An empirical study of the level of cultural education, national income, and the development of sporting goods manufacturing industries. For the above four test methods where the original assumptions exist for unit roots, the horizontal test results of variables LnEDU and LnSALE can reject the existence of units at a 1% significance level. The original hypothesis of the root, while the first-order difference test results can also reject the original hypothesis with unit roots at a 1% significance level, stating that the variables LnEDU and LnSALE are stationary time series. The LnPGDP's level test results cannot reject the unit root's original hypothesis at the 1% significance level, but the first-order difference test result can reject the original hypothesis including the unit root at the 1% significance level, indicating that the variable LnPGDP is The cointegration test of the first-order I3.2 panel data to verify whether there is a long-term cointegration relationship between the level of cultural education in each region, the national income level and the development of sporting goods manufacturing industry, was presented by Engle and Granger (1987). The two-step test. From the unit root test results of the panel data, we can see that the three indicator variables LnEDU, LnPGDP, and LnSALE are relatively stable time series data, so we can use the panel data to estimate the regression equation and derive the residual sequence μit. The change in educational level as an explanatory variable, the change in the development of sporting goods manufacturing as an explained variable, and the change in the level of cultural education as a result of the relative change in the level of education led to the change in the development of sporting goods manufacturing industry; Changes in the development of manufacturing are interpreted variables, and β indicates changes in the level of national income that have led to changes in the development of the bodybuilding industry. According to the residual sequence μit, the residual root sequence was tested by unit root using the above four test methods to determine whether the residual sequence was stable. If the residual sequence is a stationary series, it indicates that the long-term co-integration relationship between the level of cultural education, national income, and the development of sporting goods manufacturing is established.
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