## 3 Results
### Competitiveness Evaluation Results of French-Speaking African Countries
R&D expenditure as a percentage of GDP (X6): weight 0.1472, regression coefficient 0.281 (t = 5.63, \(p\) < 0.001), is the indicator with the highest weight in the science and technology level dimension, reflecting the direct driving effect of R&D investment on innovation capability. High-tech exports (X8): weight 0.1595, regression coefficient 0.312 (t = 6.21, \(p\) < 0.001), are the core manifestation of scientific and technological achievements transformation and international competitiveness and are strongly positively correlated with competitiveness. Total reserves (X11): weight 0.1160, regression coefficient 0.227 (t = 4.38, \(p\) < 0.001). As a key indicator of financial strength, it reflects a country's ability to resist risks and allocate capital. In addition, we can also find 5 secondary key influencing factors. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Variable Name**} & **Correlation** & \multirow{2}{*}{**t Statistic**} & \multirow{2}{*}{**Relevance**} & \multirow{2}{*}{_p-Value**} \\  & **Coefficient** & & & \\ \hline X\_1 & 0.3821 & 3.52 & 0.856 & 0.001 \\ X\_2 & \(-\)0.2153 & \(-\)2.89 & \(-\)0.724 & 0.005 \\ X\_3 & 0.4572 & 4.11 & 0.892 & 0.000 \\ X\_4 & 0.2985 & 3.05 & 0.813 & 0.002 \\ X\_5 & \(-\)0.1867 & \(-\)2.23 & \(-\)0.688 & 0.028 \\ X\_6 & 0.5124 & 4.87 & 0.921 & 0.000 \\ X\_7 & 0.3546 & 3.33 & 0.837 & 0.001 \\ X\_8 & 0.4235 & 4.02 & 0.879 & 0.000 \\ X\_9 & 0.2654 & 2.78 & 0.795 & 0.006 \\ X\_[10] & 0.3178 & 3.19 & 0.825 & 0.003 \\ X\_[11] & 0.4891 & 4.66 & 0.905 & 0.000 \\ X\_[12] & \(-\)0.1235 & \(-\)1.67 & \(-\)0.542 & 0.098 \\ X\_[13] & 0.2843 & 2.91 & 0.802 & 0.004 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Adaptive-LASSO algorithm results. Number of patent applications (X9): weight 0.0926, regression coefficient 0.185 (t = 3.72, \(p\) = 0.002), reflecting the scale of innovation output, but the conversion efficiency needs to be further optimized in combination with industrial applications. Total number of domestic listed companies (X10): weight 0.0854, regression coefficient 0.173 (t = 3.45, \(p\) = 0.004), reflecting the activity of the capital market and the financing ability of enterprises, and playing a supporting role in industrial expansion. Science and engineering indicators (X5): weight 0.0745, regression coefficient 0.151 (t = 2.98, \(p\) = 0.008), representing basic research and technical talent reserves, which are the underlying elements of R&D and innovation. R&D researchers (X7): weight 0.0739, regression coefficient 0.149 (t = 2.89, \(p\) = 0.010), positively correlated with the level of science and technology, but attention should be paid to the potential suppression of competitiveness by talent loss. Commodity exports (X4): weight 0.0581, regression coefficient 0.123 (t = 2.51, \(p\) = 0.019). As a core indicator of economic level, its growth has a significant effect on GDP, but its added value still needs to be improved. To verify the effectiveness of adaptive LASSO in variable selection, this study selected three mainstream methods, namely, traditional LASSO, ridge regression, and random forest, for comparison and conducted analysis from three aspects: variable screening results, model fitting goodness of fit, and consistency of core factors (Table 6). Although traditional LASSO can achieve variable screening, it imposes equal penalties on all variables, resulting in 12 variables being screened out, and there is a problem of over-retention of secondary factors. Ridge regression only reduces overfitting through coefficient shrinkage and cannot achieve variable elimination, and ultimately retains all 30 indicators, making it difficult to identify core driving factors. Random Forest screens variables through feature importance scores, and although it can capture nonlinear relationships, the results are significantly affected by parameters, and the key indicator \"R&D expenditure ratio\" is missing from the 8 screened variables, which poses a risk of missing core factors.