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Vol. 187, Issue 4, April 2015, pp. 82-93




The Study of Classical Polynomial Regression Models Without a Constant Term. Building Empirically Effective Estimates of the Parameters of Regression Models

Orest Kochan

Department of Information-Measuring Engineering, Lviv Polytechnic National University, S. Bandery Str., 12, Lviv, 79013, Ukraine
Tel.: +380 681366892

E-mail: orestvk@gmail.com


Received: 14 January 2015 /Accepted: 27 March 2015 /Published: 30 April 2015

Digital Sensors and Sensor Sysstems


Abstract: There is a drawback of direct method of least squares application for polynomial regression without a constant term found: sum of residuals, as a rule, is not zero. This contradicts to standard assumption of equality to zero of residual expectation and makes correct calculation the coefficient of determination impossible. It is discovered that applied software, all versions of MS Excel in particular, do not take into account this drawback. Classical method of least squares is modified to design statistical estimates of unknown parameters and investigated their properties. Obtained estimates and their numerical characteristics are expressed using corresponding least squares characteristics and parameters. Effective algorithm for designing other linear estimates of unknown coefficients is developed in this paper. One of these variants has smallest standard deviations of coefficients of empirical regression equation for a fixed sample.


Keywords: Classical polynomial regression, The method of least squares, Least-squares estimates, Modified least squares, Linear unbiased prediction, Minimization of standard deviations.


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