## 5 Discussion
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Size of the** & **Number of** & **Avg. Fitness** & **Avg. Execution Time (s)** \\
**Population** & **Generations** & & \\ \hline
20 & 110 & 0.85583 & 0.404229 \\
30 & 100 & 0.90717 & 0.497875 \\
40 & 80 & 0.94555 & 0.58785 \\
50 & 100 & 0.962 & 0.878382 \\
60 & 100 & 0.98761 & 1.200938 \\
70 & 110 & 0.99284 & 1.465077 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The fitness function value sensitivity to the variation of the input parameters. Figure 13: The execution time variation when number of generations is changed, and population size is maintained constant. variation in fitness value can be explained by the change in the population size and number of generations. The standard error measures the precision of our analysis model, and the lower the value is, the more precise predictions are provided. In our case, we obtained a standard error of 0.024, thus the regression model produces precise predictions. Finally, the observation represents the number of configurations of the parameters considered which in our case is the combination of the number of generations and the size of the population in our model. The analysis of variance, ANOVA table, (see Table 5) provides information about the variability level of our regression model reflected by several components. At the same time, Figure 14 shows details of the spread and distribution of the results achieved on how the control variables of population size and the number of generations influence the value of the fitness function. The residuals show the difference of the mean sample (i.e., positive when the value is greater and negative when the value is smaller). The degree of freedom, df, is associated with the variance sources, while the sum of squares SS provides information about data dispersion, and how well the data fits into the regression model. As can be seen in our case the value of the residual SS is lower compared to the total SS, indicating that the model fits well the data. The mean squares parameter, MS, provides an estimate of the variance concerning the regression and is calculated as the ratio between the sum of squares and the degree of freedom. It is used to determine the F value which provides information about the fitness model's importance in relation to the null hypothesis. Significance F shows if our solution with the two independent variables (that is, the population size and the number of generations) can be used to explain the variability of the fitness value. Since in our case, the value of Significance F is lower than 0.05 the model is statistically significant. The regression analysis from Table 6 provides more in-depth information on the influence of the size of the population and the number of generations. The coefficients are the least square estimates for the independent variables (i.e., the size of the population and the number of generations), the standard errors for coefficients are the standard errors of  
Figure 14: Boxplot for data distribution of ANOVA analysis. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **df** & **SS** & **MS** & **F** & **Significance F** \\ \hline Regression & 2 & 0.238686198 & 0.119343 & 192.1951 & 1.52266 \(\times\) 10\({}^{-27}\) \\ Residual & 63 & 0.039119699 & 0.000621 & & \\ Total & 65 & 0.277805898 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: ANOVA table. the least squares estimates for the independent variables and the \(p\)-value is the value for hypothesis testing. The coefficients values reflect the mathematical relation between an independent variable either the population size or the number of generations and the dependent variable, while the \(p\)-value indicates if the relation between an independent variable and the dependent variable is statistically significant or not (i.e., if there is a correlation between an independent variable and the dependent variable). In the case of our algorithm, the coefficient for the size of population is 0.003, while for the number of generations is 0.0008.