Correlation analysis is to judge whether two factors are related according to whether the correlation coefficient between one factor (variable) and another factor (variable) is greater than the critical value. Among the related factors, the close relationship between the two factors is judged according to the size of the correlation coefficient. The greater the correlation coefficient, the closer the relationship between the two factors (He, 2002). This method can have a general understanding of the problem as a whole, but it is difficult to grasp the essence of the phenomenon in the complicated relationship, find out which are the main factors and which are the secondary factors, and sometimes even draw wrong conclusions. Therefore, this paper puts forward the method of combining mathematical partial correlation analysis with stepwise regression to solve this kind of problem.

The basic principle of partial correlation analysis is that if multiple factors affect one factor, then when analyzing the influence of one factor, all other factors are limited to a certain level, and the influence of this factor on one factor is analyzed separately, so as to exclude the interference caused by other factors. For example, when analyzing the influence of compaction (or buried depth) on porosity and permeability, the compaction is discussed separately by limiting the rock composition, grain size and cementation type within a certain range, and mathematical partial correlation analysis is precisely the method to solve this kind of problem, and the magnitude of partial correlation coefficient represents the degree of this influence. Combined with the stepwise regression analysis method of multi-factor introduction and elimination, we can also eliminate the mutual interference between multiple factors (independent variables) and the repeated influence of multiple factors on dependent variables, retain useful information, select the factors that have significant influence on dependent variables, and eliminate some secondary factors. The standard regression coefficient and partial regression sum of squares of the selected principal factor reflect the influence of each parameter on the dependent variable (fullness). Therefore, according to the partial correlation coefficient between each factor (independent variable) and the dependent variable, combined with the sum of squares of standard regression coefficient and partial regression, the influence of each factor on the dependent variable can be quantitatively sorted. The basic steps are as follows:

The first step is to find out all the factors (or parameters) that may affect the dependent variable, and at the same time quantify some non-numerical parameters;

Step 2, calculate the simple correlation coefficient between the dependent variable and each parameter, and preliminarily analyze the simple correlation relationship between them and the dependent variable according to the size of these simple correlation coefficients;

Step 3, calculate the partial correlation coefficient, standard regression coefficient and partial regression square sum between the dependent variable and each parameter;

The fourth step, according to the size of partial correlation coefficient, combined with the sum of squares of standard regression coefficient and partial regression, comprehensively analyze the close relationship between dependent variables and parameters. The greater the value, the closer the relationship and the greater the influence, and vice versa.