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.