It is intended in the following paragraphs to give an outline of a very general statistical method which originated in agricultural experimentation and which has since been used in many other fields, including that of mortality investigations. We will start with a special case, that of regression analysis involving only one independent variable. Well-known formulae will be developed with the aid of orthogonal polynomials and it will be shown how this tool can be used for generalizations. A new theorem referring to these polynomials, and its significance for the analysis of variance, will also be mentioned.