In the second part of our small series about sales modeling (you can find the first part here) we will talk about regression analysis, the core of sales modelling. Since sales modelling is methodically based on the regression analysis, which determines the causal relationship between advertising activity and sales, it is indispensible for the implementation.

Regression analysis is itself one of the most often used multivariate analyses. This method examines the dependence between a dependent variable and one or more independent variables. With the help of a regression analysis connections can be discovered which are not visible to the naked eye.

Moreover, forecasts for future development can be extrapolated through this method of analysis. Regression analysis is of great use in economic sciences, providing answers for all sorts of problems, for example:

- Estimating the dependence of the quantity of sales of a product on the preferences of specific target groups
- Estimating the dependence of the quantity of sales of a product on the price level
- Estimating the dependence of the quantity of sales of a product on the advertising budget, price, and field of operation

Regression analysis is thus especially advantageous because individual dependent variables can simultaneously be juxtaposed with one or more independent variables. A holistic explanation can be therefore given and the trajectory of the dependent variables can be better explained than by analyzing the separate dependencies.

A linear regression analysis is employed to assess sales within the framework of sales modelling. The linear regression analysis supposes a linear relationship between the dependent variable, which is scaled metrically, and one or more independent variables. The regression function proceeds as follows:

To conduct a regression analysis, the values of the dependent variable Yi as well as the independent variables Xk,i must be available. Without these values a regression analysis cannot be conducted. All other values, like the constant of the regression function b0, the regression coefficients bk (k∈K) and the residuals ei (i∈I) are estimated within the framework of the regression analysis.

Complex mathematical algorithms are used to estimate the regression function. These methods entail huge computational efforts. Therefore powerful statistical programs are often employed to determine the functional relationship.

Should the data be available, it can be read into the program and analyzed. The relationships can finally be extrapolated and interpreted form the results of the regression analysis. However the challenge that regression analysis poses lies not in the estimation of the function (which the program does automatically) or the interpretation of the results, but in all of the preliminary work. This includes:

- The establishment of hypotheses regarding functional relationships
- The selection of an approximation method appropriate to the established hypotheses
- Data collection
- Data preparation: adaptation of data in a way that it can be used for the selected method

A great amount of time should be allotted for these activities. However if these operations are carefully thought through and carried out, the regression function can be unproblematically estimated and interpreted. Using the interpretations, recommendations can be formulated based on fixed mathematical facts, which can be neither identified nor extrapolated by the naked eye.

In the third part of our sales modeling series we will give you a concrete example, where the regression analysis will find practical application. On the basis of a case study the result of sales modeling will be discussed and its advantages over conventional methods will be explained. The entry will talk about the estimation of the function, the interpretation of the results, and the extrapolation of recommendations.