Objective
Introduction
Scatter Plot
Concentration Ellipse
Examples
Exercises
This module examines how the association between two quantitative variables is measured and assessed. The relationship is viewed in a scatter plot.
Two numeric variables may be (jointly) normally distributed just as a single numeric variable may be normally distributed. If this is the case, the variable values plotted jointly in a scatter plot will lie approximately in an concentration ellipse. The size of the ellipse depends on the proportion of the data expected to be within its boundary. A 50% concentration ellipse (containing approximately 50% of the data values) is smaller than a 95% concentration ellipse, but the orientations of the ellipses do not depend on the concentration values.
In the above applet, select Correlation from the Model menu and then select 95% corr. ellipse from the Options menu. You will see the 95% concentration ellipse for the data. Select the upper right data point and drag it around to see how the ellipse changes.
Exercise #1 requires you to estimate the strength of the linear relationship between long jump distance and Olympic year.