The standard deviation of prediction errors (SDEP) is used to evaluate and compare the predictive ability of some regression models, namely MLR, ACE and linear and non-linear PLS, the last being the best one. The parameter is determined by a cross-validation approach as an average of several runs obtained on forming groups in a random way. The variation in SDEP with the number of latent variables in PLS is also discussed.
KEY WORDS
Predictive ability Regression PLS SDEP Cross-validation 1. INTRODUCTION
Correlation analysis is a well-established term in various branches of chemistry and especially in physical organic chemistry, where it encompasses linear free energy relationships (LFERs) and quantitative structure-activity relationships (QSARs). Unfortunately, end-user chemists call correlation what is in fact regression analysis, and until a few years ago did not care too much for regression models other than ordinary least squares. l S 2
The availability of different regression methods, e.g. multiple linear regression (MLR), partial least-squares projection to latent structures (PLS), 4 -7 alternating conditional expectation (ACE), etc., raises the problem of their comparison in order to investigate their power and limits. However, the choice of the appropriate statistical parameters t o be used for this purpose requires some discussion.
Various parameters have been suggested to evaluate the 'goodness' of a modeL2 In the physical organic chemistry area the 'goodness of fit' has been expressed by the correlation coefficient, the standard deviation, the F-test, the fraction of variance explained by the model, etc. Nevertheless, all these parameters are appropriate to estimate only the adequacy of the *Presented in part at the Euchem Conference held in Trieste, 1988, and at the Symposium on Chemometrics held in Holmsund, 1989.