Regression Analysis for Marketing — From OLS to MMM, the Practical Implementation

Regression analysis for marketing is the workhorse of MMM, propensity modeling, and forecasting. The five regression types every operator should understand: OLS linear, logistic, ridge/lasso, polynomial, and time-series. The honest tradeoff for each is which assumptions you're willing to violate.

Regression is the practice of fitting a mathematical relationship between input variables and an outcome. In marketing, the inputs are typically spend across channels, audience characteristics, time, or some combination; the outcomes are revenue, conversion, or other measurable results. Every MMM ever built is a regression. Every propensity score, every churn prediction, every forecast.

OLS linear regression — the foundation

Ordinary Least Squares fits a straight line through data minimizing the sum of squared residuals. The model has the form: Y = β₀ + β₁X₁ + β₂X₂ + ... + ε. β₀ is the intercept (baseline value when all inputs are zero), each β coefficient represents the expected change in Y for a one-unit change in that X, and ε is the random error.

Five OLS assumptions: linearity, independence of residuals, normality of residuals, homoscedasticity (equal variance), and no multicollinearity. Violations matter — multicollinearity inflates standard errors and makes coefficient estimates unstable, heteroscedasticity makes confidence intervals wrong, autocorrelation in time-series data makes p-values wrong.

When to use: the relationship between inputs and outputs is roughly linear, you have continuous outcomes, and you can argue the assumptions hold reasonably.

Logistic regression — for binary outcomes

Logistic regression predicts the probability of a binary outcome (converted = 1 / didn't = 0). The model has the form: log(p/(1-p)) = β₀ + β₁X₁ + ... The log-odds is a linear function of inputs, but the probability itself is nonlinear (S-curve between 0 and 1).

Used for: propensity scoring (probability a user converts), lookalike modeling (probability a user is similar to a seed audience), click-through rate prediction in real-time bidding. Output is a probability, useful for ranking and thresholding.

Ridge and Lasso — for multicollinearity

When input variables correlate with each other (channel spends often do — paid social and search spend often move together), OLS coefficient estimates become unstable. Ridge regression adds an L2 penalty (sum of squared coefficients), shrinking coefficients toward zero proportionally. Lasso adds an L1 penalty (sum of absolute coefficient values), which can zero out coefficients entirely.

Used for: MMM where channels correlate, feature selection, regularized prediction. The penalty parameter (lambda or alpha) is tuned via cross-validation. Elastic Net combines L1 and L2 penalties for the best of both.

Polynomial regression — for diminishing returns

Marketing spend almost always exhibits diminishing returns — the first $10K of spend produces more incremental revenue than the tenth $10K. Polynomial regression captures this by including powers of the input: Y = β₀ + β₁X + β₂X² + β₃X³. The squared and cubed terms let the line bend.

Used for: MMM where saturation curves matter, response curves for budget optimization. Best practice: use a log-log specification (log(Y) = β₀ + β₁ log(X)) for natural diminishing returns interpretation — β₁ becomes the elasticity (percent change in Y for percent change in X).

Time-series regression — ARIMA and Prophet

Time-series data violates OLS independence assumption — today's value depends on yesterday's. ARIMA (AutoRegressive Integrated Moving Average) handles this by modeling the autocorrelation explicitly. The three parameters: p (autoregressive order), d (differencing for non-stationarity), q (moving-average order).

Prophet (developed by Meta, open-sourced) is an additive model with trend, seasonality, holidays, and changepoints. More accessible than ARIMA for analysts without time-series training. Good for forecasting where you have known seasonality (Q4 retail, summer apparel, January gym memberships).

RGM Experts Say

We have audited dozens of MMM implementations. The single most-common failure mode is data quality — channels with missing weeks, currencies not converted, attributions that double-count. The regression isn't the hard part. The data preparation is. Budget 70% of the time for data engineering before you touch the model.

Marketing applications in practice

  • MMM — multiple regression with channel spends as inputs, revenue as output, polynomial or log transformations for diminishing returns
  • Lookalike modeling — logistic regression with user features as inputs, probability of conversion as output
  • Propensity scoring — logistic regression for likelihood of future action (churn, conversion, upgrade)
  • Forecasting — ARIMA or Prophet on historical revenue data
  • Lift modeling — uplift regression comparing treatment vs control to estimate causal effect
  • Pricing optimization — regression on price-elasticity data to find optimal price point
  • Creative performance prediction — regression on creative features (hook type, length, format) predicting performance
  • Brand tracker analysis — regression of brand metrics on marketing investments

Tools

  • Python statsmodels — full OLS, logistic, ARIMA, with diagnostic statistics
  • Python scikit-learn — production-grade regression with cross-validation and regularization
  • R lm() and glm() — academic standard for regression
  • Excel Data Analysis ToolPak — adequate for basic OLS
  • Google Sheets XLMiner Analysis — free regression in Sheets
  • Stata / SPSS — legacy
  • JMP — for design of experiments
  • Meta Robyn / Google LightweightMMM — open-source MMM implementations

Related guides

Sources

  1. [1]Meta Robyn documentation; Google LightweightMMM documentation; Hyndman Forecasting: Principles and Practice