform linear but are harder to interpret.
• Use cases: LTV prediction, conversion probability, propensity scoring.

MMM as regression

• Sales(t) = β₀ + Σ β_i × adstock(saturation(spend_i(t))) + Σ γ_j × control_j(t)
• Specialized regression incorporating adstock and saturation transformations.
• Bayesian formulation includes priors on coefficients.
• Covered in depth in Attribution & Measurement MMM module.

Feature engineering for marketing

• Time features. Day of week, month, holiday indicators, time since last action.
• Aggregations. Customer's purchase count, total spend, recency.
• Behavioral. Number of sessions, pages viewed, products browsed.
• Lookback windows. 7-day, 30-day, 90-day, lifetime aggregates.
• Interactions. Cross-feature combinations (e.g., channel × device).
• Categorical encoding. One-hot, target encoding, embedding.
• Missing data handling. Imputation, missingness indicators.

Validation and overfitting

• Train/test split. Hold out test data; never used in training.
• Cross-validation. K-fold for hyperparameter tuning.
• Time-based splits for time-series. Train on past; test on future.
• Overfitting signals. Train accuracy high, test accuracy low.
• Regularization. L1 (Lasso), L2 (Ridge), Elastic Net to prevent overfitting.
• Holdout validation. Final test on fully unseen data before deployment.

Interpretation and inference

• Linear coefficients. Directly interpretable as effect sizes.
• Tree model interpretability. SHAP values for per-prediction explanations.
• Feature importance. Which features matter most; useful but limited.
• Partial dependence plots. How does predicted Y change with X holding others constant?
• Counterfactual analysis. What would happen if we changed X?
• Communication. Plain-language summaries for non-technical stakeholders.

Productionizing models

• Batch vs real-time. Most marketing models batch-score (daily/weekly).
• Pipeline automation. Train, score, monitor, retrain.
• Monitoring. Data drift, prediction drift, performance decay.
• Retraining cadence. Quarterly or monthly; depending on environment stability.
• Tools. MLflow, Airflow, dbt, custom pipelines.
• BigQuery ML / Snowflake ML / Databricks ML. Warehouse-native ML for many marketing use cases.

Advanced playbook

• Model registry. All deployed models documented; lineage tracked.
• Feature store. Shared features across models; consistency.
• Calibration plots. Predicted probabilities match observed frequencies.
• Drift monitoring. Production data shifts from training; retrain triggers.
• SHAP for interpretability. Per-customer explanations of model predictions.
• Bayesian regression. Uncertainty quantification on coefficients and predictions.
• Time-series-specific methods. ARIMA, Prophet, neural network forecasting where appropriate.
• Ensembling. Combine multiple models; often outperforms any single.
• Champion-challenger. Test new models against incumbent in production.
• External validation. Compare model predictions to actual outcomes; report calibration.

Common mistakes

• Overfitting on training data; production performance disappoints.
• Time-series modeled with random splits; leakage from future.
• Linear model assumptions violated; coefficients misleading.
• Tree models without interpretability layer; black box.
• Features not validated; spurious predictors included.
• No monitoring in production; drift undetected.
• Retraining cadence ad-hoc; performance decays.
• Calibration ignored; predicted probabilities mismatched to reality.
• Tools without warehouse integration; data movement overhead.
• Models documented; lineage unknown.
• Bayesian methods skipped where uncertainty matters.
• Champion model never challenged; incumbent comfort.

Operating checklist

• Train/test split with time-aware logic for time-series
• Regularization applied to prevent overfitting
• Validation on fully held-out data before deployment
• Calibration plots for probabilistic predictions
• Feature documentation and lineage
• Production monitoring (data drift, prediction drift, performance)
• Retraining cadence documented
• Model registry with lineage
• SHAP or equivalent interpretability layer
• Champion-challenger testing
• External validation against actual outcomes
• Bayesian uncertainty where appropriate

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Part of the Marketing Analytics series.