# Re: [S] What is Harmonic regression analysis

Joseph Lucke (LUCKE@pgh.auhs.edu)
Fri, 06 Mar 1998 09:41:39 -0500

Chansoo,

Harmonic regression (aka trigonometric regression, cosinor regression) is a linear regression model in which the predictor variables are trigonometric functions of a single variable, usually a time-related variable. Harmonic regression is used in modelling biological phenomena, which tends to exhibit periodic rhythms.

A simple harmonic regression model is

Y= mu + alpha*cos(2*pi/P)*t + beta*sin(2*pi/P)*t + epsilon,

where pi is 3.1415.... and P is the period for sin & cos.

More general models are

Y=mu + Sum( alpha(h)*cos(2*pi*h/P)*t + beta(h)*sin(2*pi*h/P)*t) + epsilon,

where h = 1,2,3,4 ... H

Harmonic models are much like polynomial models except that instead of using powers of t, you use the trigonometric functions of t. The terms in the harmonic model are orthogonal to one another.

An excellent brief intro is given by FA Graybill in Theory and Application of the Linear Model, 1976, Duxbury Press, MA. See his chapter 8, section 8.

Joe Lucke

>>> Chansoo Kim <cskstat@chungang.edu> 3/6/98 7:06:41 AM >>>
Hello,
Any one can explain what is Harmonic regression analysis?
How can I perform this procedure with S+?
Thank you.

!

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