In industrial economy, the main factors influencing the urban construction and development of social economy is linked to the highspeed rail site accessibility, and this has its influence on the regional economy as a whole, and as an example, this can be explained through the study using a multiple linear regression equation model, built and compared before and after 2 years of data and information. Based on the weighted average travel time and economic potential, it is clear that the construction of urban expressway can help accelerate the aggregation and flow of production factors within the region, to guide the integrated development of local society and economy.
Keywords
 multiple linear regression
 industrial economy
 social economy
 The highway
AMS 2010 codes
 76U05
Combined with the analysis of the operation process shown in Figure 1, it can be seen that from the perspective of a linear model with one variable, the index Y studied is a random variable with many factors affecting this. Assuming that the index Y is a Qelement random vector, then there are p factors affecting the index. At the same time, the conditional mathematical expectation of the index meets the linear relationship with these factors. Therefore, the relationship between the index vector Y and the factors can be studied by using the following multivariate linearity [1].
Based on clarifying the sample size, the degree of freedom will inevitably be reduced if the explanatory variables are added. Therefore, the sum of squares of residuals and the sum of squares of total deviations should be divided by the corresponding degrees of freedom respectively during the adjustment, to exclude the influence of variables on the degree of good fit. The specific equation is [5]:
The two are respectively:
The actual ANOVA table is as follows:
Analysis of variance table
Sources of variation  Sum of squares  Degrees of freedom  The variance 

Regression model 

k 

Due to the remaining  n–k–1  
Total variable 

n–1 

Fifth, the ttest. The significant overall linear relationship of the equation does not mean that all explanatory variables are significant to the explained variables. Therefore, all explanatory variables should be tested to determine whether they should be retained in the model. The ttest is required to carry out the testing work.
Because
This content is generally the use of a certain mode of transportation, in the appropriate conditions to achieve people clearly requested a destination of a space transfer ability. By analysing the accessibility levels of different regions and thinking from the perspectives of economic and spatial dimensions, the differences in various aspects of the regions can be presented intuitively.
The influence of highspeed railway on the regional economy is mainly reflected in fully mobilising the growth rate of the regional economy and triggering the transformation and upgrading of the region. From the Angle of practice, the economic increase will inevitably bring more opportunities for the local development, and can increase the internal product production quantity and demand of labour, and industrial upgrading can rapid optimisation of various elements of the local, such as information, capital and technology, and the content of social and economic development also has a positive effect [7].
In this paper, weighted average travel time and economic potential are used to study and analyse the impact of highspeed rail on the social and economic development of the region.
On the one hand, weighted average travel time. This index is mainly used to evaluate the time measurement of a node city to another destination. The level of this value will directly define the accessibility of a node and its close relationship with the economic centre. In the context of rising index scores, it is proved that the accessibility and regional connection of the region are very low, whereas the opposite is very high. The specific expression formula is as follows:
On the other hand, economic potential. In many cases, this index is determined according to the economic level of the node city. The node with a higher score indicates that the potential of the node is very large; otherwise, it indicates that the development potential of the city is too low. In the research and analysis, Newton’s universal gravitation model should be used for operation, and the specific formula is as follows:
Where, Pi represents the economic potential value of node I, Cij represents the time required from node I to economic centre j, and α represents the friction coefficient, which can generally be regarded as 1.
To facilitate the research, this paper collected and sorted out the numerical changes of a place in the 2 years before and after the opening of highspeed rail, and conducted correlation analysis from the weighted average travel time and economic potential between major counties and cities. The cities in this region have four highspeed railway lines, namely 1, 2, 3 and 4, with A total distance of 1,000 km, and 10 important stations are designed along the border, including A, B, C and D, with an average speed of 230 km.
After the completion of the construction of a highspeed railway, the most obvious thing about the city is that the travel time between nodes is becoming less and less. Combined with the comparative analysis in Table 2 below, we can see that:
Comparison of running time before and after construction of highspeed railway
Section  Before the construction of highspeed rail  After the construction of the highspeed rail 

A—B  2 h and 9 min  45 points 
A—C  1 h and 08 min  41 points 
B—C  2 h and 30 min  1 h and 3 min 
A—D  30 per minute  14 points 
The construction of a highspeed railway reduces the urban transportation time, and at the same time effectively controls the cost, increases the speed of the flow of people and information, and speeds up the flow of various elements between each node city.
Combined with the calculation formula analysis of the above weighted average travel time index, the time values of each city are shown in Table 3 below:
Weighted average travel time rating table
City  Before the construction of highspeed rail  After the construction of the highspeed rail  Growth probability% 

A  119.35  43.76  36.67 
B  121.36  62.00  51.08 
C  91.84  32.06  34.90 
D  117.79  45.79  38.20 
Combined with the analysis results in the table above, the index scores of each region increase rapidly, and the accessibility growth rate of cities along the highspeed railway can exceed 30% or more. In this process, highspeed rail will surely accelerate the pace of local economic development and promote economic cooperation and exchanges between regions.
Combined with the above calculation formula analysis of economic potential, the following results can be obtained as shown in Table 4:
Economic potential index analysis results
City  Before the construction of highspeed rail  After the construction of the highspeed rail  Growth probability 

A  21.07  96.13  4.56 
B  25.98  112.63  4.34 
C  27.19  192.26  7.07 
D  24.00  168.33  7.01 
Combined with the analysis results in the above table, the growth rate of indicators in all regions after the construction of a highspeed railway is > four times, and the average growth value increases by 5.77 times. This proves that the construction of highspeed rail has a great impact on the accessibility of surrounding cities.
The construction of a highspeed railway can further optimise the local economic environment and allocate local resources, to promote the flow of local factors, improve the wage level, labour production efficiency and service level of surrounding cities, and thus accelerate the level of economic development of the region.
According to the above build by multiple linear regression model analysis, and the weighted average travel time index and economic potential index, operation of highspeed railway construction inevitably can optimise the local traffic level, and improve accessibility in region, prompting the city economic integration development, and accelerate the flow of factors of production. Take Land A as an example. As the economic centre of urban construction and development, the capital and technological advantages contained in it will inevitably be transferred to regions with rich resources and low prices. At this time, regions with too low economic development levels can obtain more economic benefits based on the rapid flow of production factors [8].
In addition, after the completion of highspeed railway construction, various production factors, such as capital, technology and human resources, will continue to flow in the region, which will also promote the accumulation of talents and funds in the region, to accelerate the improvement of social and economic development level.
In the process of industrial structure adjustment and economic development, the construction of a highspeed railway has increased the opportunities for exchanges between talents and industries, and can rapidly expand the development scope of the tertiary industry, thus promoting the upgrading and adjustment of industrial structure. At the same time, the continuous flow of production factors can also help the steady development of modern emerging industries, thus improving the actual service level. For example, based on accelerating the development of the secondary industry, A also drives the development of the tourism and service industry. In this process, the construction of a highspeed railway can help the unreasonable industrial structure in the region to optimise and improve comprehensively.
The emergence of highspeed rail has reduced the distance between different regions and promoted the integration of urban construction across the country. In the context of the new era, regional integration refers to the proximity of regions from a geographical point of view and requires multiple cooperation and exchanges between regions to achieve common development goals, and finally constitutes a development process that integrates various elements of each other. According to the analysis of research results proposed by U. Blum et al., highspeed railway construction will optimise the urban market structure and organisation, drive the economic development of the station cities, comprehensively improve the local labour productivity and promote the economic development level of residents based on showing its own construction advantages. From a practical point of view, the goal of integrated development is to promote communication and cooperation between cities, give full play to their own advantages, solve problems existing in each other’s development, and finally achieve the development goal of common progress.
According to the analysis results of this paper, the cooperation and communication between the economic development of central cities and surrounding cities can accelerate the flow of talents, technology and other elements by building a good cooperative relationship based on deepening mutual connection. For A city like A, which has A very high level of economic development, it has A lot of development opportunities, and the construction of a highspeed railway will certainly bring obvious influence on the development of other elements. For cities with weak development levels, the opening and construction of a highspeed railway can also give full play to this radiation effect, to provide more impetus for the optimisation of local industrial structure.
To sum up, based on the multiple linear regression equation to study the effect of the industrial economy on the social economy, the article mainly in somewhere of the highspeed rail, for example, before and after construction are obtained by calculation equation and economic potential of the weighted average travel time index, and then from the specific changes of practice development, analysis of the various elements of city construction and development around the change. The trend of economic integration based on transportation networks has not only increased the original highspeed railway distance to 2,500 kilometres, accounting for 15% of the national total but also further clarified the influence of the industrial economy on the local social and economic development process. In this process, the urban highspeed rail network constructed by the current urban development can not only fully show the advantages of various industrial elements, improve the actual economic development level, but also lay a foundation for the coordinated economic development of various cities in the external communication and communication [9,10].
Analysis of variance table
Sources of variation  Sum of squares  Degrees of freedom  The variance 

Regression model 

k 

Due to the remaining  n–k–1  
Total variable 

n–1 

Weighted average travel time rating table
City  Before the construction of highspeed rail  After the construction of the highspeed rail  Growth probability% 

A  119.35  43.76  36.67 
B  121.36  62.00  51.08 
C  91.84  32.06  34.90 
D  117.79  45.79  38.20 
Economic potential index analysis results
City  Before the construction of highspeed rail  After the construction of the highspeed rail  Growth probability 

A  21.07  96.13  4.56 
B  25.98  112.63  4.34 
C  27.19  192.26  7.07 
D  24.00  168.33  7.01 
Comparison of running time before and after construction of highspeed railway
Section  Before the construction of highspeed rail  After the construction of the highspeed rail 

A—B  2 h and 9 min  45 points 
A—C  1 h and 08 min  41 points 
B—C  2 h and 30 min  1 h and 3 min 
A—D  30 per minute  14 points 
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