  I consider the task of experimental data fitting. Unlike the traditional
approach I do not try to minimize any functional based on available
experimental information, instead the minimization problem is replaced with
constraint satisfaction procedure, which produces the interval hull of
solutions of desired type. The method, called 'box slicing algorithm', is
described in details. The results obtained this way need not to be labeled with
confidence level of any kind, they are simply certain (guaranteed). The method
easily handles the case with uncertainties in one or both variables. There is
no need for, always more or less arbitrary, weighting the experimental data.
The approach is directly applicable to other experimental data processing
problems like outliers detection or finding the straight line, which is tangent
to the experimental curve.
