In classic regression analysis, we use a linear model to learn the relationship between a set of independent variables and a dependent variable. In finding this relationship, we expect to be able to predict the value of the dependent variable given the values of the independent variables. 

A second important reason to do regression analysis is to understand the impact a single independent variable has on the dependent variable when all other independent variables are held constant. One of the great things about traditional multiple linear regression is the ceteris paribus property of linear models. We can interpret the impact a single independent variable has on the dependent variable without consideration to the other independent variable by using the learned weight associated with that independent variable. This type of interpretation is challenging at best and requires us to make quite a few assumptions about our data and our model; however, it is often quite useful.

Deep neural networks aren't easily interpretable, although attempting to do so is an active field of study.