I would like to explore a model to predict the value of a continuous response variable, from a set (around 100) of explanatory variables. I do not want to apply PCA like feature reduction, because I want to keep my model maximally informative.
A straightforward method is to conduct a multiple linear regression on a pre-selected subset of candidate explanatory variables. However, a multiple regression requires 1) no missing measurement from any of the explanatory variables; and 2) linear relationship. In my case, I notice some explanatory variables do show strong linear relationship but with many missing values. Therefore, conducting a multiple regression including all candidate explanatory variables is not feasible.
My questions are:
1) Are there any machine learning techniques that can handle continuous response variable, but with many NA in many explanatory variables? The relationships can be non-linear.
2) Is regression tree a proper method to use in my case?