  We consider the linear regression model along with the process of its
$\alpha$-regression quantile, $0<\alpha<1$. We are interested mainly in the
slope components of $\alpha$-regression quantile and in their dependence on the
choice of $\alpha.$ While they are invariant to the location, and only the
intercept part of the $\alpha$-regression quantile estimates the quantile
$F^{-1}(\alpha)$ of the model errors, their dispersion depends on $\alpha$ and
is infinitely increasing as $\alpha\rightarrow 0,1$, in the same rate as for
the ordinary quantiles. We study the process of $R$-estimators of the slope
parameters over $\alpha\in[0,1]$, generated by the H\'{a}jek rank scores. We
show that this process, standardized by $f(F ^{-1}(\alpha))$ under
exponentially tailed $F$, converges to the vector of independent Brownian
bridges. The same course is true for the process of the slope components of
$\alpha$-regression quantile.
