# Analysis and Prediction of Universities' Buildings' Renovation Costs Using a Regression Model
## 3 Materials and Methods
### Research Analysis--Phase 1  
In the first phase, 17 buildings (B1-B17) erected in the years 1830-2017 and owned by a university in Cracow (Poland) were compared using linear regression. The data were collected from the renovation plans for the years 2017-2020, and the correlation analysis was performed, matching three chosen attributes: building age, number of stories in the building, and the usable area of each building, with the renovation costs. These attributes were chosen by the authors because they applied to all 17 buildings. The results are presented in Table 1. The strongest relationship existed between the variables renovation cost and number of stories, where the \(r\) coefficient indicated a very strong correlation (\(r\) equals 0.81), \(R^{2}\) indicated a satisfactory determination, and the \(p\)-value indicated a significant relationship, where the value was the lowest from the whole database at 0.001. Slightly weaker relations were obtained for the renovation cost and the usable area, where \(r\) was 0.72 and the \(p\)-value was 0.008. The correlation for the renovation cost and the age of the building was not satisfactory as the \(p\)-value was 0.909, greater than 0.05, which means that this correlation was not statistically significant; therefore, in further analysis, the correlation between the building age and renovation cost was abandoned. Figure 2 shows the percentage share of renovation costs in each year of the first phase of analysis. The renovations performed in the building's interiors had higher percentage \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Variables** & \(\mathbf{r}\) & \(\mathbf{R^{2}}\) & \(\mathbf{p}\) \\ \hline Renovation cost—building age & \(-0.04\) & \(0.0016\) & \(0.909\) \\ Renovation cost—No. of stories & \(0.81\) & \(0.66\) & \(0.001\) \\ Renovation cost–usable area & \(0.72\) & \(0.52\) & \(0.008\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Correlation analysis. Figure 1: Research analysis, the two phases of the research. shares every year. The second most popular renovation type was installations. The least popular renovation type was renovations performed on the exterior of the buildings, whereby no renovations were performed in the years 2017-2020 (0%). The second least popular type were renovations of the whole buildings, with this type only being performed in the year 2017, accounting for 1% of the renovations performed in this year. Moreover, the first phase of analysis clearly shows the imperfections of renovation plans created by the university management. The renovations performed and the costs incurred add up to approximately 50% of the planned renovations. This is related to the numerous renovations that have not been carried out and not to the potentially overpriced bills of the planned renovations. Based on the information provided by the university worker who created the renovation plans, the incomplete works will be completed but since the renovation plans are verified at the beginning of each year and compared with the received funding, unfortunately, the funding received by the universities is not sufficient to cover the costs of all the renovation needs. Due to this fact, in further analysis (second phase) the correlation between planned costs with different variables instead of incurred costs has been examined. It has a logical basis because the model will yield an answer of how high the costs are to properly renovate the building instead of the real cost that is incurred regarding each building, which does not cover all its renovation needs. The dependencies between incurred and planned costs are presented in Figure 3, while Table 2 shows the percentage of the planned funds that were actually incurred. The average of the sum of incurred costs in the years 2017-2020 in coordination with planed renovation costs was 43%, and the median was 47%. At the same time, the average of the correlation between incurred and planned costs was 48%, while the median was exactly 50%.