Linear Regression (LR) is a classical machine learning algorithm which has many applications in the cyber physical social systems (CPSS) to shape and simplify the way we live, work and communicate. This paper focuses on the data analysis for CPSS when the Linear Regression is applied. The training process of LR is time-consuming since it involves complex matrix operations, especially when it gets a large scale training dataset In the CPSS. Thus, how to enable devices to efficiently perform the training process of the Linear Regression is of significant importance. To address this issue, in this paper, we present a secure, verifiable and fair approach to outsource LR to an untrustworthy cloud-server. In the proposed scheme, computation inputs/outputs are obscured so that the privacy of sensitive information is protected against cloud-server. Meanwhile, computation result from cloud-server is verifiable. Also, fairness is guaranteed by the blockchain, which ensures that the cloud gets paid only if he correctly performed the outsourced workload. Based on the presented approach, we exploited the fair, secure outsourcing system on the Ethereum blockchain. We analysed our presented scheme on theoretical and experimental, all of which indicate that the presented scheme is valid, secure and efficient.