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Brain development in adolescence is synthetically influenced by various factors such as age, education, and socioeconomic conditions. To identify an independent effect from a variable of interest (e.g., socioeconomic conditions), statistical models such as General Linear Model (GLM) are typically adopted to account for covariates (e.g., age and gender). However, statistical models may be vulnerable with insufficient sample size and outliers, and multiple tests for a whole brain analysis lead to inevitable false-positives without sufficient sensitivity. Hence, it is necessary to develop a unified framework for multiple tests that robustly fits the observation and increases sensitivity. We therefore propose a unified flexible neural network that optimizes on the contribution from the main variable of interest as introduced in original GLM, which leads to improved statistical outcomes. The results on group analysis with fractional anisotropy (FA) from Diffusion Tensor Images from Adolescent Brain Cognitive Development (ABCD) study demonstrate that the proposed method provides much more selective and meaningful detection of ROIs related to socioeconomic status over conventional methods.