## 1 Introduction  
Wireless Sensor Networks (WSNs) consist of few or several sensor nodes which are resource constrained. Some sensor nodes gather data from external environments and send information such as temperature, humidity and light to the sink. The information is sent hop by hop (intermediate nodes) until the sink is reached. However, data traffic is a problem in WSN due to high energy consumption [1-3].  
These sensors can be used in many applications such as event detection, location, monitoring and control [4]. Among these applications, environment monitoring is a very common scenario. Therefore, data gathering is periodical, generating a large amount of data traffic in the network.  
In this scenario, the sensor nodes frequently send the same data gathered from a specific area. The overlapping of information sent to the sink causes waste of energy, which decreases the network lifetime. The problem is even worse when the number of deployed nodes increases (scalability), because data communication is responsible for most of the energy consumption in WSN [4-6].  
Figure 1 describes how the monitoring system works. Note that each sensor node gathers samples of a particular variable (such as temperature) and sends it to the sink at each cycle (epoch).  
An energy efficient communication protocol helps improve the deployment of this type of network in environments such as vegetation and weather monitoring. The correlation between the data gathered by a sensor node and its neighbors, as well as the correlation between the data gathered by the sensor node itself over a given time [2] must be explored by efficient protocols to improve energy consumption. They are known as spatial and temporal correlation. When more than one variable in the correlation is taken into account, the approach is named multivariate correlation.  
The purpose of data prediction is to reduce data traffic to the sink. It has been adopted in several papers in the literature [7]. It helps to reduce the overall energy consumption of the network. An algorithm is embedded within the sensor node to calculate the coefficients of a linear regression function. These coefficients are named \(\beta\) and \(\alpha\), and represent a sequence of variable samples gathered by the sensor, such as temperature. Thus, the sensor node sends the coefficients to the sink, instead of sending the sequence of variables samples. When \(\beta\) and \(\alpha\) arrive at the sink, they are used by the linear regression function embedded within the sink. Then the readings sequence is predicted by the monitoring system (Figure 2).  
Figure 1: Operation of the monitoring system.  
That approach usually takes into account the correlation of only one variable to be predicted (named dependent or response variable, e.g., temperature) and only one variable to predict the dependent variable (named independent or explanatory variable, e.g., time/epoch). However, the time variable is not the most correlated variable with others variables such as temperature, humidity and light.  
Thus, the prediction adopted by current solutions, is sometimes not accurate. Consequently, the questions we address here are: \"can we use the correlation between the variables gathered by the same sensor node to improve prediction accuracy?\" and \"is the multivariate prediction more accurate than published methods?\"  
Figure 3: Operation of the monitoring system based on prediction proposed on this paper (multiple linear regression).  
Figure 2: Operation of the monitoring system based on prediction proposed by current authors (simple linear regression).  
We propose a method that performs prediction of data based on multivariate correlation. In our method, we take into account the correlation between two readings of data gathered by the sensor node and also the time/epoch variable (Figure 3). Our method is different from current works which use the correlation between one variable gathered and the time variable.