## 3 Results and Discussion
### Analysis of Response Surface  
The 3-D response surface analysis (Figure 1) revealed that the fermentation rate of Huaniu apple cider increased with an increase in the initial soluble solids content. Fermentation rate refers to the process's speed, often measured by product generation (like alcohol) or substrate consumption (such as sugars) over a set time. Similar to a speedometer, it mirrors car speed comprehension. In wine, beer, or yogurt production, precise pacing is vital for desired attributes. Slow pace extends timelines, and excessive speed alters traits. Controlling rate fine-tunes variables, enabling innovation and enhancement while ensuring process consistency. The initial soluble solids content is an important parameter in the cider fermentation process. A higher initial soluble solids content provides more fermentable sugars, resulting in a higher alcohol content [15]. Hence, the selection of the initial soluble solids content needs to strike a balance between the desired alcohol content and fermentation rate [16]. The fermentation temperature decreased the fermentation rate and then gradually increased it. The fermentation temperature is one of the key factors that affect the fermentation process and quality of cider. A higher fermentation temperature can promote yeast growth and metabolic activity, thereby speeding up fermentation [17]. However, excessively high temperatures may cause the yeast to produce an excessive number of metabolites that can affect the flavor of the cider [18]. Determining the appropriate fermentation temperature depends on the yeast strain used and the desired characteristics of the final product [19]. It is important to carefully control the production of yeast metabolites while maintaining an optimal fermentation rate. The fermentation rate initially increased and then decreased with an increase in the initial pH. A suitable initial pH creates an environment conducive to yeast growth and metabolism. Higher pH values may inhibit yeast growth and fermentation activity, which can also affect the fermentation speed and product quality [20]. On the other hand, a lower pH may promote yeast growth but can also result in excessive acidity [21]. Therefore, selecting the appropriate initial pH requires considering the requirements of the yeast strain, the desired characteristics of the final product and maintaining the acid-base balance during fermentation. The fermentation rate increased with an increase in the inoculum amount. The inoculation of _Saccharomyces cerevisiae_ significantly affects the fermentation rate and product production of cider. Higher inoculum amounts generally accelerate fermentation because a larger number of yeast cells allows for faster conversion of sugars into alcohol and other metabolites. However, excessively high inoculation levels may lead to an accumulation of yeast metabolites, which can impact the flavor properties of the cider [22]. \begin{table}
\begin{tabular}{c c c} \hline
**Source** & **F Value** & **_p_-Value** \\ \hline \(\chi_{23}\) & 1.85 & 0.1951 \\ \(\chi_{24}\) & 7.07 & 0.0187 * \\ \(\chi_{34}\) & 0.14 & 0.7161 \\ \(\chi_{11}\) & 7.5 & 0.0160 * \\ \(\chi_{22}\) & 5.87 & 0.0295 * \\ \(\chi_{33}\) & 2.81 & 0.1161 \\ \(\chi_{44}\) & 12.42 & 0.0034 ** \\ Lack of fit & & 0.0692 \\ R\({}^{2}\) & & 0.8693 \\ C.V./\% & & 3.13 \\ \hline \end{tabular} \(X_{1}\) = temperature (\({}^{\circ}\)C), \(X_{2}\) = initial soluble solids (\({}^{\circ}\)Brix), \(X_{3}\) = inoculum amount (\(\%\)), and \(X_{4}\) = initial pH; level of significance * \(p\) < 0.05, ** \(p\) < 0.01, and *** \(p\) < 0.001.  
\end{table} 
Table 3: _Cont._The interaction between the initial soluble solids and initial pH had a significant impact on the model. These provide valuable insights into the effects of fermentation initial soluble solids, _Saccharomyces cerevisiae_ inoculation, fermentation temperature, and initial pH on the cider fermentation process.