# The Influence of Metro Tunnel Construction Parameters on the Settlement of Surrounding Buildings
## 1 Introduction
The authors noted that the maximum surface settlement is located above the axis of the tunnel, and when the support pressure exceeds 300 kPa, a surface uplift is observed. It should also be noted that in the work of [PERSON] [6], as in many others [1, 7, 8, 11, 15, 16], the influence of distance (r) on settlement is observed. In other words, the maximum settlement occurs above the axis of the tunnel. In the studies [17, 18], the authors use methods of artificial intelligence, which are based on applied statistics, to investigate the tunnelling rate, which is an indicator of construction efficiency. In scientific research, various regression models are used to identify the relationship between variables and determine the variables that have the greatest impact on the parameter. The main purpose of regression analysis is to find a model that most accurately explains the relationship between one or more predictors (independent variables) and a response (dependent variable). The fundamental factor for choosing a model in this study was the assumed nature of the relationship between the response and the predictors. It is assumed that forecasting precipitation and its relationship with predictors is described by a linear dependence and is not exponential or exponential. Multiple linear regression is presented in Equation (1) and is the most common type of regression [19]. The model is an equation of a straight line that best fits the data:  
\[\text{y}=\text{b}_{0}+\text{b}_{1}\cdot\text{x}_{1}+\text{b}_{2}\cdot\text{x}_ {2}+\text{b}_{3}\cdot\text{x}_{3}+\ldots+\text{b}_{n}\cdot\text{x}_{n}+\epsilon, \tag{1}\]  
here y is the the dependent variable; b\({}_{0}\), b\({}_{1}\), b\({}_{2}\), b\({}_{3}\), and b\({}_{n}\) are the regression coefficients; x\({}_{1}\), x\({}_{2}\), x\({}_{3}\), and x\({}_{n}\) are the independent variables; and \(\epsilon\) is the random variable (the unexplained part of the response value). To evaluate the quality of the regression model, there are several methods that need to be used together to check the adequacy of the model. One of the methods commonly used to assess the adequacy of the model is the coefficient of determination (R\({}^{2}\)), which indicates the proportion of the variance in the dependent variable that is explained by the independent variables [20]. This coefficient ranges from 0 to 1. The higher the value, the better the quality of the model. However, a high coefficient of determination does not always correspond to a strong relationship between the variables. A value close to 1 may be due to a pronounced trend that is not causally related [21]. The linear relationship between the independent parameters of the multiple regression model is called multicollinearity and is characterized by high correlation dependence [22]. Some consequences of this relationship between explanatory parameters can complicate the analysis of results, as it is not always possible to unambiguously determine the contribution of each independent parameter, leading to incorrect determination of the coefficient of regression, etc. [22]. Thus, when analyzing the adequacy of the model, it is necessary to consider the possible influence of this phenomenon on the results and try to prevent it through known methods, such as excluding the correlated parameter from the model or increasing the sample size [22]. The significance of the entire equation can be assessed using the [PERSON]'s F-test, which examines whether the hypothesis is different from zero by comparing the actual F-value to the critical F-value [23]. Additionally, the significance of each parameter individually can be determined using the \(p\)-value criterion, which is assessed similarly to the F-criterion [24]. Another tool for assessing the influence of regression model parameters on the independent variable can be an analysis of the coefficients b\({}_{1}\), b\({}_{2}\), b\({}_{3}\),..., b\({}_{n}\) obtained from the results of the analysis of variance.