## 3 Results and Discussion  
### Roughness  
The obtained roughness values were then statistically analyzed using Statistic software v13.1, applying backward stepwise regression with a significance level of \(\alpha=0.05\). Additionally, the Fisher-Snedecor test was conducted, and the coefficient of determination (R\({}^{2}\)) was calculated to assess the model's explanatory power (Table 6, Figure 6). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Equation** & **F(1,13)** & **R\({}^{2}\)** & \\ \hline \(R_{a}=a\times 0.031467+0.685613\) & 12.976 & 0.4995 & (1) \\ \(R_{q}=a\times 0.04346+0.874843\) & 13.358 & 0.5067 & (2) \\ \(R_{y}=a\times 0.259817\) & 12.043 & 0.4809 & (3) \\ \(R_{z}=a\times 0.262458+3.580481\) & 17.880 & 0.5790 & (4) \\ \(S_{m}=n\times 0.17878\) & 3.4247 & 0.4829 & (5) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Regression equations for roughness parameters, including Fisher-Snedecor F-values and coefficients of determination (R\({}^{2}\)). Figure 5: Box plot comparison of surface roughness parameters (Ra, Rq, Ry, Rz). Based on the conducted analysis, an extended summary can be formulated regarding the quality and usefulness of the individual regression models describing the influence of single technological parameters on various measures of surface roughness. All the considered equations are linear in nature and were evaluated both in terms of statistical significance (F-statistic from the Fisher test) and the degree of model fit to the empirical data (coefficient of determination R\({}^{2}\)). The relatively low coefficient of determination (R\({}^{2}\)) observed in the regression analysis may be attributed to several factors. One potential source of variability is the non-axisymmetric geometry of the printed samples, which could significantly influence their rotational stability and the resulting surface interaction during the MAF process. Such geometric deviations may introduce uncontrolled fluctuations in the abrasive path density and contact pressure distribution, thereby affecting the consistency of the surface finishing outcomes. Moreover, it is important to emphasize the exploratory nature of this study. To the best of the authors' knowledge, no prior research has been conducted on the application of magnetic abrasive finishing to additively manufactured Inconel 939 components. Given this context, the present work serves as a foundational investigation aimed at identifying trends and key process variables rather than constructing a high-fidelity predictive model. Accordingly, the observed R\({}^{2}\) values are considered acceptable within the scope of early-stage process characterization. The analysis indicates that the variable a, interpreted as the eccentricity value, exhibits a clear and statistically significant relationship with all four surface roughness parameters: Ra, Rq, Ry, and Rz. These models are characterized by relatively high R\({}^{2}\) values, ranging from approximately 0.48 to 0.58, which means that between 48% and 58% of the variability in the analyzed roughness parameters can be attributed to changes in eccentricity. A particularly strong association was observed for the Rz parameter, which achieved the highest coefficient of determination (R\({}^{2}\) = 0.579) and the highest F-statistic value (F = 17.88), clearly indicating the high significance of this model. This suggests that the Rz parameter, which represents the total height of the profile, is the most sensitive to changes introduced by eccentricity in the machining process and may therefore serve as a particularly reliable indicator of surface quality in relation to this technological variable. In contrast, the parameters Ra and Rq, which are classic indicators of the arithmetic average roughness and its root mean square, respectively, also demonstrate a strong dependence on eccentricity, with R\({}^{2}\) values of 0.4995 and 0.5067.