# Influence of Crushed Rock Properties on the Productivity of a Hydraulic Excavator
## 4 Results and Discussion
### Analysis of the excavator Productivity Determinants
It was determined by conducted analysis that, between the combinations of two properties, largest influence on productivity of the excavator was a combination of the slew angle of excavator \(\text{A}_{\text{T}}\) and the coefficient of uniformity of particle size distribution n.  
The results of the analysis are graphically presented in Figure 8, and the regression summary is shown in Table 6.  
Figure 7: Influence of the slew angle on productivity. It appears from the indicators of reliability of multiple regression analysis from Table 6 that excavator productivity is significantly dependent on the slew angle of the excavator A\({}_{\rm T}\) and coefficient of uniformity n. It can be seen from standardized regression coefficients b\({}^{*}\) that coefficient of uniformity n has a larger influence on excavator productivity. The probability value of error p of the assumed regression model shows that the probability of error is less than 4.601%, from which it can be concluded that the dependence of the excavator productivity on analyzed material characteristics is significant given the usual \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**R = 0.88628382; R\({}^{2}\) = 0.78549901; Adjusted R\({}^{2}\) = 0.67824851; F (2,4) = 7.324**} \\ N = 7 & \multicolumn{3}{c}{**\(P\) = 0.04601; Std. Error of estimate: 81.529**} \\ \cline{2-7}  & **b \({}^{*}\)** & **Std.Err. of b \({}^{*}\)** & **b** & **Std.Err. of b \({}^{*}\)** & **t (4)** & **\(p-\)Value** \\ \hline Intercept & & & 354,3595 & 110.2472 & 3.21423 & 0.032458 \\ A\({}_{\rm T}\) [\({}^{\circ}\)] & \(-\)0.265315 & 0.256894 & \(-\)0.8297 & 0.8034 & \(-\)1.03278 & 0.360057 \\ n & 0.738543 & 0.256894 & 52.6848 & 18.3258 & 2.87490 & 0.045245 \\ \hline \hline \end{tabular}  
* R—Pearson correlation coefficient; R\({}^{2}\)—Coefficient of determination; Adjusted R\({}^{2}\)—Adjusted coefficient of determination; F (2,4)—F-distribution; p –Probability value of error; b—regression coefficients; b\({}^{*}\)—standardized regression coefficients  
\end{table} 
Table 6: Regression summary for dependent variable Q\({}_{\rm V}\). Figure 8: Multiple regression analysis of the dependence of the excavator productivity on the slew angle of the excavator and the coefficient of uniformity of the particle size distribution. significance level of 5%. The intercept of the regression plane on the z axis and coefficient n are also significant. The results of multiple regression analyses with a combination of three, four, and five independent variables with the largest influence on productivity are shown in equations from (7) to (10), and in Table 7 together with the influence of the slew angle and coefficient of uniformity considered above. \[\text{Q}_{\text{vm}}=354.3595-0.8297\text{ A}_{\text{T}}+52.6848\text{ n}, \tag{7}\]  
\[\text{Q}_{\text{vm}}=-1.0764\text{ A}_{\text{T}}-4.0188\text{ A}_{\text{r}}+62.2419\text{ n}+513.5846, \tag{8}\]  
\[\text{Q}_{\text{vm}}=-0.9973\text{ A}_{\text{T}}-6.8447\text{ A}_{\text{r}}-0.2520\text{ d}_{80}+62.7602\text{ n}+649.3469, \tag{9}\]  
\[\text{Q}_{\text{vm}}=6.44\text{ A}_{\text{T}}-223.01\text{ A}_{\text{r}}\text{ -31.72 }\text{ d}_{80}+22.45\text{ X}_{\text{c}}+127.99\text{ n}+10574.19, \tag{10}\]  
Considering regression equations from Table 7, Equation (10) gives the smallest mean absolute deviation from productivity calculated by measured characteristics. It appears from the indicators of reliability of multiple regression analysis that for the excavator productivity, the largest common effect is provided by five tested properties. However, due to the extremely large values of performance parameters, e.g., Adj. R\({}^{2}\) is 0.995984, there is a reasonable suspicion that overfitting occurred in this model. Therefore, the estimation equation will very well approximate the initial data on which it is based. It is likely that it would not be as good as the general model by which Q\({}_{\text{vm}}\) could be estimated.