Fitting an Equation to Data Impartially

نویسندگان

چکیده

We consider the problem of fitting a relationship (e.g., potential scientific law) to data involving multiple variables. Ordinary (least squares) regression is not suitable for this because estimated will differ according which variable chosen as being dependent, and dependent unrealistically assumed be only has any measurement error (noise). present very general method estimating linear functional between noisy variables, are treated impartially, i.e., no distinction independent The follow distribution, but all variables equally reliable. Our approach extends geometric mean dimensions. This especially useful with measured in different units, it naturally scale invariant, whereas orthogonal not. our based on minimizing distances, symmetric concept correlation. coefficients easily obtained from covariances or correlations, correspond means associated least squares coefficients. ease calculation hopefully allow widespread application impartial estimate relationships neutral way.

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ژورنال

عنوان ژورنال: Mathematics

سال: 2023

ISSN: ['2227-7390']

DOI: https://doi.org/10.3390/math11183957