Basic Chemometric Techniques in Atomic Spectroscopy
CHAPTER 2: Classical Linear Regression by the Least Squares Method
Published:17 Jun 2013
José Manuel Andrade‐Garda, Alatzne Carlosena‐Zubieta, Rosa María Soto‐Ferreiro, Javier Teran‐Baamonde, Michael Thompson, 2013. "Classical Linear Regression by the Least Squares Method", Basic Chemometric Techniques in Atomic Spectroscopy, Jose Andrade-Garda
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The objective of this chapter is to present some fundamental issues that every atomic spectrometry practitioner should keep in mind when developing a calibration. However familiar this may sound it is definitely a critical step, as important as the development of proper experimental measurement conditions.
The fundamentals of the least squares fit are presented and discussed, with special emphasis on the practical limitations we currently experience in laboratories. Many discussions will be devoted to validation of the model and to clarification of some misconceptions that appear sometimes in the literature. The widely applied standard additions method is reviewed and discussed to show that extrapolation is a risky practice that can be avoided very easily.
Polynomials of order two (quadratic) provide the analyst with a readily available means of matching points from a curved calibration to a function suitable for interpolation. However, extra caution is necessary to avoid lack of fit, and even small extrapolations beyond the calibrated range are unwise.
Finally, two appendixes are included to discuss in some detail the correct use of the Mandel’s test for linearity and how to compare two regression lines (typically, the aqueous calibration fit and the standard additions one).