Exclude not important predictors from dataset or leave them all? I have a large dataset with 6 predictors, with a goal to predict bank loan interest, based on year income, time at work, loan amount, credit balance, credit utilization rate, etc. I use python with scikit-learn to do this prediction, specifically ElasticNet. When I train the model and check final model coefficients, I see something like 
[0.09342575,  0.06866633,  0.01102091,  0.07865676, -0. , 0.16359722] 
which means that some predictors are more important than others, so predictor #5 got coefficient = 0, and probably does not influence the final result much (it might change if I change ElasticNet parameters, though).
Does it mean that I should reconsider my selection of predictors, remake training data set (it might be useful in terms of memory utilization, and calculation time for example), exclude this "unimportant" predictor #5 and re-run the training? Or should I leave them all in the model and dataset?
BTW, is there a way to use ElasticNet with some categorical data (like home ownership: rent, own, mortgage, etc), somehow encoded? For neural net it would be one-of-N, like "rent" is "0,0,1", own is "0,1,0", etc, but how about ElasticNet?
 A: Elastic Net could be used to do variable selection and prediction.
In the case of prediction, the advantage of elastic net is that it doesn't allow really high coefficients, contrary to the most classic cases of linear regression.
The first case, variable selection, is what you face when the coefficient is equal to 0. Elastic net balance between a lasso and ridge model, with lasso nullifying coefficients and ridge lowering them. Consequently, the parameter lambda that you choose can make some of your coefficients be equated to 0.
If you are happy with the selected variables and the associated coefficients, you could run a classic model with only the variables kept through lasso. And enjoy the easy interpretation of a linear model.
The second case, prediction, is a prediction with the constrained coefficients. It is better to get rid of the null variable before to train your model, for an easier readibility.
For your categorical data, your could add the modalities as flag. Not sure though how python handle them.
