We consider linear regression problems for which the underlying model undergoes multiple changes. Our goal is to estimate the number and locations of change points that segment available data into different regions, and further produce sparse and interpretable models for each region. To address the complexity issue of the existing approach, we propose a sparse group lasso based approach. We prove that the solution of the proposed approach is asymptotically consistent with the true parameters under certain assumptions and a properly chosen regularization term. In particular, we show that the l2 norm of the estimation error of linear coefficients diminishes,
and the locations of the estimated change points are close to those of true change points.