  In a pioneer work, R\'ev\'esz (1973) introduces the stochastic approximation
method to build up a recursive kernel estimator of the regression function
$x\mapsto E(Y|X=x)$. However, according to R\'ev\'esz (1977), his estimator has
two main drawbacks: on the one hand, its convergence rate is smaller than that
of the nonrecursive Nadaraya-Watson's kernel regression estimator, and, on the
other hand, the required assumptions on the density of the random variable $X$
are stronger than those usually needed in the framework of regression
estimation. We first come back on the study of the convergence rate of
R\'ev\'esz's estimator. An approach in the proofs completely different from
that used in R\'ev\'esz (1977) allows us to show that R\'ev\'esz's recursive
estimator may reach the same optimal convergence rate as Nadaraya-Watson's
estimator, but the required assumptions on the density of $X$ remain stronger
than the usual ones, and this is inherent to the definition of R\'ev\'esz's
estimator. To overcome this drawback, we introduce the averaging principle of
stochastic approximation algorithms to construct the averaged R\'ev\'esz's
regression estimator, and give its asymptotic behaviour. Our assumptions on the
density of $X$ are then usual in the framework of regression estimation. We
prove that the averaged R\'ev\'esz's regression estimator may reach the same
optimal convergence rate as Nadaraya-Watson's estimator. Moreover, we show
that, according to the estimation by confidence intervals point of view, it is
better to use the averaged R\'ev\'esz's estimator rather than Nadaraya-Watson's
estimator.
