I need to clarify some things concerning correlation coefficient: 
What is the term if correlation is exactly +1? exactly -1?  What is
the difference between .8 correlation vs. +1 correlation?

Hi boobee!

If the coefficient of correlation (r) is +1, that is called "perfect
positive correlation. This means that the scatter diagram representing
the data would have an absolutely straight line going through the data
points - from lower left to upper right.

If the coefficient of correlation is -1, that is called "perfect
negative correlation". This means that the scatter diagram
representing the data would have an absolutely straight line going
through the data points - from upper left to lower right.

If r=.8, then that means that .8^2 or .64 (64%) of the variance in one
variable is predictable from the other. If r=1, then that means that
1^2 or 100% of the variance in one variable is predictable from the
other. (That's why we get a straight line!)

See the following for more details:

Correlation Coefficient (nifty interactive graph!)
http://noppa5.pc.helsinki.fi/koe/corr/cor7.html

Correlation
http://www2.chass.ncsu.edu/garson/pa765/correl.htm

websearcher-ga


Hope this helps.

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Request for Answer Clarification by boobee-ga on 25 Sep 2002 17:30 PDT

I'm not sure how you interpreted a rho of .8 to mean "64% of the
variance in one variable is predictable from the other?"  Can you
explain?

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Clarification of Answer by websearcher-ga on 25 Sep 2002 19:56 PDT

Hi boobee:

I'll try to explain in some more detail...

In Correlation Analysis, the "coefficient of determination" is
represented by r^2, and is equal to:

r^2 = (Explained Variation)/(Total Variation)

or the percentage of explained variation to the total variation. 

The "coefficient of correlation" is represented by r, and is equal to:

r = sqrt(r^2).

So, when you are given (as you were) that "correlation coefficient" is
.8, that means:

r = .8 

which implies that 

r^2 = .8^2 = .64

which means that 64% of the total variation is explained (or
predictable).

Similarly for r = 1, we get:

r^2 = 1^2 = 1 or 100%.

For more information on "explained variation" and "total variation",
see slides 2 through 6 at:

http://www.stat.colostate.edu/~johnson/st204/notes/apr_16.pdf

I hope this helps clear things up. 

websearcher-ga

thank you - great answer