## 3 Experiment 2
### Results and Discussion
#### 3.2.2 Multiple Regression Analysis  
With the aim of developing a relationship model between perceived differences and various material properties, researchers conduct a variance analysis on experimental data to identify key influencing elements. On the basis of the results of the variance analysis, a regression model is established. Under the confidence condition of \(p<0.05\), only albedo (\(p<2\times 10^{-16}\)), metallic (\(p<0.00471\)), and reference smoothness (\(p<2\times 10^{-16}\)) showed significance, while normal distribution did not show significance (\(p<0.06284\)). It can be seen that the smoothness intensity of the micro-surface of the material does not have a significant impact on perceived glossiness differences, but the values of the remaining parameters of PBR materials will have a significant impact on the perceived glossiness. After conducting an analysis of variance (ANOVA), a stepwise method is used to adjust the full combination model of albedo, metallic, and reference smoothness, with the Akaike Information Criterion (AIC) [31] set as the criterion for obtaining a suitable regression model. During each step of the process, researchers delete the factor in the full  
Figure 6: The results of differential distribution. The opacity of the circular data points in the figure indicates the standard deviation of the perceived differences under the current parameter combination. A higher opacity indicates a larger degree of discrepancy in the perceived differences at the corresponding point. The radius of each circular data point represents the absolute value of the smoothness difference, with a larger radius indicating a larger absolute value of the difference. combination model that has the greatest impact on AIC. They recalculate the AIC value of the model until they reduce the AIC value of the regression model to a lower level. The final multiple linear regression model for perceived differences is displayed in Table 2. The intercept term has a small and insignificant effect; therefore, it is subsequently removed from the model. The dependent variable of the regression model is the perceived smoothness (matching value). Subtracting the reference value from the matching value yields the perceived difference. As shown in Figure 7, the perceived differences in glossiness generally decrease monotonically with the variation of the reference smoothness parameter. When the value of the reference smoothness is low, individuals in the virtual reality (VR) environment often overestimate the glossiness of the presented materials. However, at high reference smoothness values, individuals tend to underestimate the glossiness of the materials in the VR environment. However, the specific direction of the difference change is influenced by the combined effect of metallic and reflectance and is not entirely parallel to the reference smoothness axis. As observed in Figure 7, there exists only a certain linear relationship between the perceived difference and the reference smoothness, with the albedo being around 0.35. When the albedo and metallic approach their respective extremes, the linear relationship between the perceived difference and the variation of the reference smoothness will be affected to some extent. Furthermore, the degree of this effect is inversely proportional to the distance of the albedo and metallic from their respective extremes. Moreover, the accuracy of the regression results under different parameters is examined. As shown in Figure 8, the length of the confidence interval corresponding to the center region of the image is generally small. This signifies that, under the same confidence level, the perceived glossiness differences predicted by this model have greater stability.