## 3 Results and Discussion
### Prediction Models
#### 3.4.2 Prediction Model for Fatty Acids  
For FAs, the outliers ranged from 0 to 4 for the calibration and validation sets, and the LVs used for each model ranged from 4 to 7 (Table 7). Considering the PLSR models for FAs, the NIRflex system achieved good R\({}^{2}\) values during calibration for all FAs. The 18:3 n-6 showed R\({}^{2}\)c = 0.91, while 18:1 cis-11 and the SFA and PUFA classes had R\({}^{2}\)c values \(<\) 0.85. Unfortunately, in cross-validation using the \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**Calibration Set**} & \multicolumn{2}{c}{**Independent Set for Validation**} \\ \hline
**\%** & **RPDcv** & **RERcv** & **RPDp** & **RERp** \\ \hline DM * & 4.29 & 19.36 & 4.06 & 15.62 \\ Ash & 3.04 & 14.14 & 2.95 & 13.28 \\ CP & 3.32 & 19.54 & 3.12 & 16.42 \\ EE & 2.92 & 18.28 & 2.70 & 13.10 \\ CF & 3.14 & 14.64 & 2.80 & 12.18 \\ aNDF & 3.22 & 16.55 & 3.01 & 13.70 \\ ADF & 2.98 & 13.89 & 2.71 & 12.62 \\ ADL & 2.83 & 14.27 & 2.80 & 13.57 \\ Starch & 3.45 & 16.25 & 3.22 & 14.68 \\ \hline \hline \end{tabular}  
* = expressed as % of TMR; RPDcv = SD/SECV; RPDp = SD/SEP; RERcv = range (max-min value)/SECV; RERp = range (max-min value)/SEP; DM = dry matter; CP = crude protein; EE = ether extract; CF = crude fibre; aNDF = Neutral Detergent Fibre; ADF = Acid Detergent Fibre; ADL = Acid Detergent Lignin.  
\end{table} 
Table 6: Residual Predictive Deviation (RPD) and Range of Reference Values (RER) on cross-validation (cv) and prediction (p) for chemical composition (% g of DM) of Total Mixed Rations (TMRs). five-fold approach, the R\({}^{2}\)cv values slightly decreased, and the SECV increased compared to the SEC. Applying the PLSR models to the validation set, the R\({}^{2}\) for 18:3 n-6 was confirmed at 0.90. Lower predictive performance, with R\({}^{2}\) < 0.80, was recorded for 18:1 cis-11 and SFAs. The other FAs had R\({}^{2}\) values ranging from 0.80 to 0.84. When comparing SEP to SECV, lower values were observed for 16:1, 18:3 n-6, and the PUFA class. This occurred because the validation set exhibited a lower S.D. for certain FAs compared to the data in the calibration set (Table 4). However, SEP never exceeded 1.2. Acceptable to good predictive performances were recorded for all FAs in cross-validation. The RPDcv (Table 8) was above 3 for nearly all FAs, except for 14:0, 16:0, and the SFA and PUFA classes. In prediction, however, RPDp dropped below 2.5 for 18:1 cis-11, SFA, and MUFA classes, whereas PUFAs such as 18:2 n-6, 18:3 n-2, and 18:3 n-3 exceeded the threshold of 3, classifying the models as good. This result was influenced by the high variability of the data. Other FAs showed an average RPDp of 2.66. Additionally, for all FAs, the RER never fell below the threshold of 10. The slightly lower precision in FA prediction compared to chemical composition is likely due to the more complex and variable nature of FA spectral absorption in the NIR range. Indeed, FA signals are weaker and more influenced by overlapping bands. Some dairy farms have implemented feeding strategies to improve animal welfare and enrich milk-derived products with nutraceutical compounds. One such strategy involves incorporating a significant percentage of flaxseed, which is rich in n-3 fatty acids, into the diet. This practice has led to an increase in 18:3 n-3 levels, which typically constitute around 3% of the diet, to values exceeding 15% [51]. As n-3 FAs increase, n-6 FAs tend to decrease. NIR prediction models benefit from this high variability in the dataset, allowing the PLSR model to effectively predict variations in certain PUFAs in the TMRs fed to lactating buffaloes. It has been widely demonstrated in experimental settings that high-yielding dairy animals receiving n-3 FA supplementation in their diet--either in the form of oil or oilseeds--experience metabolic, anti-inflammatory, and reproductive benefits. NIR spec