Fully statistical approach for regression analysis

A new, fully statistical approach for regression analysis is presented and used for deriving the formula for the estimation error of the parameters of the fit and the associated joint confidence levels assuming a normal (Gaussian) distribution of the measurement errors and using a type A evaluation of the uncertainties. The key feature of the approach consists in two complementary parameterizations of the error space that are equivalent to a change of coordinates. This feature makes possible all the derivations and gives a marked statistical character to the approach. Although this approach is more lengthy and laborious than the usual one, it has the advantage that follows step by step all the intricacies, statistical and topological, of the regression analysis, and the final formulae do not appear as black boxes to be used such as they are, but all their components have established meanings.