Standard deviation ellipse.

The coordinated development of urban quality and technology innovation is an important element of China’s technology innovation development strategy in the new era. Based on entropy TOPSIS, coupling coordination models, the gravity center and standard deviation ellipse method, the geographic probe, the GWR, and other methods, we explore the spatial variation and influencing factors of the coupling coordination relationship between urban quality and technology innovation in the Guangdong-Hong Kong-Macao Greater Bay Area from 2011 to 2020. It is found that: (1) the spatial distribution of the coupling coordination shows a characteristic of "high in the middle and low in the surroundings," and (2) the level of benign interaction in the central region is becoming more prominent. The center of gravity of coupling coordination moves toward the northeast, and the standard deviation ellipse shows a contraction trend away from the southwest. (3) Agglomeration capacity, human capital, cultural development, and infrastructure can significantly drive the improvement of the coupling coordination of urban quality and technology innovation, and the two-factor influence is significantly increased after the interaction. (4) The feedback effects of the coupling and coordination states of different cities on each factor have significant spatial differences and show the characteristics of hierarchical band distribution.