Analysis of the Correlation between Cross-Border E-Commerce and Economic Growth Based on Hierarchical Multilevel Gray Evaluation Model

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Introduction
In the recent years, the inherent relationship between the Internet and economic growth has also become one of the academic research hotspots. Compared with traditional trade distributors, the richness and optional categories have increased significantly, and the product update speed has been faster. anks to the aid of cross-border e-commerce platforms, more high-quality brands can be sold globally, forming new profit growth points and lowering trade barriers. is is undoubtedly important for the internationalization of brands, the sustainable development of enterprises, and the integration of industries into the global value chain [1][2][3][4][5][6].
Cross-border e-commerce is a new model of "Internet" + "manufacturing" + "brand" + "digitalization" + "trade," bringing new opportunities to manufacturing companies. It allows manufacturing companies to directly face foreign retailers and consumers. It has the characteristics of diversification, small batches, and less capital. It avoids the problems of large scale of traditional export trade, long transaction cycles, large capital, and information asymmetry. Cross-border e-commerce allows manufacturing companies with mature processing technology to go from behind the scenes to the world stage. Driven by information technology, it enables companies to overcome geographic and organizational boundaries and become more open, easier to collaborate, and more convenient to develop networks. Innovation, through the development of data technology, accumulation of data resources, application of data analysis, mining cross-cultural value, to meet the individual needs of consumers, with an international perspective, build a brand international operation mechanism on an international scale, and integrate domestic and foreign parties resources, promote multiparty collaboration to create brand value. erefore, it is necessary to in-depth research, quantitatively analyze the correlation between factors, clarify the driving force and bottleneck of cross-border e-commerce development, and propose effective development countermeasures [7][8][9]. e e-commerce model of export activities mainly includes product selection, cross-border payment, settlement, logistics, and data transmission. e cross-border e-commerce ecosystem is composed of multiple modules such as buyers and sellers, public service agencies, professional service agencies, and the government [10][11][12][13][14][15]. It also can be shown as Figure 1.
Informatization is produced on the basis of advanced technologies such as computer science technology, communication engineering technology, and bioengineering technology, and represents the most advanced productivity in today's society. Informatization is an important support for promoting economic development, and it has a huge boosting effect on the economic development of a region. Informatization can promote the overall progress of the regional economy. Informatization can speed up the accumulation of knowledge in the region and create room for innovation in economic development [16][17][18][19].
China has a large land and a large population, and is affected by resources and national development policies, and its economic regional characteristics are relatively obvious. In recent years, the central government has also paid special attention to the construction of informatization, so many domestic experts and scholars have conducted in-depth discussions and research on this. Teng Li made a quantitative estimation and comprehensive evaluation of the informatization level of various provinces in China. rough data analysis, Meng Yuan concluded that the deepening of informatization has had a positive impact on economic growth. Gaoxincai analyzed the contribution rate of information elements and found that there is a significant positive correlation between the level of regional informatization and the level of economic development. Meilin used the gray correlation method and linear regression model to analyze the regional economic growth level of a region to a large extent determined by the level of informatization construction. Li Ling used the unary linear regression model to conclude that the level of informatization development plays an indelible role in promoting the regional economy. It can be seen that domestic scholars pay more attention to the influence of informatization on economic growth and affirm the important role of informatization in economic and social development [20][21][22][23][24][25].
Zhang Yue et al. established an evaluation model of the influence of the Internet development level on economic development by collecting relevant data on the economic and Internet development level of various regions. Tang  Lingchao and others combined with time series data on   economic growth, conducted an empirical analysis of the  relationship between Internet development and GDP. More  scholars pay attention to the macro analysis of Internet  development and economic growth, while there is less research on the relationship between the two specific indicators. is paper uses the gray correlation model to quantitatively study the degree of correlation between the Internet development level and economic growth indicators, and calculate and analyze the degree of correlation between the indicators.
In 1982, Professor Deng Julong founded the Gray eory, a new type of decision-making discipline and divided the system into three categories: white, black, and gray.
e white system represents a system with completely transparent information, the black system is a system with completely unknown information, and the gray system is in the middle zone. Gray system theory is precisely through detailed analysis and in-depth mining of "known information" to predict and estimate "unknown information." It uses a small sample of "limited" and "poor information" to eliminate uncertainty.
On the contrary, the smaller the degree of relevance. e gray correlation degree is essentially a quantitative analysis method to describe and compare the dynamic development of the system [26][27][28][29]. e neural networks are shown in Figure 2. Cross-border e-commerce is achieved by buyers and sellers located in different zones, through the Internet information platform to achieve the information exchange and transaction of various goods or services, and through the provision of offline logistics services.

Gray Relational Model
It is a multi-index to examine the differences and relevance between the various elements of the system. We compare the sequence with the reference. When the sequence curves are similar, the two are considered to have a higher degree of correlation; otherwise, they are considered to have a lower degree of correlation, thus giving the strength and ranking of the relationship between the factors. Compared with other methods, the gray correlation analysis method requires less data volume, less sample size, and less calculation. e relative optimal value of each indicator can be used as a reference sequence to form the final comprehensive evaluation level. It can provide a basis for the determination without having to have high requirements on a large amount of practical data, which can better solve the problem that the flexible public transportation system as a new auxiliary public system does not have enough experience data to support its model parameters. In addition, the flexible public transportation system evaluation system is a comprehensive evaluation system based on passengers, bus companies, and the government. ere are many factors involved, the indicators are more complex, some indicators are related and repetitive, and the information is relatively incomplete. e difference information principle of the gray system and the nonuniqueness principle of the solution can solve this problem very well. In summary, it is believed that it is more suitable for the comprehensive evaluation of flexible public transportation systems. However, the gray correlation analysis method treats all indicators as equal to the influencing factors of the overall target and does not consider the impact of indicator weights. e evaluation value has a low credibility. Scientific methods should be used to determine the indicator weights and associate them with the degree of relevance.
e combination of coefficients increases the scientificity and validity of the evaluation results. e initial value processing of the absolute correlation degree adopts the initial point zeroing method, which mainly considers the relationship of the system development increment. Owing to the different measurement units of each factor, the greater the difference between the factors, the greater the impact on the accuracy of the result. e relative degree of relevance uses relative quantity for initial value processing, so the analysis result has nothing to do with the observed value of each factor. e comprehensive correlation degree also considers the relationship between increment and speed, which makes up for the shortcomings of the two to a certain extent.
Common weight determination methods include expert scoring method, equal-weight method, statistical test method, entropy method, and so on. e equal-weight method cannot well reflect the difference in the degree of influence of different indicators, and it is not conducive to the choice of the plan when the comprehensive evaluation value is not much different; the expert scoring method and the statistical test method are highly subjective and inapplicable. When there are many dry indicators, row and normalization method, column and inversion method, and so on, refer to the use of part of the data of the judgment matrix, and the result is not highly reliable; minimum deviation method, logarithmic regression method, and so on, use the same indicator with different schemes. It is believed that indicators with a greater degree of change convey more information and should have a higher weight. However, it is not applicable to the comprehensive-level evaluation of a single scheme of a flexible public transportation system. In this paper, the analytic hierarchy process is used to determine the weights of the various indicators of the system. It mathematicizes and organizes people's complex system thinking processes and integrates various factors of complex problems into orderly connected songs help to maintain the consistency of decisionmakers' thinking, apply to various types of complex comprehensive evaluation systems, can effectively integrate qualitative analysis and quantitative analysis, and have interchangeability and compatibility. Superior properties such as sex and symmetry are currently a common method for determining the weight of indicators.

Gray Absolute Relevance.
It mainly reflects the relationship between the absolute increment of the two-factor data series, and the model is introduced as follows: Suppose the following sequence exists: en, So the absolute degree of gray correlation is e size of the area between the two broken lines represented by the two-factor data series is the geometric meaning represented by the gray absolute correlation degree. erefore, the larger the ζ 0i , the higher the similarity of the two-factor data sequence.

Gray Relative Degree of Relevance.
e gray relative correlation degree mainly reflects the relationship between the growth rates of the two sequences. If the sequence is transformed into another kind of broken line, record the broken line: en, So the absolute degree of gray correlation is e larger the ω 0i is, the closer the change rate.

Gray Comprehensive Relevance.
Grey system theory includes gray system analysis, gray system prediction, and gray system decision-making, all of which are based on gray relational analysis. In order to more comprehensively reflect the closeness of the relationship between the two-factor data series, the average of the gray absolute correlation degree and the gray relative correlation degree is taken. e calculation of the average value mainly involves the value of the weight c, which is between 0 and 1. If the research is more concerned about the relationship between the rate changes of the twofactor data sequence, the value of c should be smaller; if the research is more concerned about the relationship between the incremental changes of the two-factor data sequence, the value of c can be larger. In this study, the value of c is 0.5. en e larger the θ, the stronger the comprehensive correlation between the two sequences. e gray relational analysis method has been widely used in solving the relationship between multiple factors. Its main steps are as follows: (1) Dimensionless processing of indicators. Use the range standardization method to nondimensionally process the data: (2) Generate the corresponding difference sequence. Calculate the absolute difference between the standardized reference data and the comparison data: Calculate the correlation coefficient and degree of correlation. Make the following transformations to the data in the corresponding difference sequence: λ ij represents the correlation coefficient and ρ is the standardized coefficient value. e degree of correlation is as follows: According to the closeness of the relationship between the main behavior factors and related behavior factors in the gray system, determine the main and secondary factors that affect the development of the gray system. e selection of the Internet development level and economic growth indicators must not only reflect the application level of Internet development but also be able to measure the accuracy and comprehensiveness of economic growth. Existing literature often uses indicators such as the number of domain names, the number of Webpages, the number of websites, and the number of Internet users when selecting or constructing indicators of the Internet development level. is study uses the number of domain names, webpages, websites, Internet users, Internet penetration rate, mobile phone penetration rate, telephone penetration rate, and year-end number of mobile phones as the Internet development indicators. For the selection of economic growth indicators, most relevant studies use per capita GDP or the national GDP level, and a small number of GDP is deflated index processing to adjust the nominal value to the actual value. In order to more fully reflect the economic growth level of each province, this study selects the total in and out of foreigninvested enterprises, foreign direct investment, the number of patent applications, the total fixed assets, and the GDP of each province as the economic growth indicator variables.

Cross-Border E-Commerce Development
Impact Factor Model e development of cross-border e-commerce is a systematic project, which is affected by the environment and is closely related to the support of the domestic policy system and the international market environment. Domestically, the home country's market system environment, economic development level, national support policies, market maturity, and cultural values all have a certain potential or direct impact on the promotion of corporate brand internationalization, and the laws of the country where the product is imported policies, culture, and competitive environment also have a significant impact on the development of corporate brand internationalization. Enterprise development, trade policies, and cross-border trade facilitation, regional integration, promotion of foreign direct investment, enterprise clusters, and national innovation systems can help promote the participation of enterprises in global value chains. e statistical idea of gray correlation analysis is to use the geometric similarity of the two-factor data sequence curve to represent the closeness of the relationship between the two factors. e higher the geometric similarity of the two-factor data sequence curve, the greater their correlation. e cross-border e-commerce ecosystem is shown in Figure 3. e development of cross-border e-commerce requires necessary regulation, support, and training. Xu Mingxia and others believe that the factors that determine the development of trade include not only the hardware environment such as geographic location, natural resources, transportation routes, and infrastructure, but also the software environment such as market maturity, industrial development, institutional advantages, and policy dividends. Zhou Fang believes that industrial input and output, technological innovation, technological environment, development policies, support, and incubation have a greater impact. Xu Jinbo has constructed a cross-border e-commerce development evaluation system that includes five dimensions: network marketing, international logistics, electronic payment, electronic customs clearance, and government policies. Yang Jianzheng and others believe that online marketing, international payments, crossborder e-commerce logistics, cargo clearance, legal protection, and so on will have a huge impact on cross-border e-commerce.
Hao Binkai summarized the four major factors, including production factors, demand conditions, and corporate behavior. Chen Nan conducted research based on the perspective of complex networks and found that government support policies can increase the enthusiasm of enterprises to participate in cross-border e-commerce, but it will show short-term characteristics. Brand managers should focus on making products traceable, empower consumers, and strengthen coordination with local authorities to control counterfeiting. Zhang Xiaodong took e-commerce logistics, economic development, social consumption, talent environment, and technological innovation. e degree of coupling and coordination of the system.
Cross-border e-commerce is a complex industry that drives a wide range of industries, involves many industries, and has many regions and countries. It is related to all levels of economic development. First, the most important influence system for the development of cross-border e-commerce is the foundation of e-commerce, including trade, e-commerce platforms, and logistics and distribution; among them, the trade dimension includes trade basic factors and trade radiation factors, and the e-commerce dimension includes e-commerce development factors, e-commerce scale factor and e-commerce penetration factor. e logistics dimension includes logistics income factor and logistics business volume factor. Second, the development of export cross-border e-commerce needs the support of the local industrial economy. A large number of cross-border e-commerce industries can only provide products suitable Journal of Mathematics for the international market and can highlight the scale effect and improve industrial efficiency; economic dimensions include economic scale factors and economic structure factor. e third is consumption power, which is directly related to the development of imported cross-border e-commerce. Only with certain consumption power can consumers have the economic basis for choosing and consuming high-quality products from all over the world; consumption dimensions include consumption income factors and consumption expenditures factor. e fourth is the driving force for the sustainable development of crossborder e-commerce, including talents and innovation. ese two factors are ultimately the core competitiveness of crossborder e-commerce to enter the international market; the talent dimension includes talent training factors and talent attraction factors. e innovation dimension includes innovation input factor, input intensity factor, and input effect factor. e constructed cross-border e-commerce development impact factor model is shown in Figure 4. Combining existing research and the specific development of China's cross-border e-commerce industry, construct a cross-border e-commerce development impact factor analysis model.

Example Analysis
In the analysis model, the 100 million yuan is chosen as a measurement indicator. e trade basis chooses the city's total import and export (100 million yuan) as the measurement index; the indicator of trade radiation is that the pilot zone drives the province's total import and export (100 million yuan). For e-commerce development, use urban e-commerce development index; e-commerce scale use urban e-commerce scale index; e-commerce penetration use urban e-commerce penetration index. e logistics income uses the city express total revenue (100 million yuan) index; the logistics business volume uses the city express business volume (100 million pieces) index. e economic scale is measured by the city's GDP (100 million yuan); the economic structure is measured by the city's tertiary industry's share of GDP (%). e number of undergraduates and graduate students (10,000) in the experimental area is selected as the indicator for talent training; the urban talent attraction index is selected as the indicator for talent attraction. e indicator of innovation investment is the total R&D investment of the corresponding province (100 million yuan); the indicator of investment intensity is the R&D investment intensity of the corresponding province (%). e predicted results based on MATLAB are shown in Figure 5, and the other results are compared in Figure 6.
Based on the gray correlation analysis model, the calculated absolute correlation, relative correlation, and comprehensive correlation. Sorted by absolute gray correlation, the top four are innovation input, logistics revenue, economic scale, and e-commerce scale, indicating that these four factors are closely related to the absolute increase in cross-border e-commerce transaction volume. According to the gray relative degree, the top four are the talent attraction of logistics business volume, logistics income, and e-commerce scale, indicating that these four factors match the absolute growth rate of cross-border e-commerce transaction volume. From a comprehensive perspective, logistics revenue, innovation investment, logistics business volume, e-commerce scale, and cross-border e-commerce development are the closest, as shown in Figure 7. e number of year-end mobile phones X2, the number of domain names X3, the number of URLs X4, the number of Webpages X5, the mobile phone penetration rate X6, the Internet penetration rate X7, and the telephone penetration rate X8. e economic growth indicators are foreign direct investment Y1, the number of patent applications Y2, the total fixed assets Y3, the total entry and exit of foreign-invested enterprises Y4, and GDP Y5. Empirical analysis has been done.
According to the aforementioned analysis steps of the gray correlation model, the gray correlation degree between the Internet development level and economic growth indicators is calculated. According to the calculation results, it can be seen that (1)

Conclusion
Selecting the annual data of 31 provinces in China in 2015, empirical analysis of the degree of correlation between the level of Internet development and economic growth indicators. According to the empirical results, the following conclusions can be drawn: foreign direct investment has the greatest correlation with the number of websites and Webpages, and the smallest correlation with the penetration rate of mobile phones and the Internet.
(1) e number of patent applications has the largest correlation with the number of domain names and URLs, and the smallest correlation with the penetration rate of mobile phones and the Internet. e total fixed assets have the greatest correlation with the number of Internet users and the number of mobile phones at the end of the year, and the smallest correlation with the number of Webpages and the penetration rate of mobile phones. (2) e total volume has the largest correlation with the number of websites and Webpages, and the smallest correlation with the penetration rate of mobile phones and the Internet. GDP has the largest correlation with the number of people surfing the Internet and the number of mobile phones at the end of the year, and the smallest correlation with the number of Webpages and the penetration rate of mobile phones. (3) Internet infrastructure and popularity have the closest relationship with economic growth, and the relationship between foreign investment and patent applications and the level of Internet development is the most significant. Cross-border e-commerce supply chain greatly affects consumer experience and corporate core capabilities. (4) A good supply chain can not only reduce operating costs but also deliver products as quickly as possible. Speed reaches the hands of consumers, so it is necessary to vigorously connect domestic and foreign logistics, unblock international logistics channels, and vigorously develop overseas warehouse business; second, enhance the R&D and design innovation capabilities of cross-border e-commerce companies and conduct in-depth research and analysis of market environment and consumer habits, and so on.

Data Availability
e data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Journal of Mathematics 9