## 7 Directions for Future Research  
In this study, we focused only on low-dimensional settings, as certain methods, such as BE, are not applicable in high-dimensional settings. Future research should extend this comparison to include both classical (FS and BSS) and penalized methods in high-dimensional settings, particularly under conditions of both sufficient and limited information, to evaluate the generalizability of our findings. Additionally, we did not examine the robustness of the methods to violations of standard model assumptions, such as heteroscedasticity and non-normal error distributions, nor did we assess the impact of influential points or outliers. In real-data analysis, it is highly relevant to check for influential points or extreme values, which can easily be identified and handled manually [68]. However, identifying influential points or outliers in simulation studies is challenging due to the large number of repetitions. Therefore, we followed a preventive strategy by truncating values at the 1 st and 99 th percentiles, as recommended in the literature [68]. Several robust extensions have been proposed, including the robust nonnegative garrote [69], robust adaptive lasso, and robust lasso [70]. These methods were not included in our evaluation. Evaluating the performance of both the standard and robust methods under such challenging conditions would offer valuable insights into their practical reliability and broader applicability. Our simulations did not incorporate interaction terms or nonlinear functional forms for continuous variables. Future research could explore how these methods perform when such complexities are included in the data-generating process. A simulation study protocol addressing nonlinearity using methods also considered in our work has been published [71], and we are currently working on a paper investigating the linearity assumption and its influence on prediction accuracy in multivariable models. Although the comparisons in this study were conducted within the framework of classical linear regression, the methods evaluated are also applicable in generalized linear models (e.g., binary outcomes) and survival models. Therefore, further studies should investigate whether the findings hold across these alternative model types. Ongoing work by [PERSON] et al. [71] is evaluating the performance of several variable selection methods, including some considered here, in both linear and logistic regression models. Such complementary research may provide additional evidence on the applicability and robustness of these methods in broader modeling contexts. Finally, other variable selection methods, such as smoothly clipped absolute deviation (SCAD), elastic net, boosting, and minimax concave penalty (MCP), were not considered. Future research could compare their performance with the methods evaluated here. The following supporting information can be downloaded at: [[https://www.mdpi.com/article/10.3390/app15137443/s1](https://www.mdpi.com/article/10.3390/app15137443/s1)]([https://www.mdpi.com/article/10.3390/app15137443/s1](https://www.mdpi.com/article/10.3390/app15137443/s1)), Figure S1. Prediction errors (measured by RTE) for NNG (L, CV), ALASSO (L, CV), and Lasso (CV) using beta-type B across different sample sizes (n = 100 and 400) in low correlation (C1 and C2) and high correlation (C3 and C4) settings. Figure S2. Prediction errors (measured by RTE) for NNG (L, CV), ALASSO (L, CV), and Lasso (CV) using beta-type D across different sample sizes (n = 100 and 400) in low correlation (C1 and C2) and high correlation (C3 and C4) settings. Figure S3. Prediction errors (measured by RTE) for classical (BE) and penalized (NNG, ALASSO, RLASSO, and Lasso) methods using beta-type B across different sample sizes (n = 100 and 400) in low correlation (C1 and C2) and high correlation (C3 and C4) settings. Figure S4.