*4.3. Determination of Regression Coefficient of W–K1 Relation Model*

It can be seen from Equation (3) that the key is to determine the regression coefficients *C* and *D*, whether it is to determine the coal seam gas content *W* through the drilling cuttings gas desorption index *K*<sup>1</sup> or to determine *K*<sup>1</sup> through *W*. Although the regression coefficients *C* and *D* of the *W*–*K*<sup>1</sup> relationship model of a specific sampling site in a coal mine can be obtained through the laboratory, combined with the measured data of the underground site, this is the result based on a large amount of experimental data such as 11 gas basic parameters and coal quality indexes measured in the laboratory and the measured coal seam gas pressure and drill cuttings gas desorption index *K*<sup>1</sup> in the coal mine. The determination of these parameters is heavy, long cycle, high cost and low efficiency. For the coal mines in the Hancheng area, only by finding out the universal law of the regression coefficients *C* and *D* in the *W*–*K*<sup>1</sup> relationship model and establishing a regression coefficient relationship model suitable for the area can the coal seam gas content be predicted quickly and accurately, and a simple and easy method for predicting the coal seam gas content in the Hancheng area is provided.

Taking 24 coal samples from 5 coal mines in the Hancheng area as samples, 24 regression coefficients *C* and 24 regression coefficients *D* (as shown in Table 2) obtained by the *W*–*K*<sup>1</sup> relationship model are taken as dependent variables, respectively. *Mad*, *Aad*, *Vdaf*, *TRD*, *ARD*, *k*, *Q*, *a*, *b*, Δ*p*, *f* and another 11 gas basic parameters and coal quality indexes corresponding to coal samples are used as independent variables. The SPSS data analysis software is used. The stepwise multiple linear regression method is used for statistical analysis. According to the order of input parameters, 11 independent variables are introduced into the regression formula one by one. The regression results show that for the dependent variable *C*, after eliminating the seven parameters that cannot have a significant impact, the final model introduces four parameters *a*, *ARD*, Δ*p* and *f*. Similarly, for the dependent variable *D*, after eliminating the nine parameters that cannot have a significant impact, the final model introduces two parameters such as Δ*p* and *Q*. Through SPSS data analysis, the multiple linear regression model of regression coefficients *C* and *D* in the *W*–*K*<sup>1</sup> relationship model is:

$$C = 11.031 + 0.148a + 0.084 \Delta p - 7.919 ARD + 2.263f \tag{4}$$

$$D = 4.724 - 0.339 \Delta p + 4.725 Q \tag{5}$$
