A probabilistic relation between the error estimates of physical quantities obtained by different methods

A distribution function for the ratio of the error estimates of physical quantities calculated using the confidence region method (based on the chi-square statistics) to the errors estimates calculated using the least-squares method is obtained. If the analytical form of this function is used, then the most probable values of the error estimates calculated by the confidence region method can easily be obtained using only the error estimates calculated by the least-squares method (without new observational data processing). Apart from a purely mathematical interest, this paper is of interest to experimenters involved in the processing of observational data, in particular, in the processing of astrophysical observations.