I'm trying to run a regression model for data with 150 features. I'm eliminating redundant features to prevent over-fitting and produce a model that is easier for illustration. There are two features that I'm not sure how to handle, a real variable and a categorical variable.

`x1` is a measure of distance

`c1` depending on a threshold (say `x1` > 100), `c1` is yes or no (encoded 1 and 0 respectively)

These two variables are obviously highly related (I'm actually not sure why both were present on the dataset). I would like to get rid of one if possible.

1) Is it safe to get rid of one of them? Could the fact that one is categorical have some unforeseen effect? And which one should I get rid of?

2) Is there a mathematical way to show that these two variables are highly related? (I've tried correlation coefficient, which didn't work)