## 9 Discussion and Conclusions  
Several sensor boards are able to monitor more than one variable (multisensor), adding new challenges, such as increasing precision by reducing prediction error. In this paper, we propose a method to improve prediction accuracy in WSN data reduction by applying multivariate spatial and temporal correlations.  
Prediction accuracy of correlation mechanisms depends on the correlation analysis to determine which variable is highly correlated. The current approaches are not focused on the analysis of correlations and hence the prediction errors tend to be higher. The correlation analysis results of Table 2 show that the time variable is the least correlated of all others. Thus, predictions using weakly correlated variables can greatly increase errors. We recommend that all proposals contemplate the analysis of correlation to obtain better results in their predictions. Although energy consumption of our solution is twice that of the simple linear regression approach, it is still smaller than the original application. Table 5 summarizes the energy savings for the application versions that perform prediction and shows that the version using simple linear regression is the most economical and multiple linear regression is the one that consumes more energy. An important observation is that the simple linear regression, using the variable temperature as independent variable, is not the best option to improve prediction, although it spends a little more energy than the version with multiple linear regression, the first does not show better accuracy results than the second.  
Figure 19: Epochs from a collect day where the light variable is less correlated with the temperature and humidity variables.  
Related works use simple linear regression based on the time variable as independent variable, so that they are more susceptible to errors than our proposal. Although multiple linear regression spends more energy than simple linear regression, it may be the best choice, especially for accuracy-sensitive applications (e.g., precision agriculture).  
We conducted simulations involving simple and multiple linear regression functions (application versions from 2 to 4) to assess our prediction solution. The values of residual sum of squares (SSerr) and coefficient of determination (R\({}^{2}\)) show that prediction accuracy may be the lowest, where simple linear regression based on the time variable is used as explanatory variable. Also, these results show that the best prediction accuracy is obtained when multiple linear regression is used. The multivariate correlation method outperforms some current methods in about 50% to humidity prediction and 21% to light prediction.  
Table 6 shows that predictions were more accurate when our solution was used, because when more than one variable is used in the prediction, error decreased, but Table 7 shows the disadvantage of our solution, because when the variables are not strongly correlated, the prediction error tends to be higher than in solutions that use simple linear regression, e.g., when the light variable is not constant.  
Finally, we have done some works trying to improve WSN solutions [19-22] and intend to further reduce energy consumption considering sensing, processing and communication. Computer intelligence algorithms [23] and cluster routing solutions [19] may be helpful in better adapting our spatio-temporal correlation solution to improve network lifetime.