## 7 Concluding Remarks  
In this paper, we make a critical look at the mainstream approach in estimating the coupling and coordination of two or more subsystems from the engineering perspective. The mainstream approach is to define a set of predictors for each subsystem. Then, the weight for each predictor is calculated towards establishing the development level of the subsystem (referred to as comprehensive evaluation index in our study). Subsequently, the coupling degree and the coordination degree are computed based on the comprehensive evaluation indices of the subsystems. A big issue with this approach is the lack of validation of the  
Figure 42: Statistical comparison of the training performance \(R^{2}\) for our dataset \(O\) in four different configurations and the reference dataset \(R\), for both LPRF (**left**) and GBR (**right**). Figure 43: The top 10 regions for the degree of coordination and the top 10 regions for the projection performance. The four regions that are present in both are highlighted. results. The set of predictors is usually subjectively defined base on the authors' expertise and perspective. As such, there is no guarantee that the set of predictors can fully model the subsystem. Consequently, the development level of each subsystem, and the following coupling degree and the coordination degree could be biased and misleading. While people who are familiar with the subsystems may have subjective perceptions regarding which regions are more developed, there is no established ground truth for validation. While in this paper we focus on the coupling and coordination of technological innovation and financial development, the issue identified above is applicable to all similar studies. Hence, the impact of the issue is wider than the specific scope of our current study. The goal of this study is to explore the feasibility of establishing an objective evaluation method on the quality of the models for the subsystems via the regression and projection performance of the coordination degree between the subsystems. The hypothesis is that if the set of predictors defined is an accurate model for each subsystem, then the intrinsic interaction between the subsystems may be reliably estimated via regression. This would lead to small regression error on the training data, and good projection performance for the near future. By performing a side-by-side comparison between our dataset \(O\) (each subsystem is modeled with 12 predictors) and a reference dataset \(R\) (each subsystem is modeled with 7 predictors), we demonstrate the feasibility of objectively evaluate alternative models. Indeed, the set of predictors that we propose lead to significantly better regression and project performance than the approach that we use as a reference. _Limitations._ Our study is the first step in establishing an objective evaluation method for the coupling and coordination studies of two or more subsystems. Due to the limited time and resources, we only compare our model with one reference system. Ideally, we should compare with all related studies, which would make the result much more compelling. Furthermore, we present a qualitative comparison. It is desirable to develop a systematic quantitative evaluation method where one or more metrics are defined. Additionally, the scope could be extended beyond regions in China to other developing countries, provided that the data are available. We also acknowledge that the selection of 12 predictors for each subsystem is quite subjective. How to determine what predictors to use to fully describe the subsystem is still an open research issue. Furthermore, assessment on the potential redundancy and multicollinearity of the predictors is also desirable. Unfortunately, in the context of financial development, it is unclear how to perform the assessment due to the lack of ground truth regarding the degree of coupling and the degree of coordination. The current study is limited in its analysis of the relationship between the development levels of two subsystems.