## 3 Results
### Steel Materials  
The results of evaluating adequate equations for steel materials are listed in Table 5.  
\begin{table}
\begin{tabular}{l l l l l l l} \hline \hline \multirow{2}{*}{**Source**} & \multirow{2}{*}{**Reported**} & \multicolumn{2}{c}{**Contour**} & \multirow{2}{*}{**Acquate**} & \multirow{2}{*}{**Normality**} & **Constant** & **Influential** \\  & & **Equations** & **Response** & **Equations** & **Test** & **Variance** & **Data** \\  & & **Plot** & & & **Test** & **Points** \\ \hline \multirow{4}{*}{[PERSON]} & \(\text{y}_{\text{SR}}=\text{f}(x_{2},x_{3},x_{2}x_{3},\) & & \(y_{\text{SR}}=\text{f}(x_{2},x_{3},x_{1}x_{2},\) & & & \\  & \(x_{3}^{2})\) & Curve & \(x_{2}x_{3},\)\({x_{3}}^{2})\) & Passed & Passed & 7, 12, 13 \\ \cline{1-1}  
[PERSON] et al. [28] investigated the performance of coated carbide tools using a CCD design. The influencing variables were \(x_{1}\), cutting speed; \(x_{2}\), feed; and \(x_{3}\), side cutting edge angle (SCEA), and the responses were \(y_{Ra}\), surface roughness (Ra), and \(y_{Fc}\), tangential force (Fc). The regression procedure was introduced in detail, and the backward elimination procedure was used. The model assessment criteria included R\({}^{2}\), R\({}^{2}\)adj, PRESS, and lack of fit [28]. The response \(y_{Ra}\) and \(y_{Fc}\) calculations in this study are presented in Appendices A.2 and A.3. The complete regression analysis produces the appropriate model, which is consistent with the report by the authors [28]. In our study, the tests of normality and constant variance are performed. Both responses, \(y_{Ra}\) and \(y_{Fc}\), pass. For the \(y_{Ra}\) response, one influential data point (7 th) is identified. Two influential data points (12 th, 13 th) exist for the \(y_{Fc}\) response. [PERSON] et al. [29] studied the physical properties in hard turning with a cubic boron nitride (CBN) tool. The factors affecting the response were \(x_{1}\), cutting speed; \(x_{2}\), feed rate; and \(x_{3}\), depth of cut. The responses were surface roughness \(y_{Ra}\), arithmetic average of absolute roughness Ra; \(y_{\text{Rt}}\), maximum height of the profile Rt; and \(y_{3}\), average maximum height of the profile \(y_{\text{Rz}}\). The ANOVA tables of \(y_{Ra}\), \(y_{\text{Rt}}\), and \(y_{\text{Rz}}\) are presented in the literature [29]. The authors use \(p<0.05\) as a criterion and then delete all other variables for which the \(p\)-value is greater than 0.05. The coefficient of the parameters at this first calculation of variables with \(p\)-values \(<0.05\) is used to propose the final equation. The interaction of these variables is not considered. The remaining variables of their proposal equation, which consist of three responses, are presented in the published table [29]. The adequate equations evaluated and checked with the regression technique are as follows:  
\[ \begin{split} y_{Ra}=0.285-0.00841x_{1}+14.410x_{2}+0.0000215x_{1 }{}^{2}-33.681x_{2}{}^{2}-0.0128x_{1}x_{2}\\ \text{R}^{2}=0.991,\text{R}^{2}{}_{\text{adj}}=0.989,\text{s}=0.01 8,\text{PRESS}=0.0115\end{split}  \tag{22}\]  
Both tests (normality and constant variance) are passed, and two influential data points are identified (6 th and 13 th). \[ \begin{split} y_{\text{Rt}}=2.221-0.0548x_{1}+86.001x_{2}+0.0001 36x_{1}{}^{2}-208.333x_{2}{}^{2}-0.068x_{1}x_{2}\\ \text{R}^{2}=0.986,\text{R}^{2}{}_{\text{adj}}=0.982,\text{s}=0.139, \text{PRESS}=0.676\end{split}  \tag{23}\]  
Both tests (normality and constant variance) are passed, and two influential data points are found (1 st, 4 th)  
\[ \begin{split} y_{\text{Rz}}=2.994-0.0409x_{1}+40.071x_{2}+1.575x_{ 3}+0.000951x_{1}{}^{2}-78.472x_{2}{}^{2}-0.0.357x_{1}x_{2}-0.00541x_{1}x_{3}\\ \text{R}^{2}=0.993,\text{R}^{2}{}_{\text{adj}}=0.990,\text{s}=0.079, \text{PRESS}=0.220\end{split}  \tag{24}\]  
The normality test is failed (\(p=0.007\)). The constant variance test is passed. Two influential data points are found (5 th, 6 th). The \(x_{3}\) variable did not significantly affect \(y_{Ra}\) and \(y_{Rt}\).