  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.
