The article analyzes the conditions, peculiarities and application techniques of the step-by-step method of iteration to the equations simple regression which are not reduced to any linear forms of their own parameters and variables. Such a practical task arises often enough during the investigation of the class of Tornquist functions. In practice, such tasks arise in economics during research and analysis of consumer demand on a narrow market segment. In particular, the 2nd equation of this class successfully describes a Russian family’s cost for the purchase of relatively expensive tourist products for foreign travels. The method of progressive approximation regards the plotting of the normal equations set with application of the Jordan–Gauß process and the expansion into Taylor’s infinite series of the function of the corrections for parameters of the desired equation. The amendments themselves are allowing to calculate the parameters of the Tornquist functions (2nd equation) and accomplish the forecast estimations of budget charges for purchase of the expensive tourist’s products. The considerations expressed in this article lead to three local outputs on the applicability of the procedure in question in dealing with similar ones on the content of economic and statistical research problems of supply and demand a high level of tourist products: in the epistemological and methodological aspects of the formulated problem of estimating the parameters in a typical nonlinear this technique (sequential iterative procedure) does not give a final decision, i. e. the results are not complete and not statistically pure; because of the inherent rounding even reliable and accurate measures of economic parameters are approximate. When using iterative procedures, approximation error is added to the actual implementation of the method, and its effectiveness depends on the more or less successful choice of initial conditions approximation and the convergence rate of the iteration process; finally, a common approach to stochastic approximation of a nonlinear function is understood by the author through the use of Taylor series and polynomials search for suitable forms. In particular, the linearization of the equations of simple regression with typical nonlinearity must be carried out by the power series expansion with all members of the first order of smallness eliminated from further calculations.