Geographically weighted regression (GWR) is an effective method for detecting spatial non-stationary features based on the hypothesis of proximity correlation. In reality, especially in the social and economic fields, research objects not only have spatial non-stationary characteristics, but also spatial discrete heterogeneity characteristics. Therefore, how to improve the accuracy of GWR estimation in this case is worth studying. In this paper, a regionally geographically weighted regression (RGWR) is proposed. Using incoming dummy variables, the zoning discrimination is added to the spatial kernel function of GWR, the spatial kernel function is modified, the spatial weight is optimized, and the influence of “near heterogeneous” observation points is reduced. In this paper, the residential sale price in Wuhan City is taken as an example in the analysis of three aspects: model performance, fitting effect and influencing factors. The results show that the introduction of a zoning dummy variables can significantly improve the model accuracy of a fixed bandwidth and adaptive bandwidth. Under a fixed bandwidth, compared with the GWR model, RGWR increases R2 and R2adj from 0.6776 and 0.6732 to 0.777 and 0.7746, respectively, and the Akaike information criterion, corrected (AICc) standard decreases by 37.4006 compared with GWR, which proves the effectiveness of the method.

In this paper, a sound quality subjective evaluation method for the high-speed train compartments using semantic scoring method with equal even intervals is proposed. The acoustic metrics in the compartment was studied at different positions and under different operating conditions, and two subjective evaluation experiments using selected sound samples were carried out. The least square method was used to point-fit the sound pressure level values of the original signal, so as to select the appropriate short-term intercepting samples. To avoid the unclear distinction between samples evaluated with the unit interval scoring table, a novel evaluation method that equals even interval semantic scoring method was designed by increasing the interval between adjacent scoring numbers in the scoring table. The results show that the proposed method distinguishes the perceived auditory differences between samples more clearly compared with the unit interval semantic scoring table. And the correlation of the evaluation results obtained by using the equal even interval scoring method between participants is also higher, so the proposed method is suitable for evaluating the sound quality of the interior high-speed train compartments. Psychoacoustic attribute metrics such as loudness, roughness, and sharpness were calculated for the various samples, and loudness was found to have a strong correlation with the subjective evaluation results obtained using the proposed equal even interval method. This further verifies that, compared with unit interval scoring, the proposed method facilitates the sound quality evaluation of the interior high-speed train compartments.

Spatial heterogeneity analysis of housing prices, in general, is crucial for maintaining high-quality economic development in China, especially in the post-COVID-19 pandemic context. Previous studies have attempted to explain the associated geographical evolution by studying the spatial non-stationary continuous heterogeneity; however, they ignored the spatial discrete heterogeneity caused by natural or policy factors, such as education, economy, and population. Therefore, in this study, we take Beijing as an example and consider educational factors in order to propose an improved local regression algorithm called the regionally geographically weighted regression affected by education (E-RGWR), which can effectively address spatial non-stationary discrete heterogeneity caused by education factors. Our empirical study indicates that the R2 and R2adj values of E-RGWR are 0.8644 and 0.8642, which are 10.98% and 11.01% higher than those of GWR, and 3.26% and 3.27% higher than those of RGWR, respectively. In addition, through an analysis of related variables, the quantitative impacts of greening rate, distance to market, distance to hospitals. and construction time on housing prices in Beijing are found to present significant spatial discrete heterogeneity, and a positive relationship between school districts and housing prices was also observed. The obtained evaluation results indicate that E-RGWR can explain the spatial instability of housing prices in Beijing and the spatial discrete heterogeneity caused by education factors. Finally, based on the estimation results of the E-RGWR model, regarding housing prices in Beijing, we analyze the relationships between enrollment policy, real estate sales policy, and housing prices, E-RGWR can provide policy makers with more refined evidence to understand the nature of the centralized change relationship of Beijing’s housing price data in a well-defined manner. The government should not only carry out macro-control, but also implement precise policies for different regions, refine social governance, promote education equity, and boost the economy.