# What to do when two covariates are highly correlated?

I have covariates X, Y, and response Z.

X is discrete ("A", "B", "C"), Y is continuous (from 0 - 100).

The issue is that for X = A, Y is usually in the range 0-50. From X = C, Y is usually in the range 50-100. Only for X = B does Y cross the entire 0-100 range.

What does this mean for my analysis? How do I handle this situation? I want to use X and Y as covariates, yet above problem almost seems to indicate that I should do a regression on X and Y (intuitively, if there IS a correlation, then it should probably be X which causes Y, i.e. E(Y) = F(X)).

## 1 Answer

What you are describing does not seem to indicate correlation of covariates, i.e. multicollinearity. Rather, $X$ indicates a grouping in your data, restricting $Y$.

How to proceed depends on what type of model you are after and what kind of statistical inference you want to make. For the "A, B, C grouping" you may want to model separate slopes for the impact on $Z$, i.e. specify an interaction effect between $X$ and $Y$.

In addition, your study may indicate that there may be missing data problems due to selection bias (A and C are not observed for all values of Y). In the context of treatment evaluation, if A, B and C indicate treatment, you might want to consider the counterfactuals of each of the groups's impact on $Z$ being in another group, based on the observable variable $Y$.