Many economic variables are interdependent, restrictive, and influential. Finding the law of change between economic variables and influencing factors and expressing this law in mathematical expressions will bring great convenience to forecasting. A statistical analysis method that uses mathematical equations to determine the quantitative relationship between two or more variables. This is more commonly used when estimating and predicting the value of the dependent variable. The article analyzes the data on the National Bureau of Statistics website and uses the method of multiple linear regression to fit the graphs of economic indicators. Finally, the forecast data is analyzed in detail. We evaluated the modeling method of the prediction model and the credibility of the prediction data from a practical level.

#### Keywords

- Linear regression analysis
- Economic variables
- Gross regional product
- Mathematical modeling

#### MSC 2010

- 62J02

At present, the main contradictions in our society are prominently manifested as unbalanced and insufficient development. The most prominent “shortcoming” in China's economic and social development is the imbalance of regional development. We need to focus on solving the problem of uncoordinated development [1]. The purpose is to reduce the difference in China's economic development caused by regional influences and make the regional economy develop in a coordinated manner.

In recent years, many scholars have viewed China's overall economic development from different perspectives. In particular, the economic development of China's Pearl River Delta has been deeply studied. The Pearl River Delta region has also achieved rapid development. Therefore, we establish multiple regression analysis models based on the influence of different indicators on the economic development of the western region [2]. After analysis, the main factors that will have a major impact on the economic development of the western region in the new period are drawn. This provides certain development ideas for the rapid development of future economic construction in the west and China's Silk Road Economic Belt.

Regression analysis is essentially a mathematical process. It quantitatively describes the correlation between variables through mathematical expressions between variables. The mathematical model is:

The formula (1) represents a typical

Since the actual observation value of the dependent variable ^{*}) is called residual dispersion, and
_{yy}

There is an intermediate-term
_{yy}

Since _{yy}

Null hypothesis _{0} : _{1} :

The _{i}

We select the calculation formula of the test statistic as

We use per capita GDP (yuan) Y as an explanatory variable to analyze the factors affecting the economic development of the western region. In this way, reasonable suggestions are made for the future economic development of the western region [6].

This article uses the economic development data of the western region from 2016 to 2021 as a sample. At the same time, we use the method of empirical analysis to identify the factors that affect the gross regional product. Establish multiple linear regression models and use SPSS software for analysis [7]. Table 1 shows the original data of the explanatory variables and the explanatory variables. Analysis of the data in Table 1 shows that the western region's economy has developed rapidly during the six years from 2016 to 2021. Per capita GDP has continued to grow with an average annual growth rate of around 3,000 yuan.

Western Economic Development Indicators (Unit: 100 million yuan)

Years | 2016 | 2017 | 2018 | 2019 | 2020 | 2021 |
---|---|---|---|---|---|---|

GDP per capita (yuan) | 30211 | 33865 | 36702 | 38369 | 40773 | 43922 |

Added value of primary industry (100 million yuan) | 888.74 | 921.67 | 960.8 | 1017.49 | 1119.28 | 1172.86 |

Added value of the secondary industry (100 million yuan) | 1867.59 | 2181.74 | 2447.25 | 2490.43 | 2584.25 | 2674.7 |

Added value of tertiary industry (100 million yuan) | 1917.84 | 2180.54 | 2357.82 | 2553.32 | 2770.85 | 3174.84 |

Port cargo throughput (100 million yuan) | 21087 | 22431 | 24640 | 26860 | 30509 | 33434 |

Investment in fixed assets (100 million yuan) | 1483.32 | 2054.77 | 2533.33 | 3120.31 | 3298.27 | 3597.47 |

Proportion of regional GDP in public budget expenditure (%) | 10.98 | 11.32 | 11.56 | 15.34 | 14.36 | 14.49 |

Proportion of urban population to permanent population (%) | 39.72 | 40.45 | 41.03 | 42.01 | 42.68 | 43.52 |

According to the selected data indicators, the per capita GDP of the western region is finally determined as the explained variable. The port cargo throughput, fixed asset investment, the proportion of public budget expenditure to total GDP, and the proportion of urban population to permanent population are multiple linear regression models with explanatory variable _{1}, _{2}, _{3}, _{4}, _{5}, _{6}, _{7}, respectively. At the same time, the linear model of variables

The article uses this to measure the closeness between variable factors. Analyze the data through the correlation analysis in SPSS statistical analysis software. From this, the correlation coefficient table is obtained and the correlation between each explanatory variable is analyzed [8]. Among them, the correlation coefficients between the four independent variables of tertiary industry added value, port cargo throughput, fixed asset investment, and the proportion of urban population to permanent population and per capita GDP are all greater than 0.9. At the same time, the probability of significant correlation is close to 0.000 and less than 0.01. Whether there is a quantitative linear relationship between GDP per capita and the four main factors that affect economic development, this is further verified by establishing an appropriate mathematical operation model. We can use the stepwise regression analysis method to perform multiple linear regression analysis on the data related to the above four variables.

Establish a model through SPSS software to perform linear regression analysis on related data. In this method, a summary table of the output data model (Table 2) is obtained through step-by-step analysis. We perform stepwise linear regression on the sample data. After analysis, a model can be fitted [9]. The adjusted R2 value is 1.000, which indicates a good fit. As a result, indicators such as the proportion of the urban population in the permanent population, the proportion of public budget expenditures in GDP, the value-added of the secondary industry, the value-added of the primary industry, and changes in port cargo throughput indicators can have a certain impact on the per capita GDP growth in the western region.

Model summary

Model | R | R party | Adjust R side | Standard estimate error |
---|---|---|---|---|

1 | 1.000a | 1 | 1.000. | . |

Table 3 is a residual statistical table showing the predicted value and residual value based on the 3σ principle. By plotting the sample data to observe the cumulative probability P-P diagram (Figure 1). The scattered points presented by the sample data from the bottom left to the top right are basically a straight line trend. It can be concluded that the sample distribution basically obeys the normal distribution.

Residual error statistics

Minimum | Maximum | Mean | Standard deviation | N | |
---|---|---|---|---|---|

Predictive value | 30222.0527 | 43921.0664 | 37307 | 4888.03521 | 6 |

Residual | −23.40751 | 25.44731 | 0 | 16.66639 | 6 |

Standard forecast | −1.449 | 1.353 | 0 | 1 | 6 |

Standard residual | −0.888 | 0.966 | 0 | 0.632 | 6 |

According to the above analysis, the regression coefficient table can be obtained (Table 4). The table mainly presents the regression coefficients of the regression model and the significance test data. From this table, the regression coefficients of the five independent variables in the model are −12.928, 3.749, 0.23, −501.736, and 4165.997 respectively. We can get the regression equation by substituting them into the linear regression model:

Regression coefficients

Model | Non-standardized coefficient | Standard coefficient | t | Sig. | |
---|---|---|---|---|---|

B | Standard error | Trial version | |||

−125757.963 | 0 | 0 | 0 | ||

(constant) | −12.928 | 0 | −0.298 | 0 | 0 |

Primary industry production value | 3.749 | 0 | 0.229 | 0 | 0 |

Secondary industry production value | 0.023 | 0 | 0.023 | 0 | 0 |

Port cargo throughput | −501.736 | 0 | −0.198 | 0 | 0 |

Public budget expenditure as a percentage of GDP | 4165.997 | 1.217 | 0 | 0 |

It can be seen from the established model that when all the explanatory variables in the model are 0, the constant term coefficient, that is, the per capita GDP of the western region is negative. The value-added of the primary industry is negatively correlated with the ratio of public budget expenditure to GDP, which is in the same direction as changes in the value-added of the secondary industry, port cargo throughput, and the ratio of urban population to permanent population [10]. When other variables remain unchanged, when the output value of the secondary industry increases by 1 unit, the average GDP per capita increases by 3.749. If other variables remain unchanged, when the port cargo throughput increases by 1 unit, the per capita GDP will increase by 0.023. It is also assumed that other variables remain unchanged. The urban population in the current year's proportion of the permanent population increased by an average of 4,165.997 per capita GDP per increase.

From the above analysis results, it can be seen that the regression model has a good degree of fit. The secondary industry value-added, port cargo throughput, the ratio of urban population to permanent population and the per capita GDP of the western region have a significant linear relationship. As the production value of the primary industry and the share of public budget expenditures in GDP increase, per capita GDP will continue to decline. Through the analysis of the comprehensive development of the western region, we can see that the government's public budget expenditure is unreasonable. But it did not promote the growth of regional GDP.

The government should make regular adjustments to public budget expenditures. Emphasis should be placed on some important, abnormal and critical differences that are not in compliance with daily norms encountered in budget execution. The purpose of this is to promote the better development of regional economic production, and to increase the income level of the people and improve the living conditions of the residents. Specifically, it can be expressed as regulating fiscal revenue and expenditure and stabilizing the relationship between the government and the market to ensure that the scale of fiscal revenue is controlled within an appropriate range [11]. At the same time, effective operation and management measures are taken to ensure that the budget goals are achieved. In this way, economic optimization can be achieved, and fiscal expenditures can be reduced, thereby effectively promoting the comprehensive, coordinated and sustainable development of the western region's economy.

In the process of the new urbanization in the new era, the traditional economic growth mode that consumes resources and destroys the environment can no longer adapt to the development of the new era. Therefore, environmental issues must be taken into consideration while developing the economy. We need to maintain a continuous innovation drive, and continue to improve science and technology to optimize the industrial structure and determine the optimal ratio of capital, labor, and resource input. We must expand investment in the construction of new-type rural urbanization, gradually promote the large-scale development of agricultural industrialization, and promote the development of a characteristic economy and a green rural economy. We need to scientifically configure the relevant infrastructure, adapt measures to local conditions, and reasonably plan the spatial layout to promote the steady development of the western economy.

While enjoying the joy of huge economic benefits brought about by newly introduced large-scale industrial projects, they must also bear the negative costs of environmental and resource consumption brought about by them. Therefore, in the process of promoting the development of the western region in the new era, advocating the integration of technological development and industry is also an indispensable part.

The proportion of public budget expenditure to GDP and the proportion of urban population to permanent population have a great impact on the per capita GDP of the western region and there is a linear relationship. For policies related to the economic development of the western region in the new period, the proportion of public budget expenditures should be adjusted to increase the investment in the transfer of rural population to urbanization.

#### Regression coefficients

Model | Non-standardized coefficient | Standard coefficient | t | Sig. | |
---|---|---|---|---|---|

B | Standard error | Trial version | |||

−125757.963 | 0 | 0 | 0 | ||

(constant) | −12.928 | 0 | −0.298 | 0 | 0 |

Primary industry production value | 3.749 | 0 | 0.229 | 0 | 0 |

Secondary industry production value | 0.023 | 0 | 0.023 | 0 | 0 |

Port cargo throughput | −501.736 | 0 | −0.198 | 0 | 0 |

Public budget expenditure as a percentage of GDP | 4165.997 | 1.217 | 0 | 0 |

#### Model summary

Model | R | R party | Adjust R side | Standard estimate error |
---|---|---|---|---|

1 | 1.000a | 1 | 1.000. | . |

#### Residual error statistics

Minimum | Maximum | Mean | Standard deviation | N | |
---|---|---|---|---|---|

Predictive value | 30222.0527 | 43921.0664 | 37307 | 4888.03521 | 6 |

Residual | −23.40751 | 25.44731 | 0 | 16.66639 | 6 |

Standard forecast | −1.449 | 1.353 | 0 | 1 | 6 |

Standard residual | −0.888 | 0.966 | 0 | 0.632 | 6 |

#### Western Economic Development Indicators (Unit: 100 million yuan)

Years | 2016 | 2017 | 2018 | 2019 | 2020 | 2021 |
---|---|---|---|---|---|---|

GDP per capita (yuan) | 30211 | 33865 | 36702 | 38369 | 40773 | 43922 |

Added value of primary industry (100 million yuan) | 888.74 | 921.67 | 960.8 | 1017.49 | 1119.28 | 1172.86 |

Added value of the secondary industry (100 million yuan) | 1867.59 | 2181.74 | 2447.25 | 2490.43 | 2584.25 | 2674.7 |

Added value of tertiary industry (100 million yuan) | 1917.84 | 2180.54 | 2357.82 | 2553.32 | 2770.85 | 3174.84 |

Port cargo throughput (100 million yuan) | 21087 | 22431 | 24640 | 26860 | 30509 | 33434 |

Investment in fixed assets (100 million yuan) | 1483.32 | 2054.77 | 2533.33 | 3120.31 | 3298.27 | 3597.47 |

Proportion of regional GDP in public budget expenditure (%) | 10.98 | 11.32 | 11.56 | 15.34 | 14.36 | 14.49 |

Proportion of urban population to permanent population (%) | 39.72 | 40.45 | 41.03 | 42.01 | 42.68 | 43.52 |

_{2} emissions, and economic growth in KSA: evidence from a non-linear ARDL model. Environmental Science and Pollution Research., 2019; 26(16): 16145–16156_{2} emissions, and economic growth in KSA: evidence from a non-linear ARDL model

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