*4.6. Multivariate Analysis*

Linear ANOVA models have been calculated for each of the factors analyzed: initial stress, sadness, initial fatigue, CO2 concentration and music tempo. In all models, the *p* value is less than 0.05. Therefore, we can state that the independent variables reliably predict the dependent variable. Table 16 shows the models with an adjusted R-squared (R2) higher than 55%. Adjusted R-squared is a statistic that gives information about the goodness of fit of a model. R-squared is defined as the fraction of the variance in the dependent variable that is explained by the model. The adjusted R-squared is a modified version of R-squared that has been adjusted for the number of predictors in the model. The higher the adjusted R-squared value, the more the model fits the real data. In Table 16, the labels labeled as "COEFFICIENT" are the values for the regression equation for predicting the dependent variable from the independent variables. Finally, the *p* value is a probability. It gauges the likelihood that the coefficient is not significant, so smaller is better. In our case, we consider that there is significance when the value is less than 0.05.

We can see that the best model is obtained in "Speeding", where the adjusted R<sup>2</sup> is higher than 70%. In view of the coefficient's values and the *p* value, we can state that the initial stress level as well as the initial fatigue and fast-paced music significantly increase the number of times the speed limits are surpassed. We can also point out that both sadness and a high concentration of CO2 do not seem to influence speeding. In these two independent variables, the *p* values are higher than 0.05.


**Table 16.** Results of multivariate analysis with high R2.

In the LF/HF ratio, we found that the initial stress level along with fatigue contributes to the occurrence of stress during driving. It is important to highlight the strong relationship between initial fatigue and the possibility of stress while driving, where the coefficient value is 4.152. In the case of the other two variables related to driving stress (pNN50 and SCR amplitude), the same thing happens, but we have not included them in the table because the adjusted R-squared value is lower than 50%. Finally, we can observe that when the driver suffers sadness, the value of the LF/HF ratio decreases, meaning less stress in driving. The *p* value for sadness is lower than 0.05 and the coefficient is −1.405. This could be explained because the drivers are focused on their own problems. Extremely low driving stress is also not good for safety because it could cause drowsiness [5].

The results of the "Harsh braking" variable are very similar to the "LF/HF" variable. However, the *p* value of sadness is higher than 0.05. Therefore, in this context, it does not significantly affect the model. The driver who is initially tired or stressed does not react early enough to road events, forcing aggressive maneuvers and increasing driving stress.

Regarding sudden accelerations, they characterize an aggressive driving style which appears especially when the driver is stressed. The coefficient value is 6.936 and the *p* value is lower than 0.05. Sadness is also an emotion that contributes. The coefficient value is 2.315 and the *p* value is lower than 0.05. People with sadness often adopt an aggressive driving style and a certain degree of passiveness that causes increased fuel consumption and can annoy other drivers [22]. On the contrary, a high concentration of CO2 decreases harsh accelerations. The coefficient value is −2.074 and the *p* value is lower than 0.05. This could be due to the possible appearance of drowsiness [96].

#### **5. Discussion and Limitations of Our Experiment**

In our experiment, the initial level of stress and fatigue has a strong impact on driving behavior and driving stress. The relationship between stress and road safety has been verified by many authors [97,98]. Several studies have corroborated that a high level of stress increases errors and traffic violations. In [46], the authors conducted a study involving 2806 drivers using the driver behavior questionnaire (DBQ) and the driver behavior inventory (DBI). The DBI assesses dimensions of driver stress, whereas the DBQ is concerned with assessing the relative frequencies with which drivers engage in different types of aberrant driving behavior. They found a strong correlation between an aggressive driving style and high levels of stress. They also observed that when the stress is high, drivers make

more mistakes, although in this case, the dislike of driving also seems to play a role. This is consistent with our findings that stressed drivers accelerate and brake more often than non-stressed drivers. Furthermore, harsh accelerations are six times higher than the values obtained by non-stressed drivers. In the case of harsh braking, the values are twice as high as those obtained by non-stressed drivers. Harsh accelerations and harsh braking are indicative of an aggressive driving style. The main di fference between our analysis and the previous literature is that we have monitored the driver's state and driving behavior. Most of the proposals are based on self-reports of drivers or tra ffic accident databases provided by the governmen<sup>t</sup> [99]. The problem with self-reports is that they depend on the drivers' perception, which could be wrong. In [99], the authors found that drivers with high confinement had a low risk perception and reported driving errors incorrectly.

Regarding the sadness factor, we observe that it is mainly characterized by a very significant increase in the number of tra ffic accidents. This emotion also contributes significantly to the increase in sudden decelerations. Attentional self-focus and repetitive negative thoughts are two main elements in sadness [100,101]. These elements a ffect information processing and attention [102]. In [103], the authors observed that sadness-induced drivers made more errors in target location. This could explain why, in our experiment, drivers with sadness su ffered more tra ffic accidents than drivers who do not feel this emotion. On the other hand, we also found in our driving test that drivers with sadness did not manifest more stress than other drivers. In [22], the researchers conducted a simulated driving experiment with two induced a ffective states to examine how sadness and anger di fferently influence driving-related risk perception, driving performance and perceived workload. The results they obtained showed that sad drivers make more driving errors, but do not perceive a higher workload than drivers with an emotionally neutral state. This could explain why we have not found significant di fferences in driving stress.

In the literature, many researchers focus on analyzing how fatigue that increases during driving a ffects driving performance and road safety [104]. These studies point out that fatigue is a very important factor that causes a lack of hazard perception [105]. This may lead to driving accidents [106]. In this regard, the European Union has a regulation that sets the maximum driving time for professional drivers [107]. The relationship between driver fatigue and hours of service regulations is a challenge [108]. Some authors have found that driving time is a significant predictor of accident risk [109]. In other studies, there is no evidence of a time-on-task e ffect [110]. This could be due to the repercussion of the driver's initial fatigue level. In our study, we have observed that initial fatigue significantly influences driving behavior and driving stress. We have also observed a non-compliance with tra ffic regulations that require high attention from the subject such as "yield to a pedestrian at a crosswalk". This demonstrates the need to not only monitor fatigue during driving, but also to do so beforehand in order to ensure driving safety.

Traditionally, the CO2 concentration inside the vehicle cabin was not considered dangerous because of its low level. However, several recent studies have shown that the concentration of CO2 can be quite high depending on the number of vehicle occupants, speed and the environment [111]. In addition, cognitive impairment has also been observed with low or moderate CO2 concentrations with short exposure times [112]. In [113], the authors observed that the mental task required more e ffort from the subjects when the CO2 concentration in the air reached 3000 ppm. In [12], the researchers concluded that decision-making performance decreased when participants were exposed to CO2 concentrations between 1000 and 2500 ppm. This is in line with what was observed in our study. The worsening of decision making when the CO2 concentration is high causes the number of tra ffic accidents to increase. A high CO2 concentration also causes fatigue and drowsiness in drivers, reducing reaction time [114]. As a consequence, we observed in our study an increase in the frequency and intensity of decelerations. Finally, the combination of high initial stress with fast-paced music causes, in our experiment, a significant increase in the number of times the maximum allowed speed is exceeded. There are many marketing studies where fast music is used to encourage customers to purchase [115,116]. In the field of driving, many researchers have observed a similar behavior. In [90], the authors concluded that listening to fast music in the background affects non-compliance with traffic rules such as speeding.

As a limitation in our study, we did not take into account variables such as personality, gender, socio-educational level or the driver's history (fines and traffic accidents). In [117], the researchers conducted a study with 41 drivers using a driving simulator, where they observed that these variables affect driving behavior, especially when drivers are tired. These factors were not included in the survey in order not to extend our experiment and discourage participants. In most of the papers, the subjects only had to fill out surveys and did not drive. Another limitation is in the evaluation of the music factor. We have only analyzed the tempo. The subject could freely adjust the volume of the music and the playlist was the same for all participants. We have not considered other elements that can influence driving behavior such as gender or music familiarity [118].
