  Partial Least Square (PLS) is a dimension reduction method used to remove
multicollinearities in a regression model. However contrary to Principal
Components Analysis (PCA) the PLS components are also choosen to be optimal for
predicting the response $Y$. In this paper we provide a new and explicit
formula for the residuals. We show that the residuals are completely determined
by the spectrum of the design matrix and by the noise on the observations.
Because few are known on the behaviour of the PLS components we also
investigate their statistical properties in a regression context. New results
on regression and prediction error for PLS are stated under the assumption of a
low variance of the noise.
