I have a data set consisting of one continuous response variable and about 70 predictors. Using this data, I want to construct a linear regression model. However, I don't know what predictors are worth including in the model, so I'll need to utilize a variable selection method that will allow me to isolate specific response variables. Unfortunately, I've noticed that my data violates a number of assumptions associated with linear regression. Therefore, I'll need to utilize a different estimation than OLS, such as robust or least squares estimation.
When running a linear regression with a different estimation method than least squares, how does one utilize a variable selection method such as stepwise? How can this be implemented in R?