Autism spectrum disorder (ASD) is a complex neurodevelopmental syndrome. Early diagnosis and precise treatment are essential for ASD patients. Although researchers have built many analytical models, there has been limited progress in accurate predictive models for early diagnosis. In this project, we aim to build an accurate model to predict treatment outcome and ASD severity from early stage functional magnetic resonance imaging (fMRI) scans. The difficulty in building large databases of patients who have received specific treatments and the high dimensionality of medical image analysis problems are challenges in this work. We propose a generic and accurate two-level approach for high-dimensional regression problems in medical image analysis. First, we perform region-level feature selection using a predefined brain parcellation. Based on the assumption that voxels within one region in the brain have similar values, for each region we use the bootstrapped mean of voxels within it as a feature. In this way, the dimension of data is reduced from number of voxels to number of regions. Then we detect predictive regions by various feature selection methods. Second, we extract voxels within selected regions, and perform voxel-level feature selection. To use this model in both linear and non-linear cases with limited training examples, we apply two-level elastic net regression and random forest (RF) models respectively. To validate accuracy and robustness of this approach, we perform experiments on both task-fMRI and resting state fMRI datasets. Furthermore, we visualize the influence of each region, and show that the results match well with other findings.