Re: Correlation Depending on 3rd Variable?

This is known as an interaction.
below my sig block is a clip from the Library of Congress catalog for an outstanding book on correlation/regression.

If you have SPSS available, do a 3-D scatterplot A by B by C. double click on the output. Use the wheels to rotate the graph so you can look at it from different angles.

Go back and graph it again using locally weighted least squares.
Double click on the output graph. Use the wheels to rotate the graph so you can look at it from different angles.

SPSS's REGRESSION or other packages can be used to implement the formal analysis.

Art
Art@xxxxxxxxxxxxx
Social Research Consultants
University Park, MD  USA


Main Title:     Applied multiple regression/correlation analysis for the
behavioral sciences / Jacob Cohen ... [et al.].
Edition Information:    3rd ed.
Published/Created:      Mahwah, N.J. : L. Erlbaum Associates, 2003.
Related Names:  Cohen, Jacob, 1923-
Cohen, Jacob, 1923- Applied multiple regression/correlation analysis for
the behavioral sciences.
Description:    xxviii, 703 p. : ill. ; 26 cm. + 1 CD-ROM (4 3/4 in.)
ISBN:   0805822232 (hard cover : alk. paper)
Notes:  Rev. ed. of: Applied multiple regression/correlation analysis
for the behavioral sciences / Jacob Cohen, Patricia Cohen. 2nd ed. 1983.
The CD-ROM contains the data for almost all examples as well as the
command codes for each of the major statistical packages for the tabular
and other findings in the book.
Includes bibliographical references (p. 655-669) and indexes.
Subjects:       Regression analysis.
Correlation (Statistics)
Social sciences--Statistical methods.
LC Classification:      HA31.3 .A67 2003
Dewey Class No.:        519.5/36 21
Other System No.:       (OCoLC)ocm49903199

Eric M. Van wrote:
Imagine that I've got a population with three variables A, B, and C. A and B have a weak and insignificant correlation.

However, when you break the population into quartiles depending on the value of C. . .

In the top quartile, A and B have a robust positive correlation.

In the next, they have a mild positive correlation.

In the 3rd quartile, a mild negative correlation.

And for the smallest values of C, A and B are robustly negatively correlated.

IOW, A and B aren't unrelated, they are profoundly related. You could presumably write a very neat regression formula, except that the slope would depend on this third variable C rather than being fixed.

I don't recall a situation like this ever being discussed in Stats 101.

My questions are pretty general:

-- Is there a name for this?

-- Is there a way to test for it among any set of n variables without dividing the data into subsets of each separate variable and running correlations?

-- Is there a way of determining the best expression for slope, other than using Solver in Excel or the equivalent?

(In case anyone is curious, I'm a player evaluation consultant for a major league baseball team. The relationship among strikeouts, power hitting, and walks may fit this a version of this A, B, C model.)

.

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