## 4 Methodology
In our case, we found \(p<0.001\), and we can therefore state that the correlation is statistically highly significant. We also performed a significance analysis of the regression model, using the F-Test. The F-test indicates whether a linear regression model provides a better fit to the data than a model that contains no independent variables. In this case, the \(p\)-value indicates whether there is a significant relationship described by the model, and the \(R^{2}\) (coefficient of determination) measures the degree to which the data are explained by the model. In particular, \(R^{2}\) is the proportion of the variance in the dependent variable that is predictable from the independent variable(s). The Adjusted Coefficient of Determination (\(R^{2}adj\)) is an adjustment for the Coefficient of Determination that takes into account the number of variables in a data set. It also penalizes you for points that do not fit the model. As in previous cases, we have considered two different scenarios, choosing the H-index as the dependent variable for the first regression, and the H-Index normalized for the subject for the second one. Results are shown in Table 3.

For both cases, we found \(p<0.001\), and we can therefore state that the regression models are statistically highly significant. The results also show that the Radius of Gyration explains the 47% of the H-Index variance and the 39% of the H-Index normalized for the subject. Even if there is a strong connection between the two variables, determination does not prove causality, and we cannot deduce a cause-and-effect relationship solely based on an observed association or correlation. ### Subject Analysis

Since this analysis regards scholars working in very different subject areas, in Figure 5 data are distinguished by the subject areas associated with scholars on Scopus. Subject codes are defined in the Scopus API ([[https://dev.elsevier.com/documentation/ScopusSearchAPI.wadl](https://dev.elsevier.com/documentation/ScopusSearchAPI.wadl)]([https://dev.elsevier.com/documentation/ScopusSearchAPI.wadl](https://dev.elsevier.com/documentation/ScopusSearchAPI.wadl)), accessed on 8 January 2022). In particular, in graph (a) the analyzed scholars are colored by subject area. It can be observed that some groups of scholars of certain subject areas are represented by nearby points and, also selecting each subject area, the two considered variables are anti-correlated. In fact, considering the most represented subjects, the following important values of anti-correlation can be observed: MATH, \(-0.636\); MEDI, \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{3}{c}{**Statistic Regression**} \\ \hline  & Y = H-Index & Y = H-Index normalized for subject \\ \hline \(R\) & 0.688247525 & 0.627967253 \\ \hline \(R^{2}\) & 0.473684656 & 0.394342871 \\ \hline \(R^{2}(adj)\) & 0.473508395 & 0.39413997 \\ ine _Standard Error_ & 0.715257263 & 0.767136911 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Statistic Regression Results. \(-0.677\); ENGI, \(-0.531\). To better highlight some possible differences among subjects, graph (b) also shows the average values of the Radius of Gyration and the H-index, grouping scholars by subjects. According to the results, researchers of different subjects behave differently, and also these average values are scattered approximately along a line with a negative slope. The subjects with the highest values of the Radius of Gyration are Economics and Business. In [38], it is shown that the differences among the average H-index calculated for each disciplinary field (or Scopus subject) can be largely accounted on both the career length and the average number of authors per article in the various fields. Figure 5 shows that in correspondence with the lower average H-index in the cases of Economics and Business, the mobility across research topics measured by the Radius of Gyration is higher. ### Country Analysis

Finally, Figure 6 takes also information about countries into account.