What is a Correlation?

Correlation is a measure of association between two variables. It varies from -1 to 1, with 0 being a random relationship, 1 being a perfect linear relationship having a positive slope (of any magnitude), and -1 being a perfect linear relationship with a negative slope.

The Correlation Coefficient

The correlation coefficient (r) also known as Pearson's r, is used to describe the strength of the association between the variables and the direction of the association. Now the question is: How does r work as a measure of association? Horizontal and Vertical lines are first drawn through the point of averages, which is the point on the averages of the x and y values (as seen in figures 1 and 2). This divides the scatter-plot into four quadrants. Now we use this method to determine whether there is a negative or positive coefficient.

Figure 1 (Positive correlation)

If a point is in the lower left quadrant, the product of two negatives is positive, in the upper right, the product of two positives is positive. These positive quadrants are depicted in Figures 1and 2 with the positive sign (+).

Figure 2 (Negative Correlation)

In the two remaining quadrants (upper left and lower right) the product of a negative and a positive is negative. The negative quadrants are depicted in Figures 1 and 2 with the negative sign (-). If r is positive then, then products from the points in the positive quadrants make a larger contribution than those from the negative quadrants, and the reverse happens if r is negative.

## Correlation coefficient (r)

In the java applet above, just move your mouse over the r value that you want to see an example of and the corresponding graph will appear in the window.

The Lifespan, GPA, and Enrollment activities use correlation to analyze data sets. The activities assume that you have access to Excel, a TI-83 calculator or another software package capable of performing inferential tests.

Original work on this document was done by Central Virginia Governor's School students Forrest Frazier, Tony Lassaletta and Lauren McGehee (Class of '98) with additional work by Adam Nakama, Adam Walthall and Beau Frazier (Class of '03)

Copyright © 1997 Central Virginia Governor's School for Science and Technology Lynchburg, VA