Partial least-squares in latent variables (PLS) is sometimes called partial least-squares regression, or PLSR. This chapter summarizes the similarities of and differences between Principal Component Regression and PLS. Just as the spectral and concentration data points are exactly congruent with each other within the planes containing the data points, the spectral and concentration eigenvectors for this noise-free, perfectly linear case must also be exactly congruent. The perfectly linear, noise-free relationship between the projections is readily apparent. The chapter considers what happens when there is noise on both the absorbances and the concentration values. PLS attempts to restore optimal congruence between each spectral factor and its corresponding concentration factor by rotating them towards each other until the angle between them is zero. The whole idea behind PLS is to try to restore, to the extent possible, the optimum congruence between the each spectral factor and its corresponding concentration factor.