Abstract
The method of least squares is the basic tool of developing and verifying models by fitting theoretical curves to data. Fitting functions that linearly depend on model parameters (linear regression) is treated first, discussing the distinct cases of known and unknown experimental uncertainties, finding confidence intervals for the optimal parameters, and estimating the quality of the fit. Regression with standard and orthogonal polynomials, straight-line fitting and fitting a constant are analyzed separately. Linear regression for binned data, linear regression with constraints, general linear regression by using singular-value decomposition, and robust linear regression are presented, followed by a discussion of non-linear regression.
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Širca, S. (2016). Method of Least Squares. In: Probability for Physicists. Graduate Texts in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-31611-6_9
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DOI: https://doi.org/10.1007/978-3-319-31611-6_9
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