## 3 Results
### Binomial Logistic Regression Analysis  
Binomial logistic regression analysis was conducted to examine the effectiveness of voice therapy in relation to various acoustic and subjective habit-related variables. The model estimation results are presented in Table 4. The analysis is conducted by starting with a full model that includes all independent variables and then removing insignificant variables using Wald backward elimination. The dependent variable was effectiveness and the independent variables were age, smoking, alcohol, coffee, and the voice user status, F0 before and after treatment (Pre-tx and Post-tx), F0 difference between Pre-tx and Post-tx, jitter before and after treatment, jitter difference, shimmer before and after treatment, NHR difference, SFF before and after treatment, SFF difference, MPT before and after treatment, F0 comparison, jitter comparison, shimmer comparison, NHR comparison, and SFF comparison. That is, a total of 27 dependent variables were used in the experiment in Table 4. In this paper, we propose new parameters for predicting the effectiveness of voice therapy using the characteristics of acoustic parameters. The detailed criteria are shown in Table 5. By employing these criteria, we aim to confirm the impact of interventions on speech disorders in relation to F0, jitter, shimmer, NHR, and SFF. For each acoustic parameter, the effectiveness was categorized according to a binary scale of 1 or 0 based on whether the difference between the pre- and post-treatment values was positive or negative. The categorization aligns with the effectiveness based on the G scale. Additionally, the normal thresholds for determining the presence or absence of effectiveness were based on clinical guidelines and prior research in the field [41]. It is important to note that the proposed criteria should be further validated through empirical studies and expert consensus. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & & & & & & & \\ \hline
**Dependent** & **Independent** & **B** & **S.E.** & **Wald** & **\(p\) Value** & **Exp(B)** & **Model** \\ \hline  & Alcohol & 2.154 & 1.204 & 3.202 & 0.074 & 8.622 & \\ \cline{2-7}  & Coffee & 2.794 & 1.243 & 5.049 & 0.025 \({}^{\star}\) & 16.340 & \(-\)2 log likelihood = 34.834 \\ \cline{2-7}  & Jitter (Post-tx) & \(-\)1.951 & 0.947 & 4.243 & 0.039 \({}^{\star}\) & 0.142 & Cox and Snell R\({}^{2}\) = 0.502 \\ \cline{2-7}  & Jitter comparison & 4.471 & 2.008 & 4.957 & 0.026 \({}^{\star}\) & 87.431 & Nagelkerke R\({}^{2}\) = 0.682 \\ \cline{2-7}  & Shimmer (Pre-tx) & 0.494 & 0.224 & 4.871 & 0.027 \({}^{\star}\) & 1.640 & \(p\) < 0.001 \\ \cline{2-7}  & Constant & \(-\)2.155 & 1.914 & 1.267 & 0.260 & 0.116 & \\ \cline{2-7}  & & & & & & & \\ \cline{2-7}  & & & & & & & \\ \cline{2-7}  & Jitter (Pre-tx) & 1.282 & 0.606 & 4.470 & 0.034 \({}^{\star}\) & 3.603 & \(-\)2 log likelihood = 21.60 \\ \cline{2-7}  & Jitter (Post-tx) & \(-\)2.358 & 1.150 & 4.206 & 0.040 \({}^{\star}\) & 0.095 & Cox and Snell R\({}^{2}\) = 0.332 \\ \cline{2-7}  & MPT(Pre-tx) & \(-\)1.202 & 0.533 & 5.089 & 0.024 \({}^{\star}\) & 0.301 & [PERSON] R\({}^{2}\) = 0.468 \\ \cline{2-7}  & Constant & 0.619 & 1.093 & 0.320 & 0.571 & 1.857 & \(p\) = 0.005 \\ \hline \hline \multicolumn{7}{c}{\({}^{\star}p\) < 0.05.} \\ \end{tabular}
\end{table} 
Table 4: Model estimation results of binomial logistic regression using all parameters in female and male voices. influence the effectiveness of voice therapy. Detailed verification results are presented in Table 4. Through the estimated coefficients and Wald statistics of the constructed model, along with the odds-ratio, it is possible to estimate how much each explanatory variable influences the effectiveness of voice therapy.