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In a recent paper [JUKIĆ, D.:  A necessary and sufficient criterion for the existence of the global minima of a continuous lower bounded function on a noncompact set , J. Comput. Appl. Math.  375  (2020)], a new existence level was introduced and then was used to obtain a necessary and sufficient criterion for the existence of the global minima of a continuous lower bounded function on a noncompact set. In this paper, we determined that existence level for the residual sum of squares of the power-law regression with an unknown location parameter, and so we obtained a necessary and sufficient condition which guarantee the existence of the least squares estimate.

An existence level for the residual sum of squares of the power-law regression with an unknown location parameter