On the theory of the method of least squares

Abstract

The content of the present article can be divided into two parts: the first is the derivation of a formula (first proposed by the author) for the mean error of the adjusted value of all measured quantities included in the adjustment; the second is a new derivation of the formula for the mean error of a single observation. Using this relationship (see the article), we provide a new, simple derivation of the aforementioned formula, which is important for the theory of least squares.

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