User`s guide

3 Fitting Data
3-54
The fit, residuals, and numerical results are shown below.
The fit appears to be reasonable for some of the data points but clearly does not
describe the entire data set very well. As predicted, the numerical results
indicate a cycle of approximately 12 months. However, the residuals show a
systematic periodic distribution indicating that there are additional cycles that
you should include in the fit equation. Therefore, as a second attempt, add an
additional sine and cosine term to y
1
(x)
and constrain the upper and lower bounds of c
2
to be roughly twice the bounds
used for c
1
.
The fit for one cycle.
The residuals indicate that at
least one more cycle exists.
The numerical results
indicate a 12 month cycle.
y
2
x() y
1
x() a
2
2π
x
c
2
-----


b
2
2π
x
c
2
-----


sin+cos+=