Modelling the Advertising Effects - Part I

Having learnt about the major KPIs that may impact sales and revenue, in this segment, you will learn how to model the relationship of the individual KPIs with the sales or the revenue. First, you will use the simple linear regression to model this relationship.

The multivariate simple regression model can capture the current effect of advertising, as discussed earlier, very well. The equation can be represented as:

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Here, the dependent variable Y can be the sales or the revenue figures. Once you have built the model, you can use R-square or adjusted R-square values to evaluate the model.

However, as you can see, this model assumes an additive relationship between the different KPIs. So, what would you do when there are interactions between the KPIs? Let's find out in the video below.

To read more about why natural log (base e) is preferred over the log of base 10, you can visit the links here and here.

The multiplicative model has three major benefits:

1. This model implies that there exists an interaction effect of the explanatory KPIs. For example, if your TV advertising has a 2x revenue impact and your newsprint has a 1.2x revenue impact, then it’s not necessary that TVC + newsprint would have a 3.2x revenue impact. When done together, it may just have an impact of 2.5x or even 5x. This depends on the interaction effect, which can be modelled through the multiplicative method.

2. The multiplicative model also implies that, based on the coefficients, the model can estimate a variety of shapes. It’s not necessarily stuck in a linear format. Therefore, the model is more flexible to estimate the relationship between the explanatory and dependent variables, as compared with Equation 1.

3. Since the model does not estimate the actual revenue but its first derivative, which is the growth of revenue, the coefficients also reflect the 'elasticity', i.e., the rate of change of revenue with a change in advertising spending.

The multiplicative model also has three major limitations. These are:

1. It fails to estimate the competitive, content, media and dynamic effects. Therefore, more advanced models are required, which we will learn about later.

2. Even though the multiplicative model has the flexibility to estimate various shapes, it fails to estimate the S-shaped curve, which is one of the most prevalent shapes in practice.

3. Since the multiplicative model is modelled at a first-derivative level, it implies that elasticity is constant, which is not always necessarily true.