The empirical interpolation method (EIM) has been introduced to extend the reduced basis technique to nonaffine and nonlinear partial differential equations (PDEs), and then widely used in the field of model order reduction and data assimilation. The efficiency of EIM is achieved through an offline-online decomposition procedure. In the offline phase, a set of the snapshots (manifold) of the underlying function are solved, and then a set of basis and interpolation points (magic point) are solved recursively based on the manifold. In the online phase, the interpolation to an unknown function is done by combining the observations of the function itself at some points and the reduced basis. In this paper, the performance of the magic points is analyzed. To further improve the accuracy and stability, we propose a least-squares framework of EIM (LS-EIM) with more points than originally required, and different kind of points sampling methods are investigated. Our numerical finding is that, with only two times of measurements from the first n EIM magic points, LS-EIM allows to reach an accuracy similar to that of best approximation in the reduce space which is spanned by the first EIM basis functions, with a high stability performance. Furthermore, these additional EIM points are better than a choice of a random sampling or other sampling methods.