To Documents

## Bivariate Normal Datasets

- A
**bivariate dataset** consists of exactly two variables.

- A a bivariate dataset is
**bivariate normal** if it is univariate
normal in any direction. In particular, both the x and y variables are
univariate normal.

- A bivariate dataset is also normally distributed in any thin rectangular
strip in any direction.

- The scatterplot of a bivariate dataset consists of an ellipse-shaped
cloud of data points:

- A
**parsimonious** description of a bivariate normal dataset consists of
five statistics:
x, SD_{x},
y, SD_{y}, and r,
where r is the correlation between x and y.

- The point (x, y) is the
center of gravity, also called the
**centroid**, of the ellipse shaped
cloud.

- The dataset in the following scatterplot is not bivariate normal.
In fact it is a mixture of three separate bivariate normal groups.