We consider the dynamic programming equation arising from the time-discretization of backward stochastic differential equations. When the sequence of conditional expectations is computed using empirical least-squares regressions, we show that the Multi step-forward Dynamic Programming (MDP) equation yields better error estimates than the usual One-step forward DP (ODP) equation. We provide full error estimates, depending on the time-grid, the number of simulations and the approximation spaces for regression. The generator is assumed to be locally Lipschitz, which includes some cases of quadratic drivers.