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Procedure: Nonlinear Least Squares Regression
Certification Method & Definitions

Data: 1 Response Variable (y)
1 Predictor Variable (x)
168 Observations
Average Level of Difficulty
Observed Data

Model: y = f(x;beta) + e  =  beta(1) + beta(2) cos[2 pi x / 12] + beta(3) sin[2 pi x / 12]
											beta(5) cos[2 pi x / beta(4)] + beta(6) sin[2 pi x / beta(4)]
											beta(8) cos[2 pi x / beta(7)] + beta(9) sin[2 pi x / beta(7)] + e

These data are monthly averaged atmospheric pressure differences between Easter Island and Darwin, Australia. This difference drives the trade winds in the southern hemisphere. Fourier analysis of the data reveals 3 significant cycles. The annual cycle is the strongest, but cycles with periods of approximately 44 and 26 months are also present. These cycles correspond to the El Nino and the Southern Oscillation. Arguments to the SIN and COS functions are in radians.