Covariance

[Daniel Carrera <dcarrera math toronto edu>]

I've spent two days looking for an answer to this.  Maybe one of the stats
experts here can help me.

How do you interpret the covariance matrix?  Can you use it to obtain a
confidence region for a dataset?

Let me illustrate my question.

Say that this is my dataset:

 y
 |                x
 |            x  x
 |           x x
 |        x x x
 |     x   x
 |       x  x
 |  x  x  x
 |    x x
 |  xx
 |x
 |___________________  x


For a confidence region for x I could use its mean +/- its standard
deviation.  That should contain about 68% of the points.

 y
 |   |         |  x
 |   |        x| x
 |   |       x x
 |   |    x x x|
 |   | x   x   |
 |   |   x  x  |
 |  x| x  x    |
 |   |x x      |
 |  xx         |
 |x  |         |
 |___________________  x


Now, this is my question:

Can I use the covariance between x and y to obtain an *elliptical* region
that contains 68% of the points?  If so, how?


Cheers,
Daniel.