UM-4 : Polynomial Regression

Abstract

For any non linear function Y=f(X) regression may be obtained by fitting a polynomial. The general form of the polynomial regression is as given under:-

Y = a

o

+ a + a + + a lX 2X2 mXm + E

where, Y is a dependent variable.

The coefficients ao, al, ,am are the regression coefficients and are determined by the least square method of parameter estimation. The power order m is chosen so as to minimize the sum of squares of deviations from the line. The user's manual gives the details of a computer programme for polynomial regression. In the programme powers of an independent variable are generated to calculate polynomials of successively increasing degrees. If there is no reduction in the residual sum of squares between two successive degrees of polynomials, the programme terminates the problem before completing the analysis for the highest degree polynomial specified. The output of the program includes regression coefficients for successive degree polynomials, analysis of variance table for successive degree polynomials, table of residuals for the final degree polynomial and plot of Y values and Y estimates versus base variable X.

This manual also describes various statistics given in the programme output with example, input data specifications and output description. The programme is written in FORTRAN IV. The manual also gives hardware and software requirements of the programme.