Known Correlation between predictors

Question

I have two predictors and an outcome, let's call them x, y and z. I know that x and y are correlated with correlation r.

I am trying to construct a linear model:

z = ax + by + c

I have an expectation of what a and b should be based on how they are generated if x and y were not correlated. However, this correlation is causing my model to give me different results. What is the best/simplest/quickest method to eliminate the correlation and/or adjust for it.

The two options I can see would be either a third variable as an adjustment term (derived from the known correlation) or a method to transform x and y to be orthogonal. What methods could I use to achieve this?

Answer 1

I think it depends on the importance of the correlation. It is difficult to avoid any correlation between two explanatory variables (e. g. blood pressure and weight are related but can be included in the same model). On the other hand, some variables can be created to avoid putting two variables that are too correlated (e. g. BMI to take into account height and weight at the same time).