An accurate and straightforward approach to Line regression analysis of error affected experimental data

The line regression problem, when both variables are subjected to errors, is re-examined and solved with a straightforward analytical approach that uses the minimisation of the shortest distance between each experimental point and the theoretical line. It is found, without any approximation or updating of parameters and variables but on the basis of error propagation law only, to be possible to obtain exact results by means of a simple procedure which is suitable for programmable calculators. Furthermore, using a more appropriate expression for weighting the observations, the effective variance algorithm is directly shown.