Dependent and independent variables, coefficients and contributions in MMM:
In full MMM, or funnel attribution modelling:
Dependent variable: Typically, the dependent variable is a commercial KPI metric like site sessions, registrations, leads, subscriptions or sales. In your MMM, this is the variable whose movement is dependent on the movement of other variables.
Independent variables: These variables are typically media spend, competitor spend, price, distribution, economy, seasonality, trends and climate variables.
Coefficients are the rate at which the dependent variable changes in relation to each one unit change in the independent (explanatory) variable, whilst holding all other variables constant.
If you transform your raw media spend variables with parameters such as adstock and diminishing returns, your raw spend variables will acquire a new value in the model and your model coefficient will relate only to that new value.
Contribution is calculated by multiplying the transformed media spend by its model coefficient.
Commercial Outcomes: To calculate your CPA’s you divide your raw spend by the contribution by channel, and to calculate ROIs, if you are modelling revenue, you divide revenue by spend, or, in some cases, revenue-spend / spend.