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