## 4 Experimental Results
In statistical analysis, it is often necessary to determine whether a dataset is from a normal population using regression analysis or multivariate analysis. Of all the analysis methods, the use of statistical graphics to make such a judgment is relatively easy and convenient. With a P-P diagram and a least-squares line, the user can easily determine whether or not the entered data are from a normal population. Another function is to aid researchers in interpreting the meaning of the P-P plot. The least-squares line is obtained from the linear equation derived from the method of least squares, which is a linear equation that obtains the sum of the squared residuals between the least-squares line and the data minimal. The regression equations adopted in this study are primarily based on concepts from reference [15], which is used as a mathematical model for derivation of the basic theory. After transforming the variables of the regression model via Box-Cox to \(\lambda=0.3\), \(\varepsilon\) matches the normal distribution, as does the \(R\) model. The linear regression model parameters are expressed in terms of  
\[Y_{i}=\beta_{0}+\beta_{i}X_{i}+\varepsilon_{i}\,, \tag{1}\]  
where \(Y_{i}\) is a random variable, \(X_{i}\) is a known fixed constant, \(\varepsilon_{i}\) is an unobservable, and \(i=1\),..., \(n_{x}\) (\(i\)-th test; \(Y_{i}\) is the reaction value corresponding to \(X_{i}\)). Expressing the main variables in the experimental linear model formula yields  
\[Y=21.259+1.905X_{1}+0.707X_{2}+0.69X_{\mathrm{B}}-5.749X_{\mathrm{C}}-1.342X_{ \mathrm{D}}+\mu\,, \tag{2}\]  
where \(X_{1}\) is the size of screen 1, \(X_{2}\) is the size of screen 2, \(X_{\mathrm{B}}\) is the scene recording brightness, \(X_{\mathrm{C}}\) indicates the mode (2D or 3D), \(X_{\mathrm{D}}\) is the photographic equipment \(EV\), and \(\mu\) is the interaction value of the variables. From analysis of the image brightness using this linear regression model, different variables affect the screen brightness by different degrees, although the interactions between variables affect the screen brightness only minimally. However, changing from the 2D to 3D mode has the most significant effect on the brightness. Once the screen changes from the 2D to 3D mode, the screen brightness declines noticeably. As detailed above, the linear regression model attempts to consider the effects of the main environment and hardware when estimating the screen brightness value. The brightness values are affected by numerous external factors; however, conversion from 2D to 3D mode has the largest impact. In fact, 3D image professionals require a certain amount of time to adjust the 3D image brightness in such scenarios. Therefore, the linear regression model can help to estimate image brightness if other environmental factors or hardware conditions are controlled. The faster the shutter speed, the lower the screen image brightness, and low-brightness value images that are difficult to observe can even be obtained. The 3D image brightness degradation in response to increased shutter speed is clearly shown in Table 7; further, the 3D image brightness values are significantly lower than the 2D image brightness values for specific shutter conditions. The experimental results show that, when the aperture is F5.6 (_i.e._, Table 7), the image brightness value is the same in 2D mode with a shutter speed of 1/250 s as it is in 3D mode with 1/125-s shutter speed. Therefore, the 3D display exhibits approximately 50% image brightness degradation. The experimental results for the F10 aperture are listed in Table 8. For this aperture setting, the image brightness value is the same in 2D mode with a shutter speed of 1/40 s as it is in 3D mode with 1/10-s shutter speed. Thus, the 3D display has only 50% of the 2D image brightness. If the low-brightness (value 0) data are removed from the experimental dataset, the 3D image brightness average value can be increased to approximately 39.2% of the 2D image brightness value.