Techniques for dimensionality reduction have attracted much attention in computer vision and pattern recognition. For supervised or unsupervised dimensionality reduction, the methods combining regression analysis and spectral graph analysis do not consider the global structure of the subspace. For semi-supervised dimensionality, there has been significant interest in extending supervised algorithms to their semi-supervised forms recently. However, how to use the unlabeled samples more effectively is still an open problem. In this paper, we propose Low Rank Regression Analysis(LRRA) to deal with these problems. For supervised or unsupervised dimensionality reduction, combining spectral graph analysis with LRRA can simultaneously make a global constraint on the subspace and reduce the noise for the projection matrix. For semi-supervised dimensionality reduction, LRRA which can explore the latent linear dependence between samples is likely to find the unlabeled samples which may exert positive effects, so it can help us to use the unlabeled samples more effectively. The experimental results show the effectiveness of our algorithms.