Roughly speaking, the algorithm is the following: “The components of X are used to predict the scores on the Y components, and the predicted Y component scores are used to predict the actual values of the Y variables. In constructing the principal components of X, the PLS algorithm iteratively maximizes the strength of the relation of successive pairs of X and Y component scores by maximizing the covariance of each X-score with the Y variables. This strategy means that while the original X variables may be multicollinear, the X components used to predict Y will be orthogonal”.

The dataset used correspond to 6 orange juices described by 16 physicochemical descriptors and evaluated by 96 judges [Source : Tenenhaus, M., Pagès, J., Ambroisine L. and & Guinot, C. (2005). PLS methodology for studying relationships between hedonic judgements and product characteristics. Food Quality an Preference. 16, 4, pp 315-325].

**Keywords**: pls regression, factorial analysis, multiple linear regression

**Components**: PLS Regression

**Tutorial**: en_Tanagra_PLS.pdf

**Dataset**: orange.bdm

**References**:

M. Tenenhaus, « La régression PLS – Théorie et pratique », Technip, 1998.S.

H. Abdi, "Partial Least Square Regression".

Garson, « Partial Least Squares Regression (PLS) », http://www2.chass.ncsu.edu/garson/PA765/pls.htm