Consider a scenario in executing quantile regression using $p=0.5$ (the quantile) using the formula $Y \sim 1 + X$ with a dataframe containing two columns. One column contains values for $Y$ and the other column contains values for $X$. However, one of the values for $Y$ is missing.
Is it possible to determine $\hat{\beta}_0$ if we don't know the missing value? Likewise, is it possible to determine $\hat{\beta}_1$ if we don't know the missing value? Is it possible to determine both of these coefficients, one of them, or neither at all?
Thank you!