The Inverse Least-Squares Model

  • Alejandro C. Olivieri


The first and simplest inverse least-squares calibration model, also called multiple linear regression, is discussed in detail. Advantages and disadvantages are discussed for a model which today is still in use for some applications. Proposals are given for developing advanced calibration models.


Inverse least-squares Matrix inversion Calibration and validation Advantages and limitations Successive projections algorithm Ridge regression 


  1. Araújo, M.C.U., Saldanha, T.C.B., Galvão, R.K.H., Yoneyama, T., Chame, H.C., Visani, V.: The successive projections algorithm for variable selection in spectroscopic multicomponent analysis. Chemom. Intell. Lab. Syst. 57, 65–73 (2001)CrossRefGoogle Scholar
  2. Ben-Gera, I., Norris, K.: Direct spectrophotometric determination of fat and moisture in meat products. J. Food Sci. 33, 64–67 (1968)CrossRefGoogle Scholar
  3. Chung, H., Lee, H., Jun, C.H.: Determination of research octane number using NIR spectral data and ridge regression. Bull. Kor. Chem. Soc. 22, 37–42 (2001)Google Scholar
  4. Cozzolino, D., Kwiatkowski, M.J., Dambergs, R.G., Cynkar, W.U., Janik, L.J., Skouroumounis, G., Gishen, A.: Analysis of elements in wine using near infrared spectroscopy and partial least squares regression. Talanta. 74, 711–716 (2008)CrossRefPubMedGoogle Scholar
  5. Galvão, R.K.H., Araújo, M.C.U., Fragoso, W.D., Silva, E.C., José, G.E., Soares, S.F.C., Paiva, H.M.: A variable elimination method to improve the parsimony of MLR models using the successive projections algorithm. Chemom. Intell. Lab. Syst. 92, 83–91 (2008)CrossRefGoogle Scholar
  6. Golub, G.H., Heath, M., Wahba, G.: Generalized cross-validation as a method for choosing a good ridge parameter. Technometrics. 21, 215–223 (1979)CrossRefGoogle Scholar
  7. Haaland, D.M., Thomas, E.V.: Partial least-squares methods for spectral analysis. 1. Relation to other quantitative calibration methods and the extraction of qualitative information. Anal. Chem. 60, 1193–1202 (1988)CrossRefGoogle Scholar
  8. Hoerl, A.E., Kennard, R.W.: Ridge regression: biased estimation for nonorthogonal problems. Technometrics. 12, 55–70 (1970)CrossRefGoogle Scholar
  9. Kalivas, J.H.: Basis sets for multivariate regression. Anal. Chim. Acta. 428, 31–40 (2001)CrossRefGoogle Scholar
  10. Massart, D.L., Vandeginste, B.G.M., Buydens, L.M.C., De Jong, S., Lewi, P.J., Smeyers-Verbeke, J.: Handbook of Chemometrics and Qualimetrics. Elsevier, Amsterdam (1997)., Chaps. 17 and 36Google Scholar
  11. Norris, K.H., Hart, J.R.: Direct spectrophotometric determination of moisture content of grain and seeds. In: Principles and Methods of Measuring Moisture in Liquids and Solids. Proceedings of the 1963 International Symposium on Humidity and Moisture, vol. 4, pp. 19–25. Reinhold Publishing Co., New York (1965)Google Scholar
  12. Paiva, H.M., Soares, S.F.C., Galvão, R.K.H., Araújo, M.C.U.: A graphical user interface for variable selection employing the successive projections algorithm. Chemom. Intell. Lab. Syst. 118, 260–266 (2012)CrossRefGoogle Scholar
  13. Soares, S.F.C., Gomes, A.A., Araújo, M.C.U., Galvão Filho, A.R., Galvão, R.K.H.: The successive projections algorithm. Trends Anal. Chem. 42, 84–98 (2013)CrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Alejandro C. Olivieri
    • 1
  1. 1.Universidad Nacional de Rosario, Instituto de Química Rosario - CONICETRosarioArgentina

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