# Statistical Methods in Bidding Decision Support for Construction Companies
## 3 Results and Discussion
### Evaluation of Models--Discussion of Results  
To evaluate the model, the classification efficiency expressed as the number of cases correctly classified into predefined classes was used. A summary of the performance of the proposed models is presented in Tables 9 and 10. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Eigenvalue**} & **Canonical Correlation** & **Wilks’ Lambda** & **Chi-Square Statistics** & _df_ **Number of Degrees of Freedom** & \(p\) **Value** \\  & \(R\) & **1**-** & **2**-** & **0** \\ \hline
1.125553 & 0.727691 & 0.470466 & 62.58464 & 6 & 0.000000 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Parameters for assessing the statistical significance of the discriminant function. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{2}{c}{**Observed Numbers**} & \multicolumn{2}{c}{**Reality**} & \multicolumn{2}{c}{**Total**} \\ \hline \multicolumn{2}{c}{**Answer from the Model**} & \multicolumn{1}{c}{\(y_{i}\) = 1} & \multicolumn{1}{c}{\(y_{i}\) = 0**} & \\  & **(W—win)** & **(L—loss)** & \\ \hline \multirow{4}{*}{LOG Model} & \(\hat{y}_{i}\) = 1 (W—win) & 13 & 7 & 20 \\  & \(\hat{y}_{i}\) = 0 (L—loss) & 11 & 57 & 68 \\ \cline{1-1}  & Total & 24 & 64 & 88 \\ \cline{1-1}  & Correct & 54.17\% & 89.06\% & 79.55\% \\ \cline{1-1}  & Incorrect & 45.83\% & 10.94\% & 20.45\% \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Summary of classification for the LOG model. The data in Tables 8 and 9 enable the basic parameters of the classification model to be determined. The results are given in Table 11.  
From the values in Table 10, the LOG model correctly classified 79.55% of the cases, more correctly predicting tender failure (83.82%). The values obtained show a good fit of the model, but it is worrying that the model indicated only three tender factors as statistically significant: \(x_{3}\)--contractal conditions, \(x_{6}\)--need for work, and \(x_{15}\)--degree of difficulty of the works. In the case of the LDA model, classification into the set L--87.14% means that the model (analogous to the LOG model) more accurately predicts tender failure than winning (83.33%). The results obtained by the LDA model are better as it rendered 86% of correctly classified cases. The discriminant analysis, apart from the variables \(x_{3}\), \(x_{6}\), \(x_{15}\) indicated also \(x_{1}\)--type of works, \(x_{5}\)--value of the project, and \(x_{13}\)--possible participation of subcontractors, as significant variables for the model, where the greatest independent influence on the result of the discriminant function is exerted by the variable \(x_{6}\)--the need for work, while the least \(x_{3}\)--contractal conditions. The following is an extract from the LDA model results sheet with the values of the classification functions in relation to the observed (actual) values shown in Table 12.  
The analyses presented in this paper do not exhaust the issue of modeling contractors' decisions to participate in tenders for construction works. They can become a supplement of the models proposed so far in the literature. It should be noted that the construction of classification models requires having an appropriate database, which is built based on tender factors selected by the author of each model. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Case Number**} & \multicolumn{2}{c}{**Group**} & \multicolumn{2}{c}{**Group**} & \multirow{2}{*}{**Function Value**} \\  & **Membership:** & & & \\ \cline{2-4}  & **Observed** & **Model** & \(K_{0}\)—win & \(K_{1}\)—loss \\ \hline
10 & W & W & 208.994 & 211.747 \\
28 & L & L & 189.970 & 186.249 \\
* 29 & W & L & 207.961 & 206.832 \\
30 & L & L & 199.490 & 196.887 \\
* 35 & L & W & 220.759 & 222.847 \\ \hline \hline \end{tabular} \({}^{*}\)Cases misclassified.  
\end{table} 
Table 12: Classification function values for selected cases.