## 2 Data and Methods
### Methods
#### 2.3.2 Driving Factors Analysis Method for the Landscape Aggregation Degree of Cultivated Land
Therefore, most of the information of the factors could be generalized by extracting only two principal components. Factors were then rotated by Varimax, and factor loading was calculated. As seen in Table 9, X11, X12, X13, X21, X22, X32, X33, and X34 had higher loads on the first principal component, and X31 and X41 had higher loads on the second principal component. It can be concluded that the driving factors of the first principal component are economic development, industrial restructuring and urbanization factors, and the driving factors of the second principal component are increase in urban resident population and total power of agricultural machinery. \begin{table}
\begin{tabular}{|c c c|} \hline Kaiser-Meyer-Olkin Measure of sampling Adequacy & 0.732 \\ \hline \multirow{3}{*}{Bartlett test for sphericity} & Approximate Chi-Square & 280.459 \\ \cline{2-3}  & Degrees of freedom & 45 \\ \cline{2-3}  & Statistical significance (Sig.) & 0.000 \\ \hline \end{tabular}
\end{table} 
Table 7: Kaiser-Meyer-Olkin (KMO) and Bartlett spherical tests. \begin{table}
\begin{tabular}{c c c c} \hline
**Component** & **Value of Characteristic Root** & **\% of Variance** & **Cumulative \%** \\ \hline
1 & 8.121 & 81.207 & 81.207 \\
2 & 1.403 & 14.033 & 95.240 \\
3 & 0.368 & 3.682 & 98.922 \\
4 & 0.060 & 0.600 & 99.522 \\ \hline \end{tabular}
\end{table} 
Table 8: The results of principal component analysis (PCA). \begin{table}
\begin{tabular}{c c c} \hline
**Index** & **First Principal Component** & **Second Principal Component** \\ \hline X11 & 0.975 & \(-\)0.171 \\ X12 & 0.951 & \(-\)0.279 \\ X13 & 0.978 & 0.194 \\ X21 & 0.974 & 0.024 \\ X22 & 0.972 & \(-\)0.005 \\ X31 & \(-\)0.122 & 0.951 \\ X32 & 0.991 & 0.058 \\ X33 & 0.970 & \(-\)0.238 \\ X34 & 0.979 & \(-\)0.139 \\ X41 & \(-\)0.721 & \(-\)0.523 \\ \hline \end{tabular}
\end{table} 
Table 9: Factor loading matrix after rotation. (3) Regression Analysis  
Through the above analysis, two unrelated principal components (Y1 and Y2) were obtained. Taking Y1 and Y2 as independent variables and the landscape aggregation degree of cultivated land (Y) as dependent variables, we established the regression model between the dependent variable and principal components, and the following regression equation was obtained:  
\[\mathrm{Y}=-0.044*\mathrm{Y1}-0.049*\mathrm{Y2}+97.623 \tag{1}\]  
In order to determine the validity of the analysis results, the regression model was tested so that R\({}^{2}\) = 0.939 was close to 1, indicating that the regression model had a high degree of fit (Table 10). F-test and _t_-test results were both less than 0.05, indicating that the regression model had statistical significance and that the regression equation could be used to explain the change of landscape aggregation degree of cultivated land. To make the model more intuitive, the independent variable was restored to the original variable; that is, the expressions of F1 and F2 regarding the original variable were substituted into the regression Equation (2), and the final regression model was obtained as follows:  
\[\mathrm{Y}=-0.0345*\mathrm{X}_{11}-0.0282*\mathrm{X}_{12}-0.0525*\mathrm{X}_{ 13}-0.0440*\mathrm{X}_{21}\]  
\[ \begin{array}{c}-0.0425*\mathrm{X}_{22}-0.0413*\mathrm{X}_{31}-0.0465* \mathrm{X}_{32}-0.0310*\mathrm{X}_{33}\\ -0.0499*\mathrm{X}_{34}+0.0573*\mathrm{X}_{41}+97.623\end{array}  \tag{2}\]