# Analysis and Prediction of Universities' Buildings' Renovation Costs Using a Regression Model
## 4 Results and Discussion  
Finally, the prepared database consists of two independent variables (last modernization--\(X_{1}\), usable area--\(X_{2}\)) which are statistically significant. The dependent variable in this database is the attribute related to planned renovation costs, \(Y\). The coefficient of determination (\(R^{2}\)) was calculated for the database and its value was: \(R^{2}\) = 0.844. The random component and the regression coefficient values were calculated and were, respectively: \(\beta_{0}\) = 27,608,375.9, \(\beta_{1}\) = \(-\)13,681.63, and \(\beta_{2}\) = 118.024891. Figure 4: Renovation costs (in EUR) per 1 m\({}^{2}\) for the analyzed database and the analyzed period (2017–2021). The trend line equation, which allows to predict the future cost expenditures in the accurate short term, was determined as follows:  
\[\mathbf{y}=\mathbf{27608375.9}+\mathbf{13681.63}*\mathbf{X_{1}}+\mathbf{118.024891}*\mathbf{X_{2}} \tag{3}\]  
Table 4 shows the results of Statistica software calculations. The coefficient of determination value shows that the data points were properly selected. The accurate planned costs for educational buildings can be predicted in the following years knowing the usable area (m\({}^{2}\)) and the period since the last major renovation until today, in years. The regression coefficients b* and b are given in the table below, moreover the statistical linearity of the regression function was smaller than 5%, which shows that the function model was statistically relevant. The comparison of predicted values and planned renovation costs is shown by the graph in Figure 5.  
Figure 6 shows the results from the multiple regression analysis performed for the 55 analyzed buildings. The graph (Figure 6a) shows the predicted renovation costs in relation to the independent variable \(X_{1}\)--the last modernizatio \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Regression Summary for Dependent Variable: Planned Renovation**} \\  & & \multicolumn{4}{c}{**Costs**} \\  & & \multicolumn{4}{c}{\(R\) = 0.91867847} \\  & & \multicolumn{4}{c}{\(R^{2}\) = 0.84397014} \\  & & \multicolumn{4}{c}{**Adjusted \(R^{2}\)** = 0.83796899} \\ N = 55 & & \multicolumn{4}{c}{**F(2.52) = 140.63**} \\  & & \multicolumn{4}{c}{\(p\) < 0.0000} \\  & & \multicolumn{4}{c}{**The Standard Error of the Estimate: 45,259**} \\ \cline{2-6}  & \multicolumn{1}{c}{**b***} & \multicolumn{4}{c}{**Standard Error of b*} & \multicolumn{1}{c}{**b**} & \multicolumn{1}{c}{**Standard Error of b**} & \multicolumn{1}{c}{\(p\)**-Value**} \\ \hline Intercept & & & \(-11\),176.2 & 11,861.21 & 0.350424 \\ last moderniz (years) & 0.253398 & 0.054901 & 2736.3 & 592.85 & 0.000026 \\ usable area (m\({}^{2}\)) & 0.900218 & 0.054901 & 23.6 & 1.44 & 0.000000 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Regression summary. Figure 5: Predicted values and planned renovation costs. graph (Figure 6b) shows the predicted renovation costs in relation to the independent variable \(X_{2}\)--usable area, in m\({}^{2}\). The trend line of predicted renovation costs' growth from the graph in Figure 6a is not as significantly related to the last modernization period (in years) as the trend line presented on the graph in Figure 6b, where the predicted renovation costs' growth was greater in relation to the usable area growth. The predicted renovation costs, which were calculated according to chosen independent variables, are presented in the last graph (Figure 6c). The linearity of this graph proves the correctness of the multiple regression model calculations. Figure 7 shows the correlation between the planned renovation costs and the predicted renovation costs obtained from the regression analysis together with the residual values obtained during the analysis. The residual value is the difference between planned renovation costs and the predicted renovation costs.