3.4.3. Geographical Detector

The spatial differentiation of tourism's carbon emission efficiency (TCEE) and the tourism economy's high-quality symbiotic development (TEHQD) in the Yellow River Basin is explored by using geographic detectors [56]. The driving factors behind it were revealed, and the interactive mechanism of the two was explored.

Factor detection was used to analyze the spatial differentiation of dependent variable *Y* and the explanatory power of independent variable *Xi* to the dependent variable, which is measured by the *q* value and expressed as follows:

$$q = 1 - \frac{1}{N\sigma} \sum\_{h=1}^{L} N\_h \sigma\_h^2 = 1 - \frac{SSW}{SST}, \text{ } SSW = \sum\_{h=1}^{L} N\_h \sigma\_{h\prime}^2, \text{} ST = N\sigma^2 \tag{11}$$

where *q* represents the explanatory power of the influencing factor *Xi*, *q* ∈ [0, 1]. The larger the *q* value is, the stronger the explanatory power of the independent variable *X* to attribute *Y* is, and vice versa. *N* is the total number of provincial units, and *Nh* is the total number of units in the province of the layer *h* divided by the variable factor. *σ*<sup>2</sup> is the total variance of *Y* value, and *σ*<sup>2</sup> *<sup>h</sup>* is the variance of the *h* layer. *SSW* and *SST* are the sum of variances and total variances within layers, respectively.
