## 3 Results
### Machine Learning Results  
To begin with, we conducted a comparison of various machine learning algorithms on both training and testing datasets. The findings indicated that the \"shrinkage\" techniques, specifically ridge, lasso, and elastic net regression algorithms, performed marginally better than the other algorithms in terms of the smallest RMSE and MAE values, as well as the largest R-squared values (see Table 2). Among these three algorithms, lasso regression was the top-performing one. Regarding the explained variance, ridge and lasso algorithms resulted in 36% in the training set and around 34% in the test set.  
Subsequently, we utilized the models created by the \"shrinkage\" algorithms to evaluate the relative significance of the predictor variables in forecasting problematic smartphone use. Our findings demonstrated that, compared to other predictors, Fear of Missing Out (FoMO) was the most influential explanatory variable in forecasting problematic smartphone use in Canadian adolescents. Additionally, after FoMO, emotional and cognitive self-regulation was the next most robust predictor of problematic smartphone use (see Table 3).  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Variable** & **M** & **SD** & **Min** & **Max** & **Cronbach’s \(\boldsymbol{\alpha}\)** \\ \hline Gender & 0.73 & 0.72 & 0 & 3 & _NA_ \\ Ethnicity & 2.34 & 0.85 & 1 & 3 & _NA_ \\ \hline \multicolumn{5}{l}{Note: Ethnicity was coded as East Asian (1), White (2), and others (3) (included participants who selected more than one ethnicity, Black, Indigenous, Latin American, South Asian, Southeast Asian, and West Asian). Gender was coded as girls (1), boys (0), and others (2); included participants who selected more than one gender, non-binary, transgender, not sure).} \\ \end{tabular}
\end{table}
Table 1: _Cont._  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** \\ \hline
1. Problematic smartphone use & 1 & & & & & & & & \\
2. Screen time & 0.35 ** & 1 & & & & & & & \\
3. Stress & 0.40 ** & 0.21 ** & 1 & & & & & & \\
4. Anxiety & 0.30 ** & 0.21 ** & 0.63 ** & 1 & & & & & \\
5. Depression & 0.34 ** & 0.22 ** & 0.67 ** & 0.51 ** & 1 & & & & \\
6. FOMO & 0.40 ** & 0.16 ** & 0.42 ** & 0.32 ** & 0.38 ** & 1 & & & \\
7. Emotional self-regulation & \(-\)0.36 ** & \(-\)0.23 ** & \(-\)0.53 ** & \(-\)0.35 ** & \(-\)0.44 ** & \(-\)0.44 ** & 1 & & \\
8. Behavioural self-regulation & \(-\)0.31 ** & \(-\)0.18 ** & \(-\)0.40 ** & \(-\)0.32 ** & \(-\)0.37 ** & \(-\)0.31 ** & 0.42 ** & 1 & \\
9. Cognitive self-regulation & \(-\)0.19 ** & \(-\)0.14 ** & \(-\)0.12 ** & \(-\)0.08 ** & \(-\)0.16 ** & \(-\)0.02 & 0.11 ** & 0.17 ** & 1 \\ \hline \multicolumn{5}{l}{Note: ** \(p<0.01\).} \\ \end{tabular}
\end{table}
Table 2: Correlations among Main Study Variables.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Mean Model Fit Findings over**} \\  & **Repeated Cross-Validations in the** & & & & **Model Fit Findings in the Test Sample** \\  & & **Training Sample** & & & & \\ \hline  & RMSE & MAE & R\({}^{2}\) & RMSE & MAE & R\({}^{2}\) \\ Lasso & 0.663 & 0.523 & 0.36 & 0.656 & 0.519 & 0.34 \\ Ridge & 0.664 & 0.525 & 0.35 & 0.655 & 0.520 & 0.34 \\ Elastic Net & 0.663 & 0.524 & 0.35 & 0.655 & 0.519 & 0.34 \\ Extreme & & & & & & \\ Gradient & 0.737 & 0.573 & 0.27 & 0.738 & 0.574 & 0.21 \\ Boosting & & & & & & \\ Random & 0.677 & 0.536 & 0.33 & 0.738 & 0.532 & 0.29 \\ Forest & & & & & & & \\ \hline \hline \multicolumn{5}{l}{Note: RMSE = Root Mean Squared Error; MAE = Mean Absolute Error.} \\ \end{tabular}
\end{table}
Table 3: Comparison of Five Machine Learning-based Regression Algorithms.