Transforming the Method of Least Squares to the Dataflow Paradigm

Transforming the Method of Least Squares to the Dataflow Paradigm

Ilir Murturi
Copyright: © 2021 |Pages: 8
DOI: 10.4018/978-1-7998-7156-9.ch008
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Abstract

In mathematical statistics, an interesting and common problem is finding the best linear or non-linear regression equations that express the relationship between variables or data. The method of least squares (MLS) represents one of the oldest procedures among multiple techniques to determine the best fit line to the given data through simple calculus and linear algebra. Notably, numerous approaches have been proposed to compute the least-squares. However, the proposed methods are based on the control flow paradigm. As a result, this chapter presents the MLS transformation from control flow logic to the dataflow paradigm. Moreover, this chapter shows each step of the transformation, and the final kernel code is presented.
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The MLS is known to be published for the first time by Adrien Marie Legendre (Legendre, 1805). However, the method was not used as well as no mathematical proof was given. Legendre formulate the problem and starts with the linear equation of the form 978-1-7998-7156-9.ch008.m01 where the requirement determines unknown variables 978-1-7998-7156-9.ch008.m02 that 978-1-7998-7156-9.ch008.m03 decreases to zero or a very small number for each equation. However, such equations are derived without the explicit use of calculus. The equations are generated by multiplying the linear form in the unknowns by the coefficient 978-1-7998-7156-9.ch008.m04. Each of the unknowns are summed over all the observations and then setting the sums equal to zero (Harter, 1975). When the results produce errors, the proposed approach rejects the equations that produce such error while determining the unknowns from the rest of the equations. On the other side, Puissant, discusses theoretical aspects of the MLS (Puissant, 1805). He also presents an application to the determination of the earth's ellipticity from measures of degrees meridian.

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