# Pigment Dyeing of Atmospheric Pressure Plasma-Treated Cotton Fabric
## 3 Results and Discussion
### Multiple Linear Regression Analysis  
Correlations among the three parameters--(i) discharge power; (ii) oxygen flow rate, and (iii) head moving speed--and the colour yield of the 1g/L and 5g/L pigment-dyed cotton samples are shown in Table 7. Based on the results in Table 7 (positive Pearson Correlation value), the level of discharge power and oxygen flow rate have a significant relationship with the colour yield, i.e., increasing the level of discharge power or oxygen flow rate increases the colour yield when pigment concentrations are 1 g/L and 5 g/L. Table 8 is the ANOVA table that shows the regression models of colour yield, which can be used for predicting the colour yield of the atmospheric pressure plasma-treated cotton fabric (with different discharge powers, oxygen flow rates, and head moving speeds) dyed with a pigment-dyeing concentration of 1 g/L or 5 g/L. The results reveal that the effect of the three atmospheric pressure plasma operations parameters have a significant influence on the colour yield. The significance (based on \(F\)-test results) for the 1 g/L and 5 g/L pigment-dyed colour yield are 0.002 and 0.007 in the 95% confidence interval, respectively. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & **Colour Yield** & **Discharge** & **Oxygen** & **Head** \\  & & & **Power** & **Flow Rate** & **Moving Speed** \\ \hline \multirow{3}{*}{Pearson Correlation} & 1 g/L Colour yield & 1.000 & 0.567 & 0.525 & 0.125 \\  & Discharge power & 0.567 & 1.000 & 0.742 & 0.620 \\  & Oxygen flow rate & 0.525 & 0.742 & 1.000 & 0.475 \\  & Head moving speed & 0.125 & 0.620 & 0.475 & 1.000 \\ \hline \multirow{3}{*}{Sig. (1-tailed)} & 1 g/L Colour yield & - & 0.001 & 0.001 & 0.255 \\  & Discharge power & 0.001 & - & 0.000 & 0.000 \\  & Oxygen flow rate & 0.001 & 0.000 & - & 0.004 \\  & Head moving speed & 0.255 & 0.000 & 0.004 & - \\ \hline \multirow{3}{*}{Pearson Correlation} & 5 g/L Colour yield & 1.000 & 0.366 & 0.374 & -0.126 \\  & Discharge power & 0.366 & 1.000 & 0.742 & 0.620 \\  & Oxygen flow rate & 0.374 & 0.742 & 1.000 & 0.475 \\  & Head moving speed & -0.126 & 0.620 & 0.475 & 1.000 \\ \hline \multirow{3}{*}{Sig. (1-tailed)} & 5 g/L Colour yield & - & 0.023 & 0.021 & 0.253 \\  & Discharge power & 0.023 & - & 0.000 & 0.000 \\ \cline{1-1}  & Oxygen flow rate & 0.021 & 0.000 & - & 0.004 \\ \cline{1-1}  & Head moving speed & 0.253 & 0.000 & 0.004 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Correlations between colour yield and atmospheric pressure plasma operation parameters. Figure 7: SEM images of 5 g/L pigment-dyed samples treated with different atmospheric pressure plasma conditions. \[\text{Y}_{1}=9.364+0.003_{\text{Discharge\,power}}+0.421_{\text{Oxygen\,flow rate}}-0.041_{\text{Head\,moving speed}} \tag{4}\]  
Y\({}_{1}\) is the predicted value of the colour yield of 1 g/L yellow pigment-dyed cotton fabric with different inputs for the discharge power, oxygen flow rate, and head moving speed. \[\text{Y}_{2}=47.981+0.013_{\text{Discharge\,power}}+1.935_{\text{Oxygen\,flow}}-0.290_{\text{Head\,moving speed}} \tag{5}\]  
Y\({}_{2}\) is the predicted value of the colour yield of 5 g/L yellow pigment-dyed cotton fabric with different inputs for the discharge power, oxygen flow rate, and head moving speed. After having the two linear regression models (Y\({}_{1}\) and Y\({}_{2}\)), as shown in Equations (4) and (5), respectively, Table 10 shows the verification of the two linear regression models (Y\({}_{1}\) and Y\({}_{2}\)). It is revealed that the two regression models can provide reliable predictions of colour yield when using the existing range of parameters.