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Block-Term Tensor Regression (BTTR) is a powerful method for modeling complex, high-dimensional data through multilinear relationships, making it well-suited for healthcare and neuroscience. However, its reliance on centralized datasets raises privacy concerns and limits collaboration. To address this, we propose Federated Block-Term Tensor Regression (FBTTR), an extension of BTTR for federated learning that enables decentralized model building while preserving privacy and regulatory compliance. We evaluate FBTTR in two case studies: finger movement decoding from Electrocorticography (ECoG) signals and disease risk prediction. On the BCI Competition IV dataset, FBTTR outperforms non-multilinear models and achieves higher accuracy than centralized BTTR (e.g., subject 3 thumb decoding: <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$0.76 \pm 0.05$</tex> vs. <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$0.71 \pm 0.05$</tex>). On real-world clinical data, FBTTR surpasses both standard federated approaches and centralized BTTR (e.g., Fed-Heart-Disease Dataset AUC-ROC: <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$0.872 \pm 0.02$</tex> vs. <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$0.812 \pm 0.003$</tex>; accuracy: <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$0.772 \pm 0.02$</tex> vs. <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$0.753 \pm 0.007$</tex>). These results show that FBTTR is scalable, computationally efficient, and achieves predictive performance comparable to centralized models. Released as open-source software, it provides a practical and transparent framework for advancing federated analytics in healthcare and brain-computer interface applications.