Quantile Regression variance attribution

Question

For multi OLS regression. I normally use variance attribution to explain how much contribution an independent/predictor variable has to the dependent variable. For example, a standard two factor regression (independent variables $X_1$ and $X_2$) model can be written as
$$ y = \alpha + \beta X_1 + \beta X_2 + \epsilon $$ I can explain variance attribution using $$ var(y) = \beta_1^2var(x_1) + \beta_2^2var(x_2)+2\beta_1\beta_2Cov(X_1,X_2) + var(\epsilon) $$ This allows me to attribute variance to $X_1$ and $X_2$. Is there a similar or better way to do this for quantile regression. Since this formula does not work for quantile regression and I would like to attribute variance to the independent variables.