## 4 Results
### Results of the Sensor Network over the Sleep Metrics
#### 4.2.5 Regression Analysis  
At this point, we know how the metrics are impacted by the sensor network on a qualitative scale (low, middle, and high impact). With this information, we could perform a regression analysis and identify predictive tendencies using the nine metrics gathered without the use of the sensor network as independent variables and the tag (high impact, middle impact, and low impact) as the target variable. In this way, we performed a multinomial logistic regression to discover how effective the sensor network can be for improving the sleep metrics once we know the nine metrics without the use of the sensor network. Because the tag is a nominal variable, it is good practice to take the first class as a reference to estimate the parameters, in this analysis we took the low impact as the reference class. Taking the low impact class as a reference class for the estimation of parameters clarifies the visualization of impact in the use of the sensor network over the nine metrics because in this way we can compare the possibilities to have a middle impact or high impact versus a low impact. Table 19 shows the estimation parameters with the reference class low impact of the multinomial logistic regression made with a steep back Wald test methodology. Using a steep back Wald test methodology in the multinomial logistic regression, it was possible to appreciate that the heart rate variability and deep sleep metrics are not in the estimation of the parameters of Table 19. In the estimation of the multinomial logistic regression, if the p-value of a metric is higher than 0.05 in the Wald test, the variable modifies less than 5 percent of the variance of the class to predict. The steep-back Wald test methodology performs the model only with the variables that predict more than 5% of the predicted class variance, which means that heart rate variability and deep sleep have \(p\)-values above 0.05 for the two predicted classes. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Metric** & \(p\)**-Value** & **Test** & \
\begin{tabular}{c} **Statistically** \\ **Different** \\ \end{tabular} &
\begin{tabular}{c} **Difference** \\ **Direction** \\ \end{tabular} \\ \hline DS & 0.264 & Wilcoxon & No & \(SN>NSN\) \\ HR & 0.130 & \(t\)-test & No & \(SN>NSN\) \\ BF & 0.494 & \(t\)-test & No & \(SN<NSN\) \\ T & 0.000 & \(t\)-test & Yes & \(SN<NSN\) \\ REMS & 0.016 & [PERSON] & Yes & \(SN>NSN\) \\ OS & 0.901 & \(t\)-test & no & \(SN>NSN\) \\ HRV & 0.000 & [PERSON] & Yes & \(SN>NSN\) \\ S & 0.026 & \(t\)-test & Yes & \(SN<NSN\) \\ TST & 0.000 & [PERSON] & Yes & \(SN>NSN\) \\ \hline \hline \end{tabular}
\end{table} 
Table 18: Results of paired tests between metrics with and without the use of the sensor network for the class low impact. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Metric** & \(p\)**-Value** & **Test** & \
\begin{tabular}{c} **Statistically** \\ **Different** \\ \end{tabular} &
\begin{tabular}{c} **Difference** \\ **Direction** \\ \end{tabular} \\ \hline DS & 0.001 & [PERSON] & Yes & \(SN>NSN\) \\ HR & 0.003 & \(t\)-test & Yes & \(SN<NSN\) \\ BF & 0.000 & \(t\)-test & Yes & \(SN<NSN\) \\ T & 0.000 & \(t\)-test & Yes & \(SN<NSN\) \\ T & 0.000 & \(t\)-test & Yes & \(SN<NSN\) \\ REMS & 0.000 & [PERSON] & Yes & \(SN>NSN\) \\ OS & 0.623 & \(t\)-test & No & \(SN>NSN\) \\ HRV & 0.000 & \(t\)-test & Yes & \(SN>NSN\) \\ S & 0.022 & [PERSON] & Yes & \(SN<NSN\) \\ TST & 0.000 & [PERSON] & Yes & \(SN>NSN\) \\ \hline \hline \end{tabular}
\end{table} 
Table 17: Results of paired tests between metrics with and without the use of the sensor network for the class middle impact. For the class high impact, the metrics heart rate, breathing frequency, temperature, oxygen saturation, total sleep time, and snoring are significant predictors, and the metric REM sleep is a non-significant predictor.