n Original Research Paper 117 Chemometrics and Intelligent Laboratory Systems, 12 (1991) 117-120 Elsevier Science Publishers B.V., Amsterdam A fast method for the calculation of partial least squares coefficients E. Marengo * via Druento 115, 10151 Torino (Italy) and R. Todeschini Dipartimento di Chimica Fisica ed Elettrochimica, via Golgi 19, 20133 Milan0 (Italy) (Received 28 February 1991; accepted 5 August 1991) Abstract Marengo, E. and Todescbini, R., 1991. A fast method for the calculation of partial least squares coefficients. Chemometrics and Intelligent Laboratory Systems, 12: 117-120. Partial least squares (PLS) has proved to be more effective than ordinary least squares (OLS) in the study of complex systems. However, its use is made difficult by the splitting of the information into several latent variables. In an effort to overcome this difficulty, PLS coefficients which are analogues of the OLS have been introduced to provide an easy and immediate method to interpret numbers. This paper presents a method for the fast calculation of PLS coefficients. It is based on the use of PLS models to predict the response at proper points of the original variable space. The predicted responses directly render the PLS coefficients. INTRODUCTION In recent years the partial least squares (PLS) algorithm has gained great popularity due to its undoubted advantages over other regression methods like ordinary least squares (OLS), prin- cipal component regression (PCR) or step-wise regression (SWR). In fact it has been demon- strated that the PLS predictive ability is always at least equal to or better than the widely used OLS [1,2]. Moreover, PLS allows the contemporary treatment of more than one response variable and does not suffer from such well-known short- comings as high-variable collinearity which may affect OLS calculations, high object/variable ra- tios being necessary for stable results. The success of the PLS philosophy has led to the introduction of more refined regression meth- ods based on the PLS algorithm, involving non- linear applications [3] as in the case of CARS0 [4], SPECTRE [5], QPLS [6] and NLPLS [7]. The usual problem connected with the use of the partial least squares algorithm, even in the classical linear form, is caused by the difficulty of interpreting its results. When using PLS the in- formation on the regression model is generally