Studies in the theory of least squares

Abstract

The content of this article can be divided into two parts: the first is the derivation of a formula (first proposed by the author) for the average error of the balanced value of all measured quantities included in the balance, the second is a new derivation of the formula for the average error of one observation. Using this relation (see article), we give a new simple derivative of the formula mentioned above, which is important for the theory of least squares.