## 3 Related Work  
[PERSON] and [PERSON] [10] applied the concepts of MPEG compression to reduce energy consumption. They proposed a prediction based on a monitoring mechanism, called PREMON, which abstracts the data stream sent by sensor nodes to the sink as a video stream encoded by MPEG standard. After PREMON, some works [8, 11-14] have shown the feasibility of the use of spatial and temporal correlation to optimize the communication protocols in WSN. They use algorithms embedded within motes, in a distributed way, to reduce data transmission to the sink. These techniques reduce energy consumption and consequently increase the network lifetime. [PERSON] and [PERSON] [15] proposed a localized prediction mechanism based on object tracking that reduces energy consumption due to hierarchy topology. According to [PERSON] and [PERSON] [13], sensor nodes in a distributed way are not able to operate, by itself, a data reduction system that can be as accurate as a centralized system. It uses statistics of the data history gathered by sensor nodes. [PERSON] _et al._[7] proposed a simple linear regression to reduce data generated by sensor nodes which gather temperature from the external environment. They compared the prediction accuracy performance of the simple linear regression with prediction based on the average. The difficulty lies in the fact that prediction accuracy based on simple linear regression depends on only one variable, which in many situations, is not correlated with any other. The time variable is usually less correlated than other variables gathered in the field, such as temperature, humidity or light. Therefore, prediction errors tend to be higher, _i.e._, less accurate. That paper is the closest to our proposed solution, but it performs prediction of user's queries, instead of constantly performing stream predictions. [PERSON] _et al._[16] carried out evaluations of some techniques for reducing the multivariate data traffic. These techniques are based on wavelet, sampling, hierarchical clustering and Singular Value Decomposition--SVD. [PERSON] _et al._[17] reduced the multivariate dimensionality of data gathered by sensor nodes. The authors used Principal Component Analysis--PCA as a reduction technique in an air quality monitoring application. The algorithm identifies the more significant samples and then sends them to the sink. The highlight of that work is that the parameters' performance, such as reduced data quality, energy consumption and delay, are taken into account in the experiments. Therefore, it is possible to observe the effects of applying the technique in multivariate data reduction. However, multivariate spatial correlation is not addressed. Also, there are few details about the solution operation, mainly about the error resulting from the dimensionality reduction procedure. Multivariate spatial and temporal correlation is the key to solve problems of prediction accuracy and improve energy savings through data reduction techniques. The papers found in the literature have superficially addressed prediction accuracy, but it is an essential issue in WSNs. This paper has the advantage (Table 1) of performing correlation analysis of variables gathered by sensor nodes before prediction is implemented. Also, the effects of using prediction based on multivariate spatial and temporal correlation in WSN were checked. Implementation details of our solution are highlighted, revealing the challenges of embed simple and multiple linear regression in WSN. In addition, we show when the use of prediction based on the multivariate correlation method is more appropriate, according to results. Our work is inspired on these techniques and concepts (spatial and temporal correlation, data reduction and prediction), already known in the literature to address energy saving issues in WSN. However, we focus on the challenge of improving prediction accuracy of WSN data based on a multivariate correlation method.