Regression analysis is a statistical method for modeling relationships between different variables (dependent and independent). It is used to describe and analyze relationships in data. Predictions can also be made using regression analyses, whereby the relationships in the data would be used as a basis for the forecast and generated by a prediction model. Regression and correlation analyses are considered to be part of multivariate analytical methods and are used in many different areas, including science, statistics, finance, and now also online marketing, in order to analyze and partly predict the costs and turnover of products, campaigns, channels, and advertising media.
Regression is undoubtedly no new topic. The associated mathematical instruments have already been used to determine the planetary orbits with data from astronomical observations. The method of the least squares was published by Carl Friedrich Gauss in 1809, after Adrien-Marie Legendre and other mathematicians created the theoretical foundations. This method is considered a precursor for regression analysis. The instruments were further developed and first used in biology and geology. Regression procedures continue to be a research area that involves many different scientists.
A regression is based on the idea that a dependent variable is determined by one or more independent variables. Assuming that there is a causal relationship between the two variables, the value of the independent variable affects the value of the dependent variable. For example, if you wanted to find out how your advertising investments impact sales, a regression analysis would be used to examine the relationship between the investments and the sales. If this relationship is clearly represented, it can serve as a prediction.^{[1]} Regression analyses have two central objectives. They are supposed to:
Overview of various regression analyses:
Although different regression methods exist, the structure of these methods is often similar in terms of steps:
Decisive for the benefit of a regression analysis is the extent to which the model describes the actual data and its possible relationships. An important problem is the choice of a model and along with it, the selection of the explanatory variables. Only significant correlations should be investigated. Therefore, each regression analysis includes different approaches for increasing accuracy, minimizing errors, and excluding statistical outliers that are not relevant to the investigated object. For these reasons, these models are often compared based on the key figures such as the coefficient of determination or, more generally, the information criterion.
Regression analyzes are used in online marketing, for example, to understand the customer journey using web analytics data or to support multi-channel marketing with reliable data. In practice, such analyses are complex and require professional know-how and knowledge. But the results can be very clear and tangible, depending on the model. For example, if attribution modeling is used for checking multiple channels like direct sales, display ads, affiliates, social media, email or referrals, regression analyzes can clearly show which of these channels have a good balance between investments and sales. At corporate levels and with specific partners who can realize such analyses, the results are likely to be extremely helpful and could significantly increase the ROI of individual digital assets.^{[2]}