**5. Conclusions**

Canonical correlation analysis is an optimized multivariate technique for evaluating the existence or non-existence of relationships between complex groups of variables. In this study it proves to be a powerful tool to study the relationship between the selected set of carcass traits and the proximate, lipid and mineral components, particularly when it is expected that certain degree of interaction exists among these three groups of chemical variables. This work demonstrates an important relationship between backfat thickness, marbling and the content of total lipids and fatty acids in beef LDL muscle from cattle fed on pastures under tropical conditions. Instead, carcass traits are poorly associated with beef mineral content. These findings allow for the possibility to develop selection criteria based on BFT and/or marbling to sort carcasses with differing nutritional values. For the experience gained in beef carcass grading in Venezuela, the evaluation of marbling levels requires more intense training and supervision of graders than the BFT measurement. Moreover, marbling is seldom used to grade beef carcasses in the developing, tropical countries. Therefore, it is more practical to use BFT in future regression analyses to explain the variation in lipid composition of beef *longissimus* muscle.

Further analyses are needed to determine the potential influence of sex condition on the magnitude of the associations among carcass traits and beef fatty acid composition.

**Supplementary Materials:** The following are available online at https://www.mdpi.com/article/ 10.3390/foods10061364/s1, Figure S1: Graphical description of sample preparation and chemical analyses; Figure S2: Dendrogram for samples from the hierarchical cluster analysis identifying clusters. The samples were numbered randomly from 1 to 109; Figure S3: Projection of variables from the subgroup proximate composition by clusters; Figure S4: Projection of variables from the subgroup mineral content by clusters; Figure S5: Projection of variables from the subgroup lipid profile by clusters; Figure S6: Projection of variables from the subgroup carcass traits by clusters.

**Author Contributions:** N.H.-L. designed the investigation and field data that supported this research. L.A.d.M. was responsible for the selection of chemical procedures and training of personnel who conducted the chemical analyses and collected lab data that support this research. S.U.-B. conducted the chromatographic analysis of the samples. N.J.-T., E.M.-V. and L.A.d.M. performed statistical analyses, and tabulated results. L.A.d.M., N.J.-T., M.G.-M. and N.H.-L. interpreted, designed, and revised the structure of the manuscript. All authors searched and reviewed the literature, discussed the contents of the manuscript, and approved submission. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Consejo de Desarrollo Científico y Humanístico de la Universidad del Zulia (CONDES-LUZ), AND Facultad de Agronomía, Universidad del Zulia, Venezuela.

**Institutional Review Board Statement:** Data collection was carried on in compliance with the criteria for animal care and welfare described in the Bioethics and Biosafety guide of the Fondo Nacional de Ciencia, Innovación y Tecnología (FONACIT) of Venezuela.

**Data Availability Statement:** Data are not available in public datasets, please contact the authors.

**Acknowledgments:** The authors are grateful to Matadero Industrial Centro Occidental (MINCO) for their valuable support during the live and carcass data collection, and donation of beef samples. We thank Martin OConnors for providing further training in carcass evaluation according to the USDA standards. The authors also gratefully acknowledge the cooperation of Daniel Huerta-Sánchez (Department of Economics and Finance, Florida Gulf Coast University) in the review of technical English to improve the statistical discussion, and Javier Aracena in the editing of the supplementary figures.

**Conflicts of Interest:** The authors declare no conflict of interest.
