## 3 Results and Discussion
### Ecological Compensation Mechanism for the Tourism Industry during the COVID-19 Pandemic
#### 3.3.2 Correction of Ecological Compensation Coefficient in the Tourism Industry
Therefore, in the second component, PECG and LONS are variable indicators for ecological compensation in the tourism industry. The third and fourth components primarily reflect REEC and NUOC, with contributions of \(-0.445\) and \(0.838\), respectively. In the fourth component, REEC and NUOC have significant contributions of \(0.563\) and \(0.481\), respectively. In the third and fourth components, REEC in \(2020\) represents the residents' living standards more than PECG in the second component. It is more reasonable to consider REEC instead of PECG as the variable indicator for the R coefficient when conducting ecological compensation in the region. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline  & **PECG** & **AMOR** & **REEC** & **LONS** & **AROT** & **PRON** & **GDOE** & **NUOC** \\ \hline PECG & \(1.000\) & \(0.179\) & \(-0.429\) & \(-0.163\) & \(0.515\) & \(0.731\) & \(0.448\) & \(0.037\) \\ AMOR & \(-0.179\) & \(1.000\) & \(-0.002\) & \(-0.457\) & \(-0.312\) & \(0.297\) & \(-0.685\) & \(-0.049\) \\ REEC & \(-0.429\) & \(-0.002\) & \(1.000\) & \(-0.034\) & \(0.151\) & \(-0.427\) & \(-0.217\) & \(-0.178\) \\ LONS & \(-0.163\) & \(-0.457\) & \(-0.034\) & \(1.000\) & \(0.662\) & \(0.346\) & \(0.492\) & \(0.221\) \\ AROT & \(0.515\) & \(-0.312\) & \(0.151\) & \(0.662\) & \(1.000\) & \(-0.279\) & \(0.189\) & \(0.131\) \\ PRON & \(0.731\) & \(-0.297\) & \(-0.427\) & \(0.346\) & \(-0.279\) & \(1.000\) & \(0.473\) & \(0.075\) \\ GDOE & \(0.448\) & \(-0.685\) & \(-0.217\) & \(0.492\) & \(0.189\) & \(0.473\) & \(1.000\) & \(0.104\) \\ NUOC & \(0.037\) & \(0.049\) & \(-0.178\) & \(0.221\) & \(0.131\) & \(0.075\) & \(0.104\) & \(1.000\) \\ \hline \end{tabular} Note: Correlation levels of \(0.8\)-\(1.0\) indicate a robust correlation, \(0.6\)-\(0.8\) indicate a strong correlation, \(0.4\)-\(0.6\) indicate a moderate correlation, \(0.2\)-\(0.4\) indicate a weak correlation, and \(0.0\)-\(0.2\) indicate a very weak or no correlation. PECG (Per capita GDP by region): AMOR (Amount of reduced tourism revenue); REEC (regional Engel coefficient); LONS (area of local nature scenic spots); AROT (Area of tourism scenic spots in each province); PRON (The proportion of the area covered by natural scenic areas); GDOE (GDP of each province); NUOC (Number of confirmed COVID-19 cases.). Correlation analysis using \(2020\) data.  
\end{table} 
Table 5: Correlation matrix of indicators. In conclusion, the relevant indicators for the R coefficient are determined as follows: 2020 reduction in tourism revenue (AMOR), 2020 regional Engel coefficient (REEC), 2020 ratio of natural scenic area to total tourist area (PRON), and 2020 GDP of each province (GDOE). Subsequently, these four indicators are used to derive Formula (10). In Formula (10), \(S\) represents the GDP of each province (city), and \(Sn\) represents the total reduction in tourism revenue in the study area due to the COVID-19 pandemic. The ratio of these two variables visually represents the impact on the regional tourism economy caused by the pandemic. A logarithmic function is used as a control mechanism to regulate the overall ratio within a reasonable range. \(t\) represents the Engel coefficient of each province (city). The Engel coefficient can effectively reflect the living standards of the regional population and the willingness to pay for ecological values under different levels of economic development and living standards. Using the natural logarithm as the base, when the Engel coefficient is significant, it indicates a lower willingness to pay for ecological values in that area. As a result, the \(R\)-value becomes smaller, indicating less ecological compensation for that region. This reflects the consideration of people's willingness to pay in the calculation of \(R\). \(Q\) represents the natural aggregation degree of scenic areas in each province (city), which is equal to the proportion of the natural scenic areas in each province (city) to the total area of scenic areas.