## 4 Model Performance Analysis  
### Variables Importance Analysis  
In constructing a regression analysis or machine learning supervised model, selecting variables that are highly correlated with target variables can prevent overfitting and reduce computation time.  
The Pearson correlation is a method to analyze whether there is a linear relationship between response variables and input variables. In data mining, [PERSON]'s correlation is used to remove variables when the squared value is less than 0.005. However, there is a disadvantage in that only linear relationships can be identified. Recursive feature elimination with cross validation (RFE) is typically used for curvilinear or nonlinear relationships. In this work, we used RF-based regression analysis. In order to better predict 36-month cumulative production, rankings can be intuitively identified. The variables importance analysis method (VIM) is a critical output of the machine learning algorithm. For each variable in the matrix, it tells you how important that variable is in classifying the data. Generally, the plot shows each variable on the y-axis, and their importance on the x-axis. They are ordered top-to-bottom as most to least important. Therefore, the most important variables are at the top, and an estimate of their importance is given by the position of the dot on the x-axis. One should use the most important variables, as determined from the variable importance plot, in the principle component analysis (PCA), canonical discriminant analysis (CDA), or other analyses. Typically, you should look for a large break between variables to decide how many important variables to choose. This is an important tool for reducing the number of variables for other data analysis techniques, but you should be careful not to have either too few or too many variables.  
In a regression tree analysis, RF uses %IncMSE and IncNodePurity to rank variable importance. %IncMSE is simply the average increase in squared residuals of the test set when variables are randomly permuted. When removing or adding a variable, if there is little change in the model, it is a importance. IncNodePurity is the increase in homogeneity in the data partitions.  
Figure 7: Workflow of productivity forecasting development model for shale gas reservoirs.  
The initial input features consisted of 18 independent variables. To perform input features ranking and finding variables importance, VIM based on random forest regression was used. Figure 8 demonstrates the results of input features ranking created by VIM (based on RF). The selected variables were mostly consistent with the findings in literature. According to the above results, both cases (VIM %IncMSE or IncNodePurity), for example, slick water, peak BOE, tubing head pressure, true vertical depth, lateral length, proppant volume, and initial production rate, correlate high enough for a 36-month cumulative production of shale reservoirs. As mentioned above, the results indicate that Qi_3M, Slickwater, and PeakBOE are three important variables, in which these variables account for over 50% of the importance of other variables and should be selected as the main variables when using this development model.