## 3 Results
### Principal Component Analysis  
Principal component analysis (PCA) is a linear dimensionality reduction technique that transforms multiple correlated variables into a smaller set of uncorrelated variables, known as principal components. PCA involves the analysis of eigenvalues and eigenvectors of the data covariance matrix (or the correlation matrix). PCA diagonalizes these matrices. Each cell of the correlation matrix contains the correlation coefficient. The correlation values measure the degree of linear relationship between each pair of variables. The probability value (or \(p\)-value) is used to determine the significance of observational data. The \(p\)-value is the probability that observed results occurred randomly, assuming the null hypothesis is true. The lower \(p\)-value indicates the greater statistical significance of the linear relationship between the variables. A study result is statistically significant if the \(p\)-value is less than or equal to the significance level of the test. Pearson's correlation coefficient is statistically significant as \(p\) < 0.05 and statistically highly significant as \(p\) < 0.001. Table 5 presents the correlation matrix across the selected physical variables (and the corresponding \(p\)-values) in native potato starch, spray-drying potato 3%, and spray-drying potato 5%. As can be seen from Table 5, most of the correlation coefficients are statistically significant. Figure 7: Hygroscopicity values of native potato starch and spray-dried potato starch powders at concentrations of 3% [SD_3%] and 5% [SD_5%] stored at relative humidity of 100% (**a**), 75.3% (**b**), and 68.8% (**c**). The vertical lines denote the 95% confidence intervals for the means, calculated using the error mean square from the analysis of variance. Groups that do not have a common letter are significantly different, as assessed by [PERSON]’s pairwise comparison of means (\(p\) < 0.05). A principal component analysis (PCA) was carried out in order to investigate the relationships among selected physical properties of the native potato starch and spray-dried starch powders. Figures 8-10 show the Pareto diagrams and PCA biplot for native potato starch (Figure 8) and spray-dried starch powders at concentrations of 3% (Figure 9) and 5% (Figure 10). Eigenvalues (characteristic roots) represent the total amount of variance that can be explained by a given principal component. The principal component analysis (PCA) decreases the number of variables by constructing principal components. The principal component corresponding to the largest eigenvalue (PC-1) is the direction along which the variance is maximized. Using the Kaiser-Guttman rule [68], only the factors with eigenvalues that are greater than 1 were retained. The Pareto chart of the PCA results in Figure 8a shows the explained and accumulated variance for each principal component in native potato starch. According to the results, the first three principal components have eigenvalues greater than 1. The first three principal components (PC-1, PC-2, and PC-3) explain 76.4% of the variation in the experimental data of the native potato starch. The principal components (PCs) are the linear combinations of the original variables that account for the variance in the data. The loading plot in Figure 8b reveals the relationships between the experimental data (original variables) in the space of the first two components (PC-1 and PC-2). The first two components explain 60.3% of the variance; component 1 and component 2 account for 32.0% and 28.3% of the variance, respectively (Figure 8a). The coefficients are the values that indicate the relative weight of each measured variable in the main principal components (Table 6). In the loading plot in Figure 8b, the variables that correlate the most with the first principal component are the Hausner ratio (0.623) and the Carr index (0.622). The first principal component is positively correlated with these two variables.