*2.2. Factor Analysis and Phenotypic Correlation among the Four Traits for Rice Grain Size and Weight*

The Pearson correlation coefficients (r) were estimated for pair-wise analysis among the studied traits (i.e., GL, GW, GT, and TGW) using diverse germplasms comprising 204 rice germplasms (Table 2). A correlation analysis between GL and GW showed a highly significant (*p* ≤ 0.01) but negative association (r = −0.604 \*\*) between these two traits. Such a negative linear relationship has also been reported by other researchers [20,55]. GL and GT were also negatively correlated (r = −0.398 \*), which was also significant (*p* ≤ 0.05) and strong. In the case of TGW, GL showed a significant (*p* ≤ 0.05) and positive association (r = 0.249 \*), depicting the linear relationship between these two traits. A highly significant (*p* ≤ 0.01) and positive relationship (r = 0.686 \*\*) was also observed between GW and GT, indicating that GW was 68.6% positively influenced by GT in the studied rice germplasm. Likewise, GW showed a significant (*p* ≤ 0.05) and positive association (r = 0.374 \*) with TGW. GT was also found to have a highly significant (*p* ≤ 0.01) and positive association (r = 0.491 \*\*) with TGW. These results further revealed that TGW was 24.9% influenced by GL, 37.4% influenced by GW, and 49.1% influenced by GT. Hence, we assume the trend of trait selection (i.e., GT > GW> GL) for improving TGW in yield enhancement programs. The same results were also confirmed using Factor analysis in the Minitab software by producing a biplot for all the traits to further study the pattern of association among the traits. The results confirmed the importance of GT followed by GW and GL in improving TGW and paddy yield. Figure 4 shows a two-dimensional (2D) representation of the associations among the traits [56–58].

**Table 2.** Correlation coefficient analysis among the four studied traits for grain size and weight.


\*\* highly significant at *p* ≤ 0.01; \* significant at *p* ≤ 0.05.

**Figure 4.** Factor analysis of the four grain size and weight related traits in rice germplasm comprising 204 genotypes; the first two factors represent more than 85% of the total variation. Traits with a positive association have vectors with an acute angle (<90) between their vectors and are closer to one another, while traits with negative associations have an obtuse (>90) angle between their vectors and are found far from one another in the biplot.
