## 3 Results
### Global Sensitivity
#### 3.2.2 Sensitivity Analysis  
This section presents the results for all the models variated with the Monte Carlo (MC) method. To begin with, the results for the three models representing different fixed levels of DH unit costs are analyzed by histograms and calculated via cumulative distribution functions. Afterwards, the results concerning the parameter sensitivity and model linearity are presented. The effect of the distinct, fixed unit costs of DH on the NPV output is shown in Figure 8. As can be observed, the spread and range of the variance of the results seem to be identical for the three cases. The magnitude of the output value differs due to the distinct unit cost of DH applied in each case (low = 34, medium = 68, and high = 108 EUR/MWh). The distribution, spread, and variance magnitude are identical. This was confirmed because the resulting standard deviation of each of the three distributions is equal (\(\sigma\) = 117,220 EUR). The mean value of the results for the low, medium, and the high price of the DH unit cost is \(-\)1.54, \(-\)1.93, and \(-\)2.31 million euros, respectively. This suggests that the DH unit cost also influences the result linearly. This can be stated due to (1) the equal variance of the three distributions and (2) the identical regression coefficients and R\({}^{2}\) values obtained from the regression analysis, presented in Appendix A. Table 4 provides a summary of the multivariate regression results for each model. The first four parameters (the unit cost of electricity, attic insulation and PV, and the amount of attic insulation) are common for all models. All four are variated in every model. In contrast, parameters 5, 6, and 7 are specific for the DH, gas, and HP models. The complete regression results for each model variation is available in Appendix A. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Category** & **Parameter** & **Unit** & **Probability Density Function** & **Source** \\ \hline Operation & Electricity—DH and gas & EUR/MWh & Normal & \(\mu\) = 157; \(\sigma\) = 4.39 & DEA [37, 39] \\  & Electricity—HP & EUR/MWh & Normal & \(\mu\) = 93.5; \(\sigma\) = 5.35 & DEA [37, 39] \\  & gas & EUR/m\({}^{3}\) & Normal & \(\mu\) = 0.6; \(\sigma\) = 0.04 & DEA [37, 39] \\ \hline Implementation & Attic insulations & EUR/m\({}^{2}\) & Uniform & 104–156 & Assumed \\  & Roof-mounted PV & EUR/system & Uniform & 49.5–134.2 K & TDC [35] \\  & New windows & EUR/m\({}^{2}\) & Normal & \(\mu\) = 147.1; \(\sigma\) = 50 & Assumed \\ \hline Lifespan & Heat pump & year & Uniform & 15–25 & TDC [34] \\ Amount & Attic insulation & m\({}^{2}\) & Uniform & 1400–2400 & Assumed \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Summary of variation parameters applied in Monte Carlo method. Figure 8: Probabilistic NPV for LCC calculation models incorporating three distinct unit costs for district heating. All sensitivity indexes in Table 4, except the lifetime of the HP, are negative. This means that an increase in a variated value would result in a decrease in the output. Since the calculations consider only expenses (disregard positive cash flow/income), the NPV output is negative; therefore, decreasing the output asserts a more costly solution. The results of the DH and gas models suggest a close to equal importance for the four common parameters. The unit cost of electricity is the parameter with the most negligible influence on the output. For gas and DH, it is noticeably less impactful than the remaining variated inputs. The unit cost for attic insulation and the implementation of a PV system is the next most influential parameter, where minor differences can be noted for gas and DH. In the case of DH, the unit cost for the implementation of a PV system is more influential than the unit cost of attic insulation and vice versa for gas. The model-specific parameters in the DH and gas scenarios (unit cost for new windows and gas, respectively) are the most influential in the respective cases. The HP scenario presents a couple of differences, compared to the results for DH and gas.