# Correlation and Regression Analysis of Spraying Process Quality Indicators
## 3 Results  
The results were statistically analyzed. Table 3 presents the results of the analysis of variance of the indicators of spray quality. The F test was used to evaluate the significance of the results at a significance level of \(p=0.05\). The analysis of variance was divided into two parts depending on the nozzle type. XR and DF are standard nozzles, while CVI and CVI TWIN are air-induction nozzles. The analysis was performed separately for each surface. Based on the correlation coefficients (R) presented in Table 3, it can be stated that all relationships are strong or very strong with very high statistical significance (\(p<0.0005\)). The results of linear regression are shown in Figures 4-9. The values of the degree of coverage are presented on the x-axis and the values of the deposition of liquid are shown on the y-axis. The regression line, regression equation and the value of the coefficient of determination are also depicted in the plots. Figures 4-6 present the scatter plots of the degree of coverage and deposition of liquid for selected standard nozzles. The values of the deposition of liquid increase with the increase in the degree of coverage. In the case of upper horizontal surfaces, the coefficient of determination R\({}^{2}\) is higher than 0.88, which means the high quality of the regression model. While in the case of the vertical surfaces, the very high quality of the models is observed with an R\({}^{2}\) higher than 0.94. \begin{table}
\begin{tabular}{c c} \hline
**Correlation Coefficient** & **Interpretation** \\ \hline
0 & no linear relationship \\ \hline (0; 0.40)/(\(-0.40\); 0) & weak positive linear relationship/ \\  & weak negative linear relationship \\ \hline \(<\)0.40; 0.70)/(\(-0.70\); \(-0.40\)\(>\) & moderate positive linear relationship/ \\  & moderate negative linear relationship \\ \hline \(<\)0.70; 0.90)/(\(-0.90\); \(-0.70\)\(>\) & strong positive linear relationship/ \\  & strong negative linear relationship \\ \hline \(<\)0.9; 1)/(\(-1\); \(-0.9\)\(>\) & very strong positive linear relationship/ \\  & very strong negative linear relationship \\ \hline \(+1/-1\) & perfect positive linear relationship/ \\  & perfect negative linear relationship \\ \hline \end{tabular}
\end{table} 
Table 2: The interpretation of the correlation coefficient. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Nozzles** & **Surface** & **F** & **Se** & **S(a)** & **S(b)** & **Ve [\%]** & **R** \\ \hline \multirow{3}{*}{XR and DF—standard nozzles} & horizontal upper & 166.4558 & 711.7962 & 12.5976 & 622.7839 & 14.7221 & 0.9398 \\  & vertical approach & 359.9703 & 113.7631 & 11.6734 & 75.0449 & 8.3603 & 0.9708 \\  & vertical leaving & 860.9794 & 87.5600 & 7.4268 & 35.1296 & 6.9483 & 0.9875 \\ \hline CVI and & horizontal upper & 112.1109 & 817.1803 & 15.2684 & 555.8545 & 19.4904 & 0.9143 \\ CVI TWIN—air- & vertical approach & 130.0897 & 147.1545 & 24.3045 & 146.7021 & 11.6151 & 0.9249 \\ induction nozzles & vertical leaving & 578.5757 & 47.7444 & 6.0044 & 25.4283 & 4.1824 & 0.9815 \\ \hline \end{tabular}
\end{table} 
Table 3: The analysis of variance. Figure 4: The scatter plot of the degree of coverage and deposition of spray liquid for selected standard nozzles for upper horizontal surface. Figure 5: The scatter plot of the degree of coverage and deposition of spray liquid for selected standard nozzles for approach vertical surface. Figure 6: The scatter plot of the degree of coverage and deposition of spray liquid for selected standard nozzles for leaving the vertical surface. Figure 7: The scatter plot of the degree of coverage and deposition of spray liquid for selected air-induction nozzles for upper horizontal surface. The results of linear regression for the selected air-induction nozzles are presented in Figures 7-9. Based on the data presented in the figures, it can be concluded that the highest accuracy of the regression model was observed for the leaving vertical surfaces (R\({}^{2}\) > 0.96).