# Video Quality Modelling--Comparison of the Classical and Machine Learning Techniques
## 4 Results
### Objective vs. Subjective Quality Assessment  
The normality of the data distributions for the individual metrics was verified using the Shapiro-Wilk test, which in the vast majority of cases resulted in the rejection of the hypothesis of the normality of these distributions at the 5% decision level (\(p<0.05\)). This required the use of [PERSON]'s rank-order correlation test, which is a non-parametric equivalent of [PERSON]'s correlation. The authors conducted a correlation analysis. The results showed a strong relationship between the values of individual objective metrics and the quality perceived by users (see Table 3). As Table 3 shows, almost all analysed metrics correlate with subjective assessment results at levels higher than 95%, as shown by [PERSON]'s r coefficients. The VQM metric had the highest correlation coefficient (99%). In contrast, the Delta metric showed the lowest correlation (64%). The authors proposed quality of perception (QoP) models based on each individual metric using linear regression using Formula (13):  
\[\text{QoP}=\text{a}+\text{b}*\text{M}_{\text{X}}, \tag{13}\]  
where QoP is the quality perceived by the users, a and b are the equation coefficients (a is the intercept and b is the slope), and M\({}_{\text{X}}\) denotes the value of the x metric. In this work, the concept of QoP is used as a narrower version of the concept of quality of experience (QoE) often used in the literature. The determined model parameters for individual metrics are presented in Table 4. However, it should be noted that the proposed linear regression models, based on individual metrics, are characterised by much lower and more varied values of the coefficient of determination (COD), also called the R-square. COD is a statistical measure to qualify linear regression. This coefficient indicates which percentage of the variation in the response variable, in this case, QoP, is explained by the \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & **APSNR** & **Delta** & **MSAD** & **MSE** & **NQI** & **PSNR** & **SSIM** & **VIF** & **VMAF** & **VQM** \\ \hline Spearman’s r  & 0.97 & \(-\)0.64 & \(-\)0.97 & \(-\)0.97 & 0.96 & 0.97 & 0.98 & 0.97 & 0.98 & 0.99 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Correlations between the values of objective quality metrics and subjective user scores. fitted regression line. The higher the value of the coefficient of determination, the better the model will be. In order to help interpret the regression model more intuitively, a fitted curves plot is presented in Figures 6 and 7. Figures 6 and 7 show the relationships between the values of the individual objective metrics and the subjective evaluation values determined on the basis of the linear regression model. The 95% confidence bands show the limits of all possible linear regression lines for the data. In other words, we are 95% confident that we can say that the line of best fit is within the confidence intervals. The prediction band for the desired confidence level (1-\(\alpha\)) forms the interval within which 100(1-\(\alpha\))% of all experimental points in a series of measurements are expected to fall. For alpha = 0.05 for the prediction band, we can say with 95% confidence that the expected data point will fall within this range. In other words, if we add one more measurement data point whose independent variable (here the value of a given metric) is within the range of the independent variable of the original data set, there is a 95% chance that the predicted value (here a subjective assessment) will