## 3 Results
### ANOVA and Multiple Regression Analysis  
Following the reliability and validity analyses, ANOVA and multiple regression analyses were conducted to examine differences in the motivations for using senior citizen centers based on the type of eldercare system and identify the main variables influencing these motivations within each type (home-based, community-based, and institutional care). According to Table 7, the R-squared values for the home-based (Y-1), community-based (Y-2), and institutional (Y-3) care models were 0.708, 0.475, and 0.717, respectively. This signified that 70.8%, 47.5%, and 71.7% of the independent variables explained the dependent variable in the Y-1, Y-2, and Y-3 data groups, respectively. Furthermore, the autocorrelation test for the error terms in the regression models for Y-1, Y-2, and Y-3 showed Durbin-Watson values of 1.587, 2.192, and 1.628, respectively. As these values were close to 2, no significant correlation existed between the residuals of each regression model, thus confirming the reliability of the analysis results. In addition, as shown in Table 8, the variables related to the motivation for using senior citizen centers showed statistically significant differences in the Y-1 (F = 26.857, \(p\) < 0.001), Y-2 (F = 13.417, \(p\) < 0.001), and Y-3 (F = 10.281, \(p\) < 0.001) data groups, suggesting that motivations differed depending on the type of eldercare system. As shown in Table 9, significant results from the multiple regression analyses according to the type of eldercare system included the following: Y-1: A-3 (\(\beta\) = 0.086, t = 1.977, \(p\) < 0.05), B-1 (\(\beta\) = 0.103, t = 2.354, \(p\) < 0.05), B-2 (\(\beta\) = 0.146, t = 3.421, \(p\) < 0.01), B-3 (\(\beta\) = 0.059, \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Group**} & \multicolumn{3}{c}{**Bartlett’s Test of Sphericity**} & \multicolumn{1}{c}{\multirow{2}{*}{**Sig.**}} & \multicolumn{1}{c}{\multirow{2}{*}{**Kaiser–Meyer-Olkin Measure**}} \\  & **Approx. Chi-Square** & **df** & & \\ \hline Y-1 & 1101.999 & 120 & 0.000 & 0.802 \\ \hline Y-2 & 2018.576 & 120 & 0.000 & 0.895 \\ \hline Y-3 & 644.034 & 120 & 0.000 & 0.826 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: KMO and Bartlett’s test. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multirow{2}{*}{**R**} & \multirow{2}{*}{**R Square**} & **Adjusted R** & **Std. Error of** & **Durbin-** \\  & & & **Square** & **the Estimate** & **Watson** \\ \hline Y-1 & 0.842 & 0.708 & 0.682 & 0.501 & 1.587 \\ \hline Y-2 & 0.690 & 0.475 & 0.440 & 1.005 & 2.192 \\ \hline Y-3 & 0.847 & 0.717 & 0.647 & 0.568 & 1.628 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Model summary. t = 2.385, \(p<0.05\)), C-2 (\(\beta\) = 0.189, t = 3.567, \(p<0.001\)), D-2 (\(\beta\) = 0.108, t = 2.314, \(p<0.05\)), D-3 (\(\beta\) = 0.131, t = 2.809, \(p<0.01\)), and E-1 (\(\beta\) = 0.131, t = 3.208, \(p<0.01\)); Y-2: A-2 (\(\beta\) = 0.205, t = 2.514, \(p<0.05\)), B-3 (\(\beta\) = 0.192, t = 2.361, \(p<0.05\)), and D-2 (\(\beta\) = 0.166, t = 2.059, \(p<0.05\)); and Y-3: A-2 (\(\beta\) = 0.184, t = 2.538, \(p<0.05\)), B-2 (\(\beta\) = 0.245, t = 2.905, \(p<0.01\)), and D-2 (\(\beta\) = 0.363, t = 3.774, \(p<0.001\)). The VIF values for all corresponding variables were below or equal to 5, confirming that they passed the multicollinearity test. Variable D-2 emerged as a significant motivation across all eldercare system types, while variable A-2 was significant in both Y-2 and Y-3. In addition, variable B-3 had a significant effect only in Y-1 and Y-2. The usage motivations for Y-1 and Y-2 tended to be relatively straightforward compared to Y-3. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & & \multicolumn{2}{c}{**Unstandardized**} & \multicolumn{2}{c}{**Standardized**} & & & & \\  & & \multicolumn{2}{c}{**Coefficients**} & \multicolumn{2}{c}{**Coefficients**} & \multicolumn{2}{c}{**t**} & \multicolumn{2}{c}{**Sig.