The partial least squares regression (PLSR) algorithms of Wold and Martens provide alternative, powerful tools for handling ill-conditioned multivariate regression data, see e.g. Martens and Nees (1989) and Hoskuldson (1996) for overviews of the fundamental multivariate calibration concept, in which are presented the above two slightly different versions of the PLSR method. Both algorithms assume collinear regressor variables generated by underlying latent variables, and although they are different with respect to the score and loading matrices involved, they give identical predictors. There is certainly no practical need for yet another algorithm that provide the same predictor as the well-known algorithms of Wold and Martens. However, these algorithms, as presented in the chemometrical literature, make no use of the dynamic systems theory available for readers from the control community, and the main aim of the present paper is therefore to provide a predictor derivation at first especially for this category of readers. This actually also results in a simplified version of the Martens prediction algorithm making use of the so-called loading weight vectors only, which would appear to be of general interest (see Esbensen (2000) for a discussion of loadings and loading weights). The score vectors, which are also essential elements of chemometrics, are easily computed once a preliminary predictor is found. The new algorithm has a lot in common with an algorithm developed by Helland (1988), and a similar algorithm by Di Ruscio (2000). Again, the reason behind the present modifications is mainly didactic. The key step in the simplification is the use of an explicit latent variables model, which facilitates an early introduction of the Helland predictor form using only loading weight vectors. The present exposition, we believe, constitute a novel, easy, and complete introduction to the prediction aspect of multivariate calibration.