During the eighteenth century, algebraic and geometric function fitting methods were developed to express cause- and effect-relationship. The most celebrated method of least squares for function fitting was due to Legendre [1] and was discussed in reference to determination of the orbits of comets. Legendre asserted that the sum of the squares of the errors was the simplest criterion. Gauss [6] proposed that the sum of the fourth powers, the sum of the sixth powers, or, in general, the sum of even powers as alternatives to the sum of squared errors. In data analysis, standardizing data are beneficial, in particular, in the improvement of results and in understanding and reporting statistical models. Computations are often much simpler with standardized variables. Results, obtained from standardized variables, are independent of metric units and can be easily converted back to the original metric variables. In this paper, we consider new results from the Lp-regressions using standardized variables. For illustration, we will present the analysis of the experimental data on modeling the relationship between the material supplied and the percentage of material absorbed by the liquid in a chemical process. The Lp-norm regression models with standardized variables will be fitted and their performance will be studied, in particular, in making tail-end predictions.

Lp-regression, standardized variable, tail-end prediction.