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Linear regression is a basic statistical method to correlate two or more attributes in data mining, machine learning, decision tree and Bayes classification. This paper studies non-black-box two-party computation of linear regression protocols with malicious adversaries. The contribution of this paper comprises the following three-fold: - in the first fold, a general two-party computation model for linear regression protocols is introduced and formalized; - in the second fold, a non-black-box two-party computation of linear regression protocols based on the Goldreich, Micali and Wigderson's compiler technique is presented; - in the third fold, we show that the proposed non-black-box construction toleratesmalicious adversaries in the simulation-based framework assuming that the underlying Damgård and Jurik's public key encryption scheme is semantically secure and the Damgård-Fujisaki commitment scheme is statistically hiding and computationally binding.