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Linear Regression with Optimal Rotation

Author

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  • George Livadiotis

    (Southwest Research Institute, Space Science & Engineering, San Antonio, TX 78238, USA)

Abstract

The paper shows how the linear regression depends on the selection of the reference frame. The slope of the fitted line and the corresponding Pearson’s correlation coefficient are expressed in terms of the rotation angle. The correlation coefficient is found to be maximized for a certain optimal angle, for which the slope attains a special optimal value. The optimal angle, the value of the optimal slope, and the corresponding maximum correlation coefficient were expressed in terms of the covariance matrix, but also in terms of the values of the slope, derived from the fitting at the nonrotated and right-angle-rotated axes. The potential of the new method is to improve the derived values of the fitting parameters by detecting the optimal rotation angle, that is, the one that maximizes the correlation coefficient. The presented analysis was applied to the linear regression of density and temperature measurements characterizing the proton plasma in the inner heliosheath, the outer region of our heliosphere.

Suggested Citation

  • George Livadiotis, 2019. "Linear Regression with Optimal Rotation," Stats, MDPI, vol. 2(4), pages 1-10, September.
    • Handle: RePEc:gam:jstats:v:2:y:2019:i:4:p:28-425:d:271803
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    References listed on IDEAS

    as
    1. Livadiotis, George, 2007. "Approach to general methods for fitting and their sensitivity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(2), pages 518-536.
    2. Livadiotis, George, 2016. "Non-Euclidean-normed Statistical Mechanics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 445(C), pages 240-255.
    3. Livadiotis, George & Moussas, Xenophon, 2007. "The sunspot as an autonomous dynamical system: A model for the growth and decay phases of sunspots," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 379(2), pages 436-458.
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    Cited by:

    1. George Livadiotis, 2020. "General Fitting Methods Based on L q Norms and their Optimization," Stats, MDPI, vol. 3(1), pages 1-16, January.

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