## 3 Results
### Feature Matrix and Regression Algorithm Analysis  
#### 3.2.1 Model Selection and Feature Analysis  
In the process of using the iterative method to filter the features for predicting the slope S, the \(p\)-value obtained by each iteration of each model was much less than 0.001. The features finally selected by each model are shown in Figure 1. The adjusted R\({}^{2}\) value and the selected feature of each model in the iteration are shown in Figure 2 and Table 2. Compared to several other models, the ridge regression achieved the largest adjusted R\({}^{2}\) value and the smallest prediction error at the end of the iteration, so it was selected as the prediction model. Figure 2 shows that the adjusted R\({}^{2}\) value reached the highest when the ridge regression model was iterated to four features. Based on the above situation, a final feature set of four features was selected to predict the slope S: the waist-to-hip ratio (WHR), grip strength (GS), left lower limb muscle (LLLM), and bone strength index (STI). However, we can easily find that the final set of four features is not the combination that achieves the highest correlation with the slope, which seems unreasonable. This is actually because the algorithm that we propose is result-oriented. The algorithm tried a huge number of feature combinations to select the one with the highest predictive accuracy, regardless of whether the combination of features made sense. For example, the algorithm selects LLLM but not RLLM, which is easy to cause doubts. However, such a result is just because we can obtain better prediction results through LLLM by the existing experimental data. This does not mean that LLLM be more important than RLLM. The accuracy of using RLLM is only slightly lower than that of using LLLM. This difference may be due to differences in population or dominant feet. Thus, the choice of LLLM and RLLM mainly depends on the equipment that the individual already owns. Of course, we can also put forward a new feature (lower limb muscle) to remove people's doubts and make the result easier to figure out. The lower limb muscle (LLM) is the mean of LLLM and RLLM, which makes a lot more sense since, in cycling, the average power is generated by the average power of the two legs. The method of integrating features is also applicable to other pairs of body data that distinguish between right and left. Figure 1: Features used when each model was iterated to the optimal. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{2}{c}{**Number of**} & \multicolumn{5}{c}{**Machine Learning Model**} \\ \cline{2-5}
**Iterations** & **Linear** & **Ridge** & **Lasso** & **Elastic Net** & **Polynomial** \\ \hline \multirow{3}{*}{1 st} & Left lower limb & Left lower limb & Left lower limb & Left lower limb & Left lower limb \\  & muscle & muscle & muscle & muscle & muscle \\ \hline \multirow{3}{*}{2 nd} & Bone strength & Bone strength & Bone strength & Bone strength & Bone strength \\  & index & index & index & index & index \\ \hline \multirow{3}{*}{3 rd} & Grip strength & Grip strength & Grip strength & Grip strength & Grip strength \\ \cline{2-5}  & Waist-to-hip ratio & Waist-to-hip ratio & BMI & BMI & BUA \\ \hline \multirow{3}{*}{5 th} & AI & AI & Weight & Weight & Right upper limb \\  & & & & & muscle \\ \hline \multirow{3}{*}{6 th} & \multirow{3}{*}{BUA} & \multirow{3}{*}{BUA} & Right lower limb & Right lower limb & \multirow{3}{*}{-} \\  & & & muscle & muscle & muscle \\ \hline \multirow{3}{*}{7 th} & \multirow{3}{*}{-} & \multirow{3}{*}{-} & Left upper limb & STI/Expected value & \multirow{3}{*}{-} \\  & & & muscle & for Peers & \\ \hline \hline \end{tabular} Random forest is a model that uses decision trees, whose training results are random each time. Therefore, the features selected by the random forest model in the training are not listed in the table. The adjusted R\({}^{2}\) in Figure 2 is also the average value obtained from the multiple training results.  
\end{table} 
Table 2: Feature selected by each model in each iteration.