I have the following problem:
I have a dataset for which my observations have a bunch of features and a continuous response (regression problem). However, some of my observations (about a fourth of them) do not have a response. The features should also be predictive of those who have a response and those who do not (classification problem). Furthermore, a small response value can be interpreted similarly to those who do not have a response.
How would you go with that problem? Would you simply do a regression on the observations that have a response. Although this would throw away the information from the observations that do not have a response.
Or would you first do classification: predict if an observation has a response or not. And if yes, do regression on those. But then, how do you measure the cost if you make a wrong classification.