Active learning aims to reduce labeling efforts by selectively asking humans to annotate the most important data points from an unlabeled pool and is an example of human-machine interaction. Though active learning has been extensively researched for classification and ranking problems, it is relatively understudied for regression problems. Most existing active learning for regression methods use the regression function learned at each active learning iteration to select the next informative point to query. This introduces several challenges such as handling noisy labels, parameter uncertainty and overcoming initially biased training data. Instead, we propose a feature-focused approach that formulates both sequential and batch-mode active regression as a novel bipartite graph optimization problem. We conduct experiments on both noise-free and noisy settings. Our experimental results on benchmark data sets demonstrate the effectiveness of our proposed approach.