Prediction error in least squares regression: Further critique on the deviation used in The Unscrambler

In a recent critique on the deviation used in The Unscrambler a correction factor was proposed that gave improved results. However, this investigation was carried out under the standard assumption of the classical regression model, i.e. the measurement errors in the response and predictor variables were neglected. In many chemical applications this assumption is too restrictive. Moreover, even in absence of measurement errors, some problems remain and, consequently, further critique on the deviation used in The Unscrambler is in order. This paper recommends an extension of a recently derived expression for prediction variance that includes all measurement errors and is valid for multivariate calibration using ordinary least squares, principal component regression and partial least squares. The theory is illustrated on practical examples taken from the literature.