Lines, Sines, and Curve Fitting 2 — reversi
It seems natural, seeing GISTEMP over the 20th Century, to take the linear trend first. But what if we reverse the order in which we take the trends? Take the sine first and then the linear trend?
First, the sine wave on the data from 1900 to 2000
Next we extract the residuals, the difference between the actual data points and the sine wave, and fit a linear trend.
The linear trend on the residuals looks like this:
Now, just to add them together like this:
How good is the fit?
The correlation of the sine to the data is 0.58.
The correlation of the linear trend is 0.76.
And the correlation of the line and sine to the original data is 0.86.
What are the parameters?
The amplitude (A) of the sine is 0.16C.
The phase shift (b) is 28 years.
And the period (T) is 50 years.
The slope (m) of the linear trend is 0.43 degC per century.
The script is here.

2011 February 13 at 10:51 amLines, Sines, and Curve Fittings 13 – Fourier « The Whiteboard