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Paper: Looking for a Slope Change in a Linear Relationship
Volume: 512, Astronomical Data Analysis Software and Systems XXV
Page: 229
Authors: Cardiel, N.; Marino, R.A.; Pascual, S.; Ceballos, M.T.; Gil de Paz, A.; Sánchez, S.F.
Abstract: The initial understanding of many scientific problems relies on the simplifying assumption that some data of interest can initially be modelled by a linear relationship. In some cases, the simultaneous fit of two lines, joined at an intermediate point, constitutes the next natural step towards a more elaborate modelling. In this sense, the method of Lagrange multipliers can be used to obtain such a fit with the location of the intermediate point left as a free parameter. This work shows the results of simple simulations in which the simultaneous fit to two joined lines is compared to the simultaneous fit of two independent lines (i.e., two lines that do not necessarily coincide at the intermediate point), and also to the traditional single ordinary least squares fit. These simulations reveal some biases that should be taken into account when using that kind of fitting procedure.
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