Interest in orthogonal polynomials has been stimulated in recent years, especially among biologists, by Fisher's use of them in evaluating a regression integral (7), application and extension of which have followed each other in rapid succession (4) (9). Aside from this specialized use, orthogonal polynomials are valuable in the study of time series both in economics and in agronomy where one may wish to study the effect of environmental conditions on the yields of crops. If there has been a gradual depletion or improvement in the level of fertility over a period of years, it should be evaluated and deviations from trend used in the study of environmental effects. Any reduction of the labor of calculation involved in such investigations seems worthy of some effort.
If the independent variable is equally spaced, such as in time or space, the convenient method of curve fitting by orthogonal polynomials can be used. The advantage over the usual regression methods of fitting non-orthogonal polynomials arises from the fact that orthogonal polynomials are so constructed that any term of the polynomial is independent of any other term. This property of independence permits one to compute each regression coefficient independently of the others and also facilitates testing the significance of each coefficient. In addition the computing time for curve fitting by means of orthogonal polynomials is less, especially if a polynomial of degree greater than the second is fitted.
Anderson, R. L. and Houseman, E. E.
"Tables of orthogonal polynomial values extended to N=104,"
Research Bulletin (Iowa Agriculture and Home Economics Experiment Station): Vol. 25
, Article 1.
Available at: https://lib.dr.iastate.edu/researchbulletin/vol25/iss297/1