## 3 Results
### Regression Analysis of Experimental Data  
Regression analysis on the existing input and output data yielded the following equation:  
\[\text{COF}=1.899-0.686\text{ hysteresis}+0.000012\text{ hardness}-0.018\text{ s. roughness}+0.0000318\text{ speed}-0.459\text{ floor condition} \tag{1}\]  
The value of R represents the coefficient of multiple correlation. It is used to determine the quality of predicting the dependent variable, and in this case, it was 0.73, which means the predictive capability was high. The R-squared value represents the coefficient of determination, which is the proportion of the variance in the dependent variable that can be explained by the independent variables. For this regression, it was 0.53 or 53%, indicating a good relationship between variables. The significance \(F\)-value shown in the table indicates that the regression model was good for these values, and the independent variables statistically predicted the dependent variable reasonably well. Table 5 shows the \(t\)-statistic and the \(p\)-values. From the table, it can be concluded that only the coefficient for the substrate condition had a \(p\)-value less than 0.05, indicating that this variable was the most significant. Table 6 shows the correlation of variables in the regression model. The highest correlation among the variables was between rubber hysteresis and rubber hardness. There were no significant correlation values among the other variables. In the regression analysis, the elimination method revealed that the most significant variables influencing the coefficient of friction (COF) were roughness, hysteresis of the rubber, and the surface conditions. Figure 4: COF on the anti-slip and smooth tiles depends on rubber hysteresis ((**A**) dry, (**B**) wet, (**C**) soapy). Table 7 shows that the most influential parameter on the COF for the anti-slip tile (wet and soap) were rubber hysteresis and the surface conditions. Rubber hysteresis had a positive sign, and it showed that with an increase in hysteresis, the COF increased as well. All predictors were significant, with \(p\)-values less than 0.05. The coefficients obtained from this regression indicated the following: as the coefficient of hysteresis of the rubber was 0.5 with a positive sign, the COF increased (considering only wet and soapy conditions, at all speeds on the anti-slip tile). The rubber hardness had a coefficient of 0.0249, indicating that an increase in hardness slightly increased the COF. The surface conditions had a negative influence on the COF. The most significant parameter was the surface conditions, with a \(p\)-value of 1.73 \(\times\) 10\({}^{-22}\); followed by rubber hardness, with a \(p\)-value of 1.31 \(\times\) 10\({}^{-10}\), and hysteresis, with a \(p\)-value of 1.37 \(\times\) 10\({}^{-6}\). Table 8 shows that the most influential parameters on the COF for the smooth tile (wet and soapy) were rubber hysteresis and the surface conditions. Rubber hysteresis, speed, and the surface conditions had negative signs, meaning that the COF decreased with their increase. Hardness had a positive coefficient sign, meaning that the COF increased with an increase in hardness. All predictors were significant, with \(p\)-values less than 0.5, except rubber hardness, with a \(p\)-value of 0.978. \begin{table}
\begin{tabular}{c c c c c c} \hline  & **Kinetic \(\mu\)** & **r. Hysteresis** & **Hardness** & **Roughness** & **Speed** \\ \hline Kinetic & \(1\) & & & & \\ \hline R. hysteresis & \(-0.10018\) & \(1\) & & & \\ \hline Hardness & \(0.073795\) & \(-0.74763\) & \(1\) & & \\ \hline Roughness & \(-0.07805\) & \(0.006196\) & \(0.009898\) & \(1\) & \\ \hline Speed & \(0.007557\) & \(3.74\times 10^{-18}\) & \(3.54\times 10^{-18}\) & \(-1.7\times 10^{-18}\) & \(1\) \\ \hline \end{tabular}
\end{table} 
Table 6: Input variable correlation with regression method.