RegressionModeling from the Statistical Learning Perspective - with an Application toAdvertisement Data

Abstract: Advertising on social media, and on Facebook in specific, is a global industry from which the social media platforms get their biggest revenues. The performance of these advertisements in relation to the money invested in the advertisement can be measured in the metric cost per thousand impressions (CPM). Various regression modelling strategies combined with statistical learning approaches for model assessment are explored in this thesis with the objective of finding the model that best predicts CPM. Using advertisement data for 540 companies in Sweden during 2017, it is found that the data set comprising of 12 covariates suffers from a high degree of multicollinearity. To tackle this problem efficiently we apply different shrinkage regression methods. Starting from the Ridge and Lasso regression methods, combining the two by an elastic net and then finally expanding Lasso to adaptive Lasso, using cross-validation we find that the elastic net with approximately equal weightson Ridge and Lasso component is the best performing model. In conclusion, when regressing a metric such as CPM, on a set of variables which suffers from severe problems of multicollinearity, the shrinkage regression techniques are needed.