Comparative Analysis Between the Classical Least Squares (CLS) Algorithm and Partial Least Squares Analysis for the Study of CBD and THC Content in Cannabis Oil Samples Analyzed Using FT-IR ATR

Reliable analytical methods for quantifying the major phytocannabinoids cannabidiol (CBD) and Δ9-tetrahydrocannabinol (Δ9-THC) are essential to ensure quality control and regulatory compliance of cannabis-derived products. This study evaluated attenuated total reflectance Fourier-transform infrared spectroscopy (FTIR-ATR), combined with Partial Least Squares (PLS) and Classical Least Squares (CLS) chemometric models, to quantify cannabinoids in cannabis extract oils. FTIR-ATR spectra were collected over 4000–400 cm−1 and processed using principal component analysis (PCA), Multiplicative Scatter Correction (MSC), and multivariate calibration. The PLS model, built on the optimal spectral regions of 1000–1800 cm−1 and 3500 cm−1 and validated by leave-one-out cross-validation, achieved strong predictive performance (RMSEC = 0.559%, RMSECV = 0.675%; R2cal = 0.910, R2cv = 0.869), indicating good predictive ability with no evidence of overfitting. Notably, the variables with the highest VIP scores were mainly associated with the extract-to-diluent ratio rather than CBD-specific absorbance bands. The CLS model, in turn, showed excellent agreement for pure cannabinoid standards (MSE on the order of 10−6; β coefficients between 0.98 and 0.99) but performed poorly in complex matrices, yielding negative coefficients for several samples. This limitation stems from unmodeled matrix components and the near-collinearity of the THC and CBD infrared spectra, which renders the CLS system ill-conditioned and causes noise to redistribute between the two basis vectors. Taken together, these findings indicate that the FTIR-ATR/PLS approach offers a robust, rapid, and cost-effective alternative for routine cannabinoid analysis. In contrast, the CLS model remains valuable for residual-based detection of unmodeled spectral contributions that may signal sample anomalies or contamination.