# Effect of Mix Proportion Parameters on Behaviors of Basalt Fiber RPC Based on Box-Behnken Model
## 3 Results and Discussion  
### Establishment and Verification of Response Surface Model  
The response surface model was established by using a multiple regression analysis method in the Design Expert 8(r) software. The accuracy of the regression model and the significance of influencing factors were tested by an analysis of variance (ANOVA). Statistical parameters were used to verify the accuracy of the model, the specific parameters are shown in Table 7. For data with non-normal distribution of response variables, the Box-Cox transformation method was adopted to determine the optimal transformation mode for dependent variables, as shown in Table 7[29]. \(R^{2}\) is the coefficient of determination whose value can judge the degree of model fitting. The closer that \(R^{2}\) value approaches 1, the better the model fitting degree will be. The \(R\) values of the three response models in this study are all above 0.85, indicating a good correlation between model predictions and measurement data. The \(F\) value represents the ratio of mean square and residual mean square, which can test whether the variance is due to the model or noise [30]. As shown in Table 7, \(F\) values of the three models were 26.3, 19.32 and 14.83, respectively, indicating that all three models were significant. The \(p\) value is the probability value that is associated with the \(F\) value, which is used to test whether the result of \(F\) value is statistically significant. Small probabilities (\(p<0.05\)) indicate that there is a significant model effect, large values (\(p>0.1\)) suggest no significant effect [31]. It can be seen from Table 3 that the \(p\) values of models were all less than 0.05, which proved that the model had statistical significance. In the process of modeling, non-significant variables were judged and removed from the model according to the \(p\) value. In these models, \(A\), \(B\), \(D\), \(AD\) and \(BD\) were significant model terms of fluidity (\(R1\)); \(A\), \(B\), \(C\), \(D\), \(CD\), \(C^{2}\) and \(D^{2}\) were significant model terms of the flexural strength (\(R2\)); \(A\), \(B\), \(C\), \(D\), \(AD\), \(BC\), \(BD\) and \(CD\) were significant model terms of the compressive strength (\(R3\)). In addition, lack of fit can further measure how well the model fits the data. Strong lack of fit (\(p<0.05\)) indicates that the model does not fit the data well. It is desirable to have non-significant lack of fit (\(p>0.1\)). As shown in Table 7, the \(p\) values of lack of fit in the three models were all greater than 0.1 and implied the lack of fit was not significant relative to the pure error. In other words, the established models could well reflect the relationship between experimental variables and response values. The final equations were developed in terms of actual factors for the fluidity (\(R1\), cm), flexural strength (\(R2\), MPa) and compressive strength (\(R3\), MPa) as follows:  
\[R1=6.75-48.67\cdot A+336.67\cdot B-3.58\cdot D+127.5\cdot A\cdot D+675\cdot B\cdot D \tag{3}\]  
\[\text{Ln }(R2)=4.14-0.166\cdot A-4.3\cdot B-1.007\cdot C-0.61\cdot D-6.6\cdot C \cdot D+7.21\cdot C^{2}+2.728\cdot D^{2} \tag{4}\]  
\[(R3)^{2}=774.04-38373.37\cdot A+173679\cdot B+161764\cdot C+23425.17\cdot D+1253 13\cdot A\cdot D- \tag{5}\]  
\[520259\cdot B\cdot C-505066\cdot B\cdot D-198720\cdot C\cdot D\]  
In order to further verify the accuracy of the models, the statistical parameters of data were analyzed, and the predicted-to-measured values were compared. The ANOVA results of the models are shown in Table 8. The square root of the residual mean square (std. dev. ), which is often referred to as RMSE that means the root mean square of point error between the predicted values and measured values. The coefficient of variation is the error expressed as a percentage of the mean. It is determined by Equation (4). The repeatability of the models is good when the coefficient of variation is less than 10%.