Basic Analysis and Graphing - SAS

112 Performing Bivariate Analysis Chapter 4
Density Ellipse
Figure 4.15 Example of Density Ellipses
The density ellipsoid is computed from the bivariate normal distribution fit to the X and Y variables. The
bivariate normal density is a function of the means and standard deviations of the X and Y variables and the
correlation between them. The Other selection lets you specify any probability greater than zero and less
than or equal to one.
These ellipses are both density contours and confidence curves. As confidence curves, they show where a
given percentage of the data is expected to lie, assuming the bivariate normal distribution.
The density ellipsoid is a good graphical indicator of the correlation between two variables. The ellipsoid
collapses diagonally as the correlation between the two variables approaches either 1 or –1. The ellipsoid is
more circular (less diagonally oriented) if the two variables are less correlated.
Correlation Report
The Correlation report that accompanies each Density Ellipse fit shows the correlation coefficient for the X
and Y variables.
Note: To see a matrix of ellipses and correlations for many pairs of variables, use the Multivariate command
in the Analyze > Multivariate Methods menu.
Table 4.13 Description of the Correlation Report
Variable
Mean
Std Dev
Gives the names of the variables used in creating the ellipse
Gives the average of both the X and Y variable.
Gives the standard deviation of both the X and Y variable.
A discussion of the mean and standard deviation are in the section “The Summary
Statistics Report” on page 39 in the “Performing Univariate Analysis” chapter.