1. Exploratory Data Analysis
1.3. EDA Techniques
1.3.3. Graphical Techniques: Alphabetic
1.3.3.26. Scatter Plot

1.3.3.26.7.

Scatter Plot: Sinusoidal Relationship (damped)

Scatter Plot Showing a Sinusoidal Relationship

Discussion

The complex relationship between X and Y in this plot of the LUTHER.DAT data set appears to be basically oscillatory, and so one is naturally drawn to the trigonometric sinusoidal model:

$$Y_i=C+\alpha \sin (2\pi \omega t_i+\varphi )+E_i$$

Closer inspection of the scatter plot reveals that the amount of swing (the amplitude α in the model) does not appear to be constant but rather is decreasing (damping) as X gets large. We thus would be led to the conclusion: damped sinusoidal relationship, with the simplest corresponding model being

$$Y_i=C+(B_0+B_1\ast t_i)\sin (2\pi \omega t_i+\varphi )+E_i$$