## 4 Predictive Modelling of Sound Design Elements and User's Emotional Evaluation  
### QTTI Prediction Model Construction and Analysis  
QTTI is often used to establish a linear relationship between quantitative and qualitative variables in the form of a multiple linear regression equation (as shown in Equation (7)). The equation was constructed using the sound design elements (13 items) as the independent variables and each user emotional evaluation values as the dependent variable, e.g., the coefficient represents the score point of the \(b\)-th class under the \(a\)-th item as the coefficient of this multiple linear regression equation; \(X_{11}\), \(X_{12}\)...... \(X_{52}\), \(X_{53}\) represent the individual categories; \(k\) denotes the constant term of the multiple linear regression equation under the \(x\)-th group of Kansei words [40]. \[ \begin{array}{ll}Y_{x}=&a_{11}X_{11}+a_{12}X_{12}+a_{13}X_{13}\\ &+a_{21}X_{21}+a_{22}X_{22}+a_{23}X_{23}\\ &+a_{31}X_{31}+a_{32}X_{32}+a_{33}X_{33}\\ &+a_{41}X_{41}+a_{42}X_{42}\\ &+a_{51}X_{51}+a_{52}X_{52}\\ &+k\end{array}  \tag{7}\]  
The design element codes of the 30 experimental samples and user emotional evaluation values were analyzed by SPSS 23.0 for QTTI. A predictive model was constructed, and the results are shown in Table 4.  
The table above shows that the coefficient of determination \(R^{2}\) for \"Annoyance-comfortable\" is 0.891, meaning that this multiple linear regression equation is able to explain 89.1% of the variation in the dependent variable, while the coefficients of determination for the other 2 groups of perceptual words are 89.9% and 85.9%, respectively, and the three equations have a good fit. By comparing the partial correlation coefficients of the items with the category score points, the degree of influence of each sound design element on the user's imagery can be obtained. (I) Item impact analysis  
The partial correlation coefficient of the items indicates the relevance of each item to the Kansei words, with higher values indicating a stronger relevance to the imagery, i.e., a higher influence on that imagery. The most relevant item for the word \"Annoyance-Comfortable\" is loudness, with a partial correlation coefficient of 0.837, which is the strongest correlation with this word. The order is loudness > sharpness > A-weighted sound pressure level > roughness > tonality. When conducting sound design, priority can be given to items with a higher number of partial correlations. In the word \"Inexpensive-Premium\", the influence of each item is ranked as sharpness > loudness > roughness > tonality > A-weighted sound pressure level. In the words \"Weak-Powerful\", the influence of each item is ranked as loudness > sharpness > tonality > A-weighted sound pressure level > roughness. (II) Category impact analysis  
The category score points indicates the positive and negative correlation between each category and the discourse, with larger positive values indicating more correlation with the positive discourse and larger negative values indicating more correlation with the negative discourse. For example, in the case of the \"Annoyance-Comfortable\" word, the item with the highest partial correlation coefficient is 'loudness', where a positive value for the category score point belongs to 'comfortable' imagery, indicating that the lower the loudness, the more comfortable the imagery conveyed, and, conversely, the louder the loudness, the more annoying it is. The second-ranked item is sharpness, with a positive point score in the sharpness category indicating that the lower the sharpness the more comfortable the imagery is conveyed, and vice versa, the more annoying. The influence of the other categories of the word can be followed in this way (as shown in Table 4).