We study the spin-dependent zero-bias conductance through a quantum wire with a single ballistic channel side coupled to a quantum dot as a function of gate voltage ${V}_{g}$, magnetic field $B$, and temperature $T$. The system is modeled with the Anderson model, solved using an interpolative approximation for moderate values of the Coulomb repulsion $U$, and within the slave-boson mean field for infinite $U$ and $T=0$. Tuning ${V}_{g}$, for large enough $B$ and small enough $T$, the system is a very efficient spin filter.