# Personalized Daily Hand Movement Training Methods and Effects: A Case Study
## 3 Results
Although the paired t-test and box plot analysis have shown significant improvements in well-being and hand function, the specific relationship between well-being and hand function remains unclear. To verify whether well-being can promote the recovery of hand function, further exploration of the interaction effects between well-being and hand function through regression analysis is necessary and important. Figure 6 examines whether the residuals are randomly distributed around the zero line to assess the validity of the regression model's assumptions. The observed results show that the residuals are randomly distributed and the red smoothing line is approximately flat, indicating no obvious trends or systematic errors. This suggests that the model assumptions are reasonable and meet the requirements for linear regression. Figure 7 shows that most data points are close to the diagonal, indicating that the model's predicted values are very close to the actual values. Although some points may slightly deviate, the overall tight distribution of points suggests that the model has good predictive accuracy. Figure 7 indicates that the regression model performs well in prediction, with most predicted values close to the actual values, verifying the model's robustness and accuracy. The results are shown in Table 2:  
1. The Overall Model Explanation  
**R-squared (R2 = 0.97):** This value indicates that the model explains 97% of the variance in the dependent variable, DASH. This means that the model can explain most of the variability in DASH. **Adjusted R-squared (Adj. R2 = 0.96):** The adjusted R2 takes into account the number of predictors in the model and indicates that the model still has strong explanatory power. **F-statistic (F = 160.5, Prob (F-statistic) = 1.25 \(\times\) 10\({}^{-17}\)):** The result of the F-test is highly significant (\(p\)-value is extremely low), indicating that the independent variables, as a whole, have a significant effect on the model. 2. **Regression Coefficients and Significance Levels**  
**Constant (const = 60.83):** This represents the predicted value of DASH when all independent variables are zero. **Life Satisfaction (SWLS = -2.62, \(p\) < 0.001):** Life satisfaction is significantly negatively correlated with DASH. For each unit increase in SWLS, DASH is reduced by approximately 2.62 units. This indicates that higher life satisfaction is associated with lower DASH levels. **Subjective Happiness (SHS = 2.57, \(p\) = 0.24):** There is no significant linear relationship between subjective happiness and DASH, with a \(p\)-value of 0.24 (greater than 0.05), indicating that this variable is not significant in the model. **Positive Affect (PANAS_Positive = -0.11, \(p\) = 0.41):** Positive affect negatively impacts DASH, but this relationship is not significant with a \(p\)-value of 0.41. This suggests that while positive affect might reduce DASH, this effect is not statistically significant. **Negative Affect (PANAS_Negative = 0.48, \(p\) = 0.27):** Negative affect has a positive but non-significant impact on DASH, with a \(p\)-value of 0.27. This indicates no significant linear relationship between negative affect and DASH. **Psychological Well-Being (PWB = 0.23, \(p\) = 0.29):** There is also no significant linear relationship between psychological well-being and DASH, with a \(p\)-value of 0.29. This shows that psychological well-being does not have a significant impact on DASH. Through detailed analyses shown in Figures 6 and 7, the regression model's performance in explaining the variability of DASH can be further confirmed. The residual plots indicate that the model assumptions are reasonable, and the fitted value plots demonstrate the model's high predictive accuracy. These graphs further validate the model's applicability and effectiveness in regression analysis. The regression analysis indicates that life satisfaction (SWLS) is the most significant variable, having a notable negative effect on DASH. Although other variables affect DASH, their impacts are not statistically significant.