# Role of Public Entities in Suitable Provision of Public Services: Case Study from Slovakia
## 4 Results and Discussion

Table 2: The linear correlation of the number of inhabitants and the number of operations in the registry offices. Figure 4: Individual characteristics of registry offices in the individual regions in the Slovak Republic in 2018. Source: Statistical Office of the Slovak Republic—Statdat, Ministry of the Interior of the Slovak Republic, own processing. Considering differences between individual regions in the Slovak Republic (Figure 5), we first analyzed the differences using the Kruskal-Wallis test, which confirmed, at the 5% significance level, differences between regions in the number of operations per capita (W = 85.95; \(p\leq 0.01\)). The test results confirmed Hypothesis 3. Statistically significant differences in the number of operations in registry offices per capita in comparison with other regions were recorded in the Bratislava and Trnava regions. The Bratislava region is one of the most economically developed regions of the Slovak Republic, which is associated with a growing population and a progressive age structure of the population in this region. The Trnava region is in a similar situation. Although there are a relatively low number of municipalities in both regions compared to other regions, there are a relatively high number of registry offices, with a registry office located in every second municipality in the region. When comparing individual regions of the Slovak Republic (Figure 6) in terms of the total subsidy allocated to registry offices recalculated per capita, we used the Kruskal-Wallis test; a statistically significant difference was not confirmed (W = 12.617, \(p=0.082\)). This means that Hypothesis 4 was not confirmed. It can be stated that, in terms of per capita subsidies in the period 2007-2018, there were no statistically significant differences between regions. Figure 5: Differences between individual regions depending on the number of operations per inhabitant. Source: own processing. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline  & **Bratislava** & **Trnava** & **Trencin** & **Nitra** & **Zilina** & **Banská** & **Byrtica** & **Presov** & **Kosice** \\  & **Region** & **Region** & **Region** & **Region** & **Region** & **Region** & **Region** & **Region** \\ \hline \(\mathbf{r_{K}}\) & 0.7618 & 0.464 & 0.221 & 0.221 & 0.397 & 0.198 & \(-\)0.397 & \(-\)0.486 \\ \(p\)**-value** & \textless{}0.05 & \textless{}0.05 & 0.273 & 0.273 & \textless{}0.05 & 0.324 & \textless{}0.05 & \textless{}0.05 \\ \hline \end{tabular} Source: own processing.  
\end{table} 
Table 3: The linear correlation of the number of inhabitants and the number of operations in the registry offices. Based on the regression analysis results (Table 4), we can see the different development of the amount of subsidy per capita and the trend in the number of operations per capita in registry offices in individual regions in the Slovak Republic in the period 2007-2018. Differences can be observed in the absolute level of the dependent variable and in the steepness of the regression function. Based on the above results of the correlation analysis, we can describe regional differences in the amount of subsidy per capita and the number of operations per capita in the region. In five regions (Bratislava, Trnava, Zilina, Presov, and Kosice), a linear correlation between the amount of the subsidy and the number of actions performed in the region was confirmed. In four regions (Bratislava, Nitra, Presov, and Kosice), a linear relationship between the number of inhabitants and the number of operations at registry offices in the region was also confirmed.