## 4 Results
### Pearson Correlation  
Pearson's correlation coefficient is computed by dividing the covariance of two variables by the product of their standard deviations. It is the normalisation of the covariance between the two continuous variables to give an interpretable score. It quantifies the degree to which a change in one variable is associated with a change in another variable ([PERSON], 2016).  
\[\text{PearsonCorrelation (r)}=\text{covariance(X,Y)}/(\text{stdv(X)}\times\text{ stdv(Y)} \tag{2}\]  
This heatmap shown in Figure 5 above, compares the two variables var_2683, i.e.,.tINTF_General_Visu.tLaneProtection.tCover3.tMotor4.tMotor.tPT100_Group.tPT100_2.tError.bHasError and \"var_831\" i.e.,.tINTF_General_Visu.tLaneProtection.tCover1.tMotor4.tCB.SignalWithError.tError.bHasError. The heatmap displays the correlation coefficient between these variables. The diagonal quadrants (where a variable is compared to itself) show a correlation coefficient 1 (as expected). The off-diagonal quadrants reveal a weak negative correlation of approximately \(-0.079\). The colour scale ranges from \(-1\) to \(1\). Dark red represents stronger negative correlations, while dark blue indicates stronger positive correlations.  
Figure 5: [PERSON]’s correlation.  
Spearman Correlation  
[PERSON]'s correlation was calculated from each sample's relative rank of values. This approach is commonly used in non-parametric statistics, such as statistical methods where no specific distribution of the data, like the Gaussian distribution, is assumed [64]. This coefficient measures the strength and direction of the monotonic relationship between two ranked variables. It is beneficial in identifying and assessing nonlinear relationships and ordinal data.  
SpearmanCorrelation = covariance(rank(X),rank(Y))/std(rank(X)) \(\times\) std(rank(Y))  
This heatmap shown above in Figure 6, is divided into four quadrants to show the Spearman correlation coefficient between two variables labelled as var_2683--tINTF_General_Visu.tLaneProtection.tCover3.tMotor4.tMotor.tPT100_Group.tPT100_2.tError.bHasError on the \(y\)-axis and var_831--tINTF_General_Visu.tLaneProtection.tCover1.tMotor4.tCBSignalWithError.tError.bHasError on the \(x\)-axis. The two diagonal quadrants show a perfect positive correlation (a value of 1) for each variable with itself (indicated by the red colour and the number 1). The off-diagonal quadrants reveal a very low negative correlation of \(-0.079\) between the two variables (indicated by deep blue).  
The Kendall Tau rank correlation coefficient measures the degree of similarity between two sets of ranks given to the same set of objects. Unlike Spearman's coefficient, the Kendall Tau measures only directional agreement, not rank differences.  
\[\text{KendallCorrelation = (Number of Concordant Pairs -- Number of Discordant pairs)/n(n - 1)/2} \tag{4}\]  
The Kendall correlation heatmap displayed in Figure 7 reaffirms the findings of the other correlations. It focuses on the same two variables as the other correlation heatmaps, i.e., var_2683--tINTF_General_Visu.tLaneProtection.tCover3.tMotor4.tMotor.tPT100_Group.tPT100_2.tError.bHasError on the \(y\)-axis and var_831--tINTF_General_Visu.tLaneProtection.tCover1.Motor4.tCB.tSignalWithError.tError.bHasError on the \(x\)-axis. The top left and bottom right quadrants are dark red, indicating a perfect correlation of 1. This is expected since each variable correlates with itself. The top right and bottom left quadrants are blue, suggesting a weak negative correlation (approximately \(-0.079\)) between var_2683 and var_831.  
Figure 6: Spearman correlation.