  The problem of least squares regression of a $d$-dimensional unknown
parameter is considered. A stochastic gradient descent based algorithm with
weighted iterate-averaging that uses a single pass over the data is studied and
its convergence rate is analyzed. We first consider a bounded constraint set of
the unknown parameter. Under some standard regularity assumptions, we provide
an explicit $O(1/k)$ upper bound on the convergence rate, depending on the
variance (due to the additive noise in the measurements) and the size of the
constraint set. We show that the variance term dominates the error and
decreases with rate $1/k$, while the term which is related to the size of the
constraint set decreases with rate $\log k/k^2$. We then compare the asymptotic
ratio $\rho$ between the convergence rate of the proposed scheme and the
empirical risk minimizer (ERM) as the number of iterations approaches infinity.
We show that $\rho\leq 4$ under some mild conditions for all $d\geq 1$. We
further improve the upper bound by showing that $\rho\leq 4/3$ for the case of
$d=1$ and unbounded parameter set. Simulation results demonstrate strong
performance of the algorithm as compared to existing methods, and coincide with
$\rho\leq 4/3$ even for large $d$ in practice.
