*4.3. Multivariate Statistical*

Compared with univariate and bivariate statistical methods, multivariate statistical methods can analyze more than one relationship at the same time. There are many multivariate data analysis methods, each of which has a different purpose, such as Regression analysis, factor analysis, cluster analysis, analysis of variance, discriminant analysis, etc. [68]. Biplot analysis is usually employed to assess the component effects creating the genotypic variations.

The highest values indicate the highest influence of the trait on the total variation. Biplot analysis determines varietal stability in the multi-environmental trial [69]. It describes the relationship between different genotype traits. The association between morphophysiological traits among the 130 genotypes was observed by the biplot analysis [70]. Again, the biplot analysis showed the trait profiles of the genotypes, especially, those genotypes positioned far away from the origin and the results indicated a correlation between traits with genotypes (Figure 4). An acute angle between two elements indicates a positive correlation, and an obtuse angle between two elements indicates a negative correlation. As a result, principal components (PC) analysis provides a good screening of available genotypes and aids in the selection of possible parents for crop breeding initiatives. In our data, the first two PC accounted for 82.36% of the overall variation (Figure 4). The yield potential of accessions was represented in PC 1; thus, the accessions contributing to this component are likely to undergo direct selection, or selected parents can be used in hybridization operations. These PC1 results are consistent with the results of the correlation analysis. The

figure summarizes the information of the matrix in principal components, where the cosine of the angle between the vectors connecting the objects to the origin is proportional to the correlation coefficient between these objects. The heatmap shows the highest and lowest values of each genotype in different colors against all the traits comparing. The intensity of the color indicates the degree of high or low of the traits. Hierarchical clustering based on the morpho-physiological traits of the studied germplasm revealed six clusters (Figure 5). The heatmap analysis depicted the degree of correspondence among the morphological traits assessed in brinjal genotypes, and this result was consistently supported by [71,72].
