Static dipole polarizabilities for the ground-state geometries of yttrium clusters (Y-n, n <= 15) are investigated by using the numerically finite field method in the framework of density functional theory. The structural size dependence of electronic properties, such as the highest occupied molecular orbital-lowest occupied molecular orbital (HOMO-LUMO) gap, ionization energy, electron affinity, chemical hardness and softness, etc., has been determined for yttrium clusters. The energetic analysis, minimum polarizability principle, and principle of maximum hardness are used to characterize the stability of yttrium clusters. The correlations of stability, static dipole polarizabilities, and electronic properties are analyzed especially. The results show that static polarizability and electronic structure can reflect obviously the stability of yttrium clusters. The static polarizability per atom decreases slowly with an increase in the cluster size and exhibits a local minimum at the magic number cluster. The ratio of the mean static polarizability to the HOMO-LUMO gap has a much lower value for the most stable clusters. The static dipole polarizabilities of yttrium clusters are highly dependent on their electronic properties and are also partly related to their geometrical characteristics. A large HOMO-LUMO gap of an yttrium Cluster usually corresponds to a large dipole moment. Strong correlative relationships of the ionization potential, softness, and static dipole polarizability are observed for yttrium clusters.