The submicron permalloy dots with variable diameter and interdot distance were microfabricated into a rectangular lattice by means of e-beam lithography and lift-off techniques. The hysteresis loops exhibit characteristic magnetization reversal accompanied by nucleation and annihilation of magnetic vortices inside the dots. The magnetic response of the samples with well-separated elements is isotropic in the plane. The arrays with a small interdot distance show magnetic anisotropy with the easy axis along the shortest period in the array. This anisotropy is originated from the interdot magnetostatic interaction. The magnetostatic interaction is found to play an important role in determining the magnetization process for the dot arrays. For example, in the closely-packed (when interdot distance is smaller than dot radius) arrays so that d/R<1, the magnetostatic interaction decreases the vortex nucleation and annihilation fields, and increases the initial susceptibility.