## Confidence Ellipses

To learn more about correlations in the data,
add a scatter plot matrix with confidence ellipses
for all of the variables under consideration.
| Choose **Curves:Confidence Ellipse:Prediction: 80%**. |

**Figure 18.6:** Curves Menu

The lower half of the scatter plot matrix for the six
variables appears on your display with the 80% prediction
confidence ellipses drawn, as shown in Figure 18.7.

**Figure 18.7:** Multivariate Window with Confidence Ellipses
There are two ways to interpret the ellipses:
as confidence curves for bivariate normal
distributions and as indicators of correlation.

As confidence curves, the ellipses show where
the specified percentage of the data should lie,
assuming a bivariate normal distribution.
Under bivariate normality, the percentage of
observations falling inside the ellipse should
closely agree with the specified confidence level.
You can examine the effect of increasing or decreasing
the confidence level by adjusting the slider in the
**Confidence Ellipses** table below the scatter plot matrix.

Confidence ellipses can also serve as
visual indicators of correlations.
The confidence ellipse collapses diagonally as the
correlation between two variables approaches 1 or -1.
The confidence ellipse is more circular
when two variables are uncorrelated.

In this case the scatter plots for high school scores
(**HSM**, **HSS**, and **HSE**) show a granular appearance
that indicates the data are not continuous.
These scatter plots clearly do not follow a
bivariate normal distribution; therefore, it is
not appropriate to interpret confidence ellipses.

The confidence ellipses for **GPA**, **SATM**,
and **SATV** can be interpreted.
These confidence ellipses contain observations
appropriate to the 80% confidence level you specified.
The nearly circular appearance of the confidence ellipse
in the plot of **GPA** versus **SATV** reflects the small
correlation you observed in the **Correlation Matrix**
table. The ellipse in the plot of **GPA** versus **SATM**
is somewhat more elongated, reflecting a higher correlation.

Note | Visual interpretation of correlations can be subjective because changes in scale
affect your perception (Moore and McCabe 1989).
When examining correlations, you should use
correlation coefficients as well as confidence ellipses. |

Related Reading | Correlation Coefficients, Confidence Ellipses,Chapter 40. |

Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.