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Least Squares Fitting-Perpendicular Offsets

Dimitris Sardelis
Organization: American College of Greece
Theodoros Valahas
Organization: American College of Greece
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The aim of the present article is (i) to reproduce the results of the Mathworld presentation of the Least Squares Fitting-Perpendicular Offsets[1] by using a more standardized notation that simplifies matters considerably, (ii) to extend [1] by showing that only one of the two solutions derived there properly classifies as optimal-minimum, (iii) to complement [1] by deriving the appropriate coefficient of determination - the measure of the model's explanatory power- and the corresponding ANOVA for regression -the standard tool for performing hypotheses tests regarding the statistical significance of the relation between the variables involved, and, (iv) to compare the perpendicular offsets approach with the traditional approach mainly on efficiency grounds. In particular, a straight forward comparison of the determination coefficients of the two approaches reveals that the perpendicular offsets approach provides always a better fit. Finally, (v) a Mathematica coded demonstration follows which yields the essential parameters of the method for any given data.

*Applied Mathematics > Numerical Methods
*Mathematics > Calculus and Analysis > Calculus of Variations

Least Squares, ANOVA
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Least Squares Fitting-Perpendicular Offsets.nb (33 KB) - Mathematica Notebook