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Nolan and Ojeda-Revah in [16] proposed a regression model with heavy-tailed stable errors. In this paper, we extend this method for multivariate heavy-tailed errors. Furthermore, A likelihood ratio test (LRT) for testing significant of regression coefficients is proposed. Also, confidence intervals based on fisher information for [16] method, called NOR, and LRT are computed and compared with well-known methods. In the end, we provide some guidance for various error distributions in heavy-tailed caese.