## 3 Results
### Regression Analysis  
Regression analysis showed that the maximum width of the nasal aperture and sex form a statistically significant regression pattern (F (2, 52) = 13.39, \(p\) \(<\) 0.001), which explains a proportion of 34% (R\({}^{2}\) = 0.340) of the variance of the maximum width of the nose. We found that sex predicts 21.1% of the variance of the maximum width of the nose (R2 = 0.211, \(p\) \(<\) 0.001) and the maximum width of the nasal aperture brings a significant explanatory addition of 12.9% (R2 change = 0.129, \(p\) = 0.002). (Table 4). SEE have small values indicating that the observations are closer to the fitted line. \begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**Outcome (y)**} & **Independent** & \multirow{2}{*}{**B**} & \multirow{2}{*}{**Std. Error**} & \multirow{2}{*}{**Beta**} & \multirow{2}{*}{**R\({}^{2}\)**} & \multirow{2}{*}{**SE**} \\  & **Variables (\(\mathbf{\omega}\))** & & & & & \\ \hline \hline \multirow{9}{*}{Maximum} & Model 1 & \multirow{9}{*}{36.948 \({}^{**}\)} & \multirow{9}{*}{0.777} & \multirow{9}{*}{0.459 \({}^{**}\)} & \multirow{9}{*}{0.211 \({}^{**}\)} & \multirow{9}{*}{3.807} \\  & Sex & & & & & \\ \cline{1-1} \cline{4-7}  & Constant & & & & & \\ \cline{1-1} \cline{4-7}  & Model 2 & \multirow{9}{*}{36.948 \({}^{**}\)} & \multirow{9}{*}{1.035} & \multirow{9}{*}{0.367 \({}^{**}\)} & \multirow{9}{*}{0.3515} \\ \cline{1-1} \cline{4-7}  & nose & Sex & & & & \\ \cline{1-1} \cline{4-7}  & Maximum width of the nasal aperture & & & & & \\ \cline{1-1} \cline{4-7}  & Constant & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Regression model for maximum width of the nasal aperture and sex for maximum width of the nose. Figure 3: Differences between sexes for MAW and MNW. Within the predictive model, the most important predictor of the maximum width of the nose is the maximum width of the nasal aperture (\(\beta\) = 0.371, \(p\) = 0. 002), followed by the sex of the participant (\(\beta\) = 0.367, \(p\) = 0.003). The regression analysis showed that the maximum width of the nasal aperture statistically predicts the maximum width of the nose (F (1, 53) = 14.37, \(p\) < 0.001) and explains a proportion of 21.3% (R2 = 0.213) of the variance of the maximum width of the nose (Table 5). The regression equation with sex: maximum width of the nose = 18.22 + 0.813* maximum width of the nasal aperture + 3.115*sex, for sex: male is represented by code 1, and female by code 0. (Table 6). The simple regression equation (without sex) (Table 6):  
maximum width of the nose = 15.28 + 1.012*maximum width of the nasal aperture,  
All conditions of simple and multiple linear regression are met. Statistical analysis demonstrates the fact that the regression analysis is correct, with the homoscedasticity being present. Additionally, it can be observed that the errors are normally distributed, which means the regression equation is correct. All these prove that we can rely on both regression equations with precise results (Figure 4). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Predicted Dimension** & **Simplified Equation** & **R** & **R\({}^{2}\)** & **\
\begin{tabular}{} **\textless{}2.5 mm** \\ **Error (\%)** \\ \end{tabular} & **
\begin{tabular}{} **\textless{}5 mm** \\ **Error (\%)** \\ \end{tabular} \\ \hline
1. MNW (mm) & 15.28 + 1.012 * MAW & 0.462 ** & 0.213 & 98.18\% & 100\% \\ \hline
2. MAW (mm) & 18.22 + 0.813 * MAW + 3.115*sex & 0.583 ** & 0.340 & 98.18\% & 100\% \\ \hline \hline \end{tabular}  
* Indicates significance at the 0.05 level, ** Indicates significance at the 0.01 level.  
\end{table} 
Table 6: Regression equations showing correlation coefficients (R) and linearity of relationship. Figure 4: Regression plot.