In Popławski and Kaczmarczyk (2013) a method referred to as UEK was presented and used as a tool in the analysis of sustainable rural development. The purpose of this paper is to demonstrate the methodological inappropriateness of that method. In the linear regression model, the matrix of explanatory variables can have either less than full or full column rank. While all regression parameters are non-estimable in the first case, the well-known and widely used ordinary least squares method can be applied in the second one.


linear regression; Moore–Penrose pseudoinverse; UEK method

Albert, A. (1972). Regression and the Moore-Penrose Pseudoinverse. New York: Academic Press.

Geweke, J. (2005). Contemporary Bayesian Econometrics and Statistics. New York: John Wiley & Sons, Inc.

Goldberger, A. S. (1964). Econometric Theory. New York: J. Wiley.

Harville, D. A. (2008). Matrix Algebra From a Statistician’s Perspective. New York: Springer Science+Business Media, LLC.

Kawa, B., Kaczmarczyk, B. (2012). Wskaźnikowy i modelowy sposób oceny sytuacji finansowej Gminy Kraków na koniec 2011 roku [An Assessment of the Financial
Standing of the Gmina of Krakow at the End of 2011 with the Use of the Ratio and Model-based Analysis]. Zesz. Nauk. PTE,13, 199–213 [in Polish].

Kaczmarczyk, B. (2012). Wycena wartości rynkowych spółek z wykorzystaniem macierzy MP-odwrotnych [An evaluation of market values of companies using the MP-pseudoinverse matrix]. In: T. Grabiński, L. Woszczek, S. Sorys, A. Tabor (red.), W poszukiwaniu skutecznych narzędzi i modeli analizy zjawisk społeczno-gospodarczych (pp. 145–160). Chrzanów: Wyższa Szkoła Przedsiębiorczości i Marketingu [in Polish].

Pajor A. (2017). A Note on the UEK Method. Barom. Reg. Anal. Progn., 15(3), 7–10.

Popławski, Ł., Kaczmarczyk, B. (2013). Możliwości zastosowania metody UEK dla gmin województwa świętokrzyskiego – na przykładzie danych za 2006 rok [Possibilities of Adapting Authorized Method of the Cracow University of Economics for Świętokrzyskie Voivodeship Communities, According to the 2006 Data]. J. Agribus. Rural Dev., 4(30), 207–218 [in Polish].

Searle, S. (1966). Estimable functions and testable hypotheses in linear models. Tech. Rep. BU-213-M. Cornell University, Biometrics Unit.

Zellner, A. (1971). An Introduction to Bayesian Inference in Econometrics. New York: John Wiley and Sons, INC.

Published : 2019-07-03

Pajor, A., & Kawa, B. (2019). CONSIDERATIONS ON THE VALIDITY AND APPLICABILITY OF THE UEK METHOD. Journal of Agribusiness and Rural Development, 52(2), 173–177.

Anna Pajor
Department of Mathematics, Cracow University of Economics, Rakowicka 27 St., 31-510 Kraków  Poland
Barbara Kawa 
Cracow University of Economics  Poland

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