A survey researcher wants to estimate a population mean $\bar{Y}$. They use a regression estimator $\bar{y}_{lr} = \bar{y} + b(\bar{X} - \bar{x})$. If the correlation coefficient $\rho_{xy}$ between $Y$ and the auxiliary variable $X$ is $0.9$, what is the relative efficiency of the regression estimator compared to the simple mean estimator $\bar{y}$?