While constructing a regression model, bear in mind that like any other market model,
it should have a theoretical foundation, a conceptual framework. The selection of variables and
their relationship should be based on concepts and theoretical principles.
The regression equation depicts the relationship between dependent and predictor
variables, in terms of importance or magnitude, as well as direction.
The regression coefficients denote the relative importance of their respective
predictor variables, in driving the response variable. The coefficient b1 for instance,
represents the amount the dependent variable y is expected to change for one unit of change in the
predictor x1, while the other predictors in the model are held constant.
The linear model is theoretically unsound for predicting sales (and most other marketing
variables) because it suggests that sales can increase indefinitely. However, from a practical standpoint,
a linear model can provide a good approximation of the true relationship over a small operating
range, e.g., a + 15% change in a predictor such as price.
Nonlinear structural models can be transformed into estimation models that are
linear in parameters by applying transformation functions. The advantage of doing this is that the
parameters of the original nonlinear model can be estimated using linear-regression techniques.
For instance, consider the multiplicative form, which is widely used in marketing mix
models such as NielsenIQ’s Scan*Pro:
$$ y=e^α x_1^{β_1} x_2^{β_2} x_3^{β_3}\,…$$
This nonlinear structural model can be transformed into an estimation model that is
linear in parameters by taking logarithms on both sides.
