## 4 Discussion  
CCD geographical data provided the data source for spatial regression analysis with several strengths. First, the CCD data is a consistent national dataset, despite some states data being missing. Compared to the Schools and Staffing Survey (SASS), the CCD data allow geographers to freely explore or monitor the spatial-temporal and dynamic trajectory of the association between students and teachers. Second, the CCD data are based on school and school district data across states. Multiple-dimension pupil-teacher ratio spatial distributions are beneficial to reveal different angles of teacher shortages. Most importantly, the CCD dataset is easy and sufficient to be transferred to coding-languages without software limitations. SASS data and teacher follow-up surveys are limited to statistical software such as STATA. Finally, CCD data embraces census data so that it is possible to implement education deep analysis with socio-economic and environmental comprehensive assessments, eventually generating multiple-solutions.  
ArcToolbox is an integrated and basic application developed by the Environmental Systems Research Institute (Esri). It not only provides a reference to the toolboxes to facilitate user interface in ArcGIS for accessing and organizing a collection of geoprocessing tools, models and scripts, but it also accommodates all the tools required to perform any advanced task in a particular domain [36]. It is a platform in which all the tools required to carry out advanced Geoprocessing tasks are organized in a logical way. Our developed tool was built on ArcToolbox in the context of the GIS environment. In addition to ArcToolbox strengths, it is an object-oriented approach, leading to increased portability and reusability of the tools for use [37]. Most importantly, the toolbox has characteristics of high flexibility and scalability that could be widely utilized in spatial data processing. It synthetized spatial statistic functions in one toolbox, referring to spatial visualization, machine learning of the heatmap and the random forest tree model, and spatial OLS modeling. The tool was executed, and the results were automatically displayed in ArcGIS pro. The script tools can be run in the ArcGIS interface by ordinary GIS users with the Spatial Analyst extension. In general, users can conduct the tool by accepting or modifying the default parameters to meet their demands. Since the source code and software logic is also accessible to them at  
Figure 10: Results of random forest tree regression.  
the time of software distribution, they can create new script tools by modifying the code or adding parameters into the tools to support their studies [38].  
Albeit our ArcTobox is accomplished, several limitations should be considered. First, the proposed toolset is only appliable in the context of the GIS environment, which means users are required to have open access to QGIS or a valid Spatial Analyst license of the ArcGIS pro (ArcMap) software that can run the ArcPy site package. Second, the tool is limited to Python-installed packages. In other words, users are required to install the seaborn and the sci-kit-learn of the Python package, and then clone them in the GIS environment before running the ArcToolbox. Third, Python skill is necessary. The CCD data have a long period statistic from 1986 to 2021. Each year of CCD data contains school districts and schools' records in the U.S. If users don't have Python experience, once spatial data processing is problematic, the ArcToolbox will be insignificant. At last, interface limitations inevitably exist. For instance, the format of the spatial weighted matrix is an SWM file that could not automatically be opened. It is better to use the function of converting the spatial weights matrix to the table in the Spatial Statistics toolbox. With the update of ArcGIS versions, those limitations will be gradually eliminated.