Different types of variables

In standard inferential statistics one typically assumes that data consist of real or integer numbers. However, data may be qualitative as well, and the more dimensions we have, the more likely the joint presence of quantitative and qualitative variables will be. In some cases, dealing with qualitative variables is not that difficult. For instance, if we are building a multiple regression model that includes one or more qualitative explanatory variables, we may represent them as binary (dummy) variables, where 0 and 1 correspond to “false” and “true,” respectively. However, things are not that easy if it is the regressed variable that is binary. For instance, we might wish to estimate the probability of an event on the basis of explanatory variables; this occurs when we are evaluating the creditworthiness of a potential borrower, on the basis of a set of personal characteristics, and the output is the probability of default. Another standard example is a marketing model to predict purchasing decisions on the basis of product features. Adapting linear regression to this case calls for less obvious transformations, leading to logistic regression, which is also considered. In other cases, the qualitative nature of data calls for methods that are quite different from those used for quantitative variables.