## 4 Test Results
### Discriminative Function Analysis
These functions are a valuable reference material, since other mix results can be projected to this \"learned\" database and used to evaluate their similarity to their already isolated clusters. The clusters may represent areas of the recycled mix properties proposed for recommendation. The ultimate forms of the discriminant functions are shown in Table 8.  
This final stage of analysis enabled the mathematical description of the boundaries required to classify the cases of recycled mixes with waste materials (specimens) in existing clusters. As mentioned above, they can be treated as a \"learned\" reference model for the behavior of MCAS mixtures with waste materials. Therefore, based on the value of the discriminant function and the coefficients in Table 8, a new case of a recycled mixture of unknown membership can be classified in a given group. The group membership is established based on the maximum value obtained from the computation of all three classification functions. The grouping procedure adopted in the analysis was 98% effective. In Groups 1 and 3 only one case was probably misclassified--the one at the boundary between the arbitrary boundary determined by the classification function. The multidimensional analysis summarizes the projection plot of the data with respect to the values of two canonical functions. It allows global assessment of the population partition and rules applicable in the given set of recycled mixtures with waste materials. The canonical data scatter plot with the cases of recycled MCAS is shown in Figure 7.  
The canonical value scatter plot provides an overview of a number of general rules and relationships in a given set of results for the samples of recycled mixtures made with different waste materials. The samples of recycled mixtures that best represent the data sets can be defined as those at the group centroid (mean). In the case of Group 1, these were the mix samples with the addition of basalt mineral dust, regardless of the mineral dust amount, with 1.2% bitumen foam content. The RC80/VA20 mix was also close to the canonical mean in Group 1. This proves that Group 1 was represented by the mixtures whose rheological state could result from the high content of hydraulic binders. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Variable**} & \multicolumn{2}{c}{**Raw Canonical Coefficients for Variables**} \\ \cline{2-3}  & **V\_1** & **V\_2** \\ \hline Z1 & 0.032485 & \(-\)0.300443 \\ Z2 & 0.694875 & 0.069673 \\ Z3 & \(-\)0.019345 & 0.112120 \\ Z4 & \(-\)0.395212 & 0.249668 \\ Constant & 0.000000 & 0.000000 \\ Eigenvalue & 3.029339 & 1.066332 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Raw canonical function coefficients. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Variable**} & \multicolumn{3}{c}{**Classification Functions**} \\ \cline{2-3}  & **G\_1:1 \(p\) = 0.30337** & **G\_2:2 \(p\) = 0.37079** & **G\_3:3 \(p\) = 0.32584** \\ \hline Z1 & \(-\)0.44494 & 0.30543 & 0.06670 \\ Z2 & 0.36849 & 1.14900 & \(-\)1.65056 \\ Z3 & 0.16332 & \(-\)0.12652 & \(-\)0.00808 \\ Z4 & 0.23067 & \(-\)0.89327 & 0.80172 \\ Constant & \(-\)2.42206 & \(-\)2.84355 & \(-\)3.94296 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Discriminant function coefficients for recycled MCAS mixes with waste materials. Group 2 could be represented by the samples with dolomite dust, mixes with 20% RC (20 RC/80 VA) and, which is most important, by the mixtures with 80% recycled aggregate (80 RC/20 VA), which suggests that the use of large amounts of recycled aggregate should be investigated further for its suitability. The latter case makes the use of a large recycled aggregate subject to its thorough examination in terms of suitability. Analysis of the parameters assigned to Group 2 shows that the use of recycled aggregates can be an acceptable compromise between the quality and durability of mixtures produced using deep recycling with foamed bitumen. Group 3 was represented by mixtures with dolomite aggregate and a large amount of foamed bitumen (3.6%).