Traditional regression methods minimize the sum of errors of samples with various regularization terms such as the ℓ1-norm and ℓ2-norm. For the diagnosis of cardiovascular diseases, the cardiac ejection fraction (EF) represents an essential measure. However, existing regularization terms do not consider the output correlation (the correlation between ground truth volumes and estimated volumes w.r.t. each subject), which is beneficial in estimating the cardiac EF. In this paper, we first propose a sparse regression with two regularization terms of the ℓ1-norm and output correlation (SROC). Then, we propose a one-dimensional solution path algorithm for quickly finding two good regulation parameters in the formulation of SROC. The solution path algorithm can effectively handle singularities and infinities in the key matrix. Finally, we conduct experiments on a clinical cardiac image dataset with 100 subjects. The experimental results show that our method produces competitive and strong results for estimating the cardiac EF based on quantitative and qualitative analyses.