Error estimation of regression parameters in a least-squares method

A method is described for determining the parameters a and b in the equation of linear regression y=a+bx. The parameters are determined by means of a experimental points set. It is supposed that for any point are known mean-square errors. That statement of the problem permits to include in the statistical analysis experimental data, obtained in nuclear-physical experiments and in the process of radiation testings of materials and equipment. The method proposed is based on the least-square approximation. For solving the problem is developed an algorithm, the efficiency and stability of which are tested for a concrete example.