## 3 Results and Discussion
### Modeling the Color Appearance of Carpets
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Illuminant** & **Color** & **Dependent Variable** & **R Square** & \(p\)**-Value of Gauge** & \(p\)**-Value of Stich Rate** & \(p\)**-Value of** & \(p\)**-Value of Dye** &
\begin{tabular}{c} **Equation (g = Gauge of the Carpet, s = Stich)** \\ **Rate of the Carpet, p = File Height of the Carpet, p = File Height of the Carpet, and d = Dye Concentration.** \\ \end{tabular} \\ \hline \multirow{4}{*}{D65} & \multirow{2}{*}{Red} & \(\mathrm{L}^{*}\) & 0.87 & \(>\)0.05 & 0.04 & 0.03 & 0.00 & \(\mathrm{L}=\pm 476\) - \(223\,\mathrm{\SIUnitSymbolAngstrom}-\mathrm{\SIUnitSymbolAngstrom}5.9\) \\  & & \(\mathrm{a}^{*}\) & 0.92 & \(>\)0.05 & 0.01 & 0.00 & 0.00 & \(\mathrm{a}\pm 630\) - \(30.37\,\mathrm{\SIUnitSymbolAngstrom}-\mathrm{\SIUnitSymbolAngstrom}1.488-\mathrm{\SIUnitSymbolAngstrom}5.5\) \\  & & \(\mathrm{b}^{*}\) & 0.88 & \(>\)0.05 & 0.03 & 0.03 & 0.00 & \(\mathrm{b}\) = \(2894\,\mathrm{\SIUnitSymbolAngstrom}-\mathrm{\SIUnitSymbolAngstrom}1.505-\mathrm{ \SIUnitSymbolAngstrom}0.69\,\mathrm{\SIUnitSymbolAngstrom}-\mathrm{\SIUnitSymbolAngstrom}1.55\) \\  & & \(\mathrm{L}^{*}\) & 0.77 & \(>\)0.05 & \(>\)0.05 & \(>\)0.05 & 0.00 & \(\mathrm{L}\) = \(361\,\mathrm{\SIUnitSymbolAngstrom}-\mathrm{\SIUnitSymbolAngstrom}2.86\) \\  & & \(\mathrm{a}^{*}\) & 0.66 & \(>\)0.05 & \(>\)0.05 & 0.00 & \(\mathrm{a}\pm 295\,\mathrm{\SIUnitSymbolAngstrom}-\mathrm{\SIUnitSymbolAngstrom}1.216\) \\  & & \(\mathrm{b}^{*}\) & 0.74 & 0.00 & 0.00 & 0.00 & \(\mathrm{b}\) = \(33.65\,\mathrm{\SIUnitSymbolAngstrom}-\mathrm{\SIUnitSymbolAngstrom}2.34\,\mathrm{ \SIUnitSymbolAngstrom}1.64\,\mathrm{\SIUnitSymbolAngstrom}-\mathrm{\SIUnitSymbolAngstrom}1.96s- 904.4\) \\ \hline \multirow{4}{*}{A10} & \multirow{2}{*}{Red} & \(\mathrm{L}^{*}\) & 0.88 & \(>\)0.05 & 0.02 & 0.02 & 0.00 & \(\mathrm{L}=\pm 5391\) - \(265\,\mathrm{\SIUnitSymbolAngstrom}-\mathrm{\SIUnitSymbolAngstrom}1.25-\mathrm{ \SIUnitSymbolAngstrom}1.21s-308.9\) \\  & & \(\mathrm{a}^{*}\) & 0.90 & \(>\)0.05 & 0.01 & 0.01 & 0.00 & \(\mathrm{a}=\pm 938.26\,\mathrm{\SIUnitSymbolAngstrom}-\mathrm{\SIUnitSymbolAngstrom}2.47- \mathrm{\SIUnitSymbolAngstrom}1.23s-203.02\) \\  & & \(\mathrm{b}^{*}\) & 0.90 & \(>\)0.05 & 0.01 & 0.01 & 0.00 & \(\mathrm{b}=4650\) - \(244\,\mathrm{\SIUnitSymbolAngstrom}-\mathrm{\SIUnitSymbolAngstrom}1.10s-264.1\) \\  & & \(\mathrm{L}^{*}\) & 0.76 & \(>\)0.05 & \(>\)0.05 & 0.05 & 0.00 & \(\mathrm{a}=\pm 241\,\mathrm{\SIUnitSymbolAngstrom}-\mathrm{\SIUnitSymbolAngstrom}1.10s- 108.4\) \\  & & \(\mathrm{b}^{*}\) & 0.60 & \(>\)0.00 & 0.00 & 0.00 & \(\mathrm{b}=\pm 260\) - \(4654\,\mathrm{\SIUnitSymbolAngstrom}+\mathrm{\SIUnitSymbolAngstrom}2.93\,\mathrm{ \SIUnitSymbolAngstrom}-\mathrm{\SIUnitSymbolAngstrom}1.95s- 87.5\) \\ \hline \multirow{4}{*}{F02/10} & \multirow{2}{*}{Red} & \(\mathrm{L}^{*}\) & 0.86 & \(>\)0.05 & 0.04 & 0.03 & 0.00 & \(\mathrm{L}=\pm 462\) - \(241\,\mathrm{\SIUnitSymbolAngstrom}-\mathrm{\SIUnitSymbolAngstrom}1.13s-280.2\) \\  & & \(\mathrm{a}^{*}\) & 0.92 & \(>\)0.05 & 0.00 & 0.00 & \(\mathrm{a}=\pm 48.42\,\mathrm{\SIUnitSymbolAngstrom}-\mathrm{\SIUnitSymbolAngstrom}2.519 -\mathrm{\SIUnitSymbolAngstrom}1.21s-302.02\) \\  & & \(\mathrm{b}^{*}\) & 0.92 & \(>\)0.05 & 0.00 & 0.01 & 0.00 & \(\mathrm{b}=\pm 308.76\,\mathrm{\SIUnitSymbolAngstrom}-\mathrm{\SIUnitSymbolAngstrom}0.81s- 185.5\) \\  & & \(\mathrm{b}^{*}\) & 0.76 & \(>\)0.05 & \(>\)0.05 & 0.00 & \(\mathrm{L}\) = \(359\,\mathrm{\SIUnitSymbolAngstrom}-\mathrm{\SIUnitSymbolAngstrom}2.384\) \\  & & \(\mathrm{a}^{*}\) & 0.79 & 0.00 & 0.05 & 0.01 & 0.00 & \(\mathrm{a}=\pm 31.58\,\mathrm{\SIUnitSymbolAngstrom}+\mathrm{\SIUnitSymbolAngstrom}1.41\, \mathrm{\SIUnitSymbolAngstrom}-\mathrm{\SIUnitSymbolAngstrom}1.495s+ 075s+ 902p\) \\  & & \(\mathrm{b}^{*}\) & 0.70 & 0.00 & 0.00 & 0.00 & \(\mathrm{b}=\pm 33.78\,\mathrm{\SIUnitSymbolAngstrom}-\mathrm{\SIUnitSymbolAngstrom}4 +\mathrm{\SIUnitSymbolAngstrom}3.317g-216s-96.3\) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Summary of the outcome of the regression analysis.