Correlation Coefficient

The Linear Correlation Coefficient measures the strength of the relationship between the paired x   and y   values in a sample.  The equation is as follows:

How do we interpret r  ?  The value of r  must always fall between 1 and -1.  A value closer to 1 indicates a strong positive relationship, while a value closer to -1 indicates a strong negative realtionship.  Values with no significant linear correlation possess an r  closer to 0.

We can deduce that the variables from the previous page would produce an r   extremely close to 1. But hardly is the conclusion so obvious. how do we decide whether a significant relationship exists between variables when confronted with an r   that does not closely approach any of the extremes?

We do this by conducting a hypothesis test, which if you remember is also known as a test of significance.