Values of the Pearson Correlation
David M. Lane
to Bivariate Data
- Describe what Pearson's correlation measures
- Give the symbols for Pearson's correlation in the sample and in the
- State the possible range for Pearson's correlation
- Identify a perfect linear relationship
The Pearson product-moment correlation coefficient
is a measure of the strength of the linear
relationship between two variables. It is referred to as Pearson's
correlation or simply as the correlation coefficient. If the relationship
between the variables is not linear, then the correlation coefficient
does not adequately represent the strength of the relationship
between the variables.
The symbol for Pearson's correlation is "ρ"
when it is measured in the population and "r" when it is measured
in a sample. Because we will be dealing almost exclusively with
samples, we will use r to to represent Pearson's correlation unless
Pearson's r can range from -1 to 1. An r of -1
indicates a perfect negative linear relationship between variables,
an r of 0 indicates no linear relationship between variables,
and an r of 1 indicates a perfect positive relationship between
variables. Figure 1 shows a scatter plot for which r = 1.
|Figure 1. A perfect linear relationship,
r = 1.
Figure 2 shows a perfect negative linear relationship.
Notice that as X increases, Y decreases.
|Figure 2. A perfect negative linear relationship,
r = -1.
Figure 3 shows a scatter plot for which r = 0. Notice that there
is no relationship between X and Y.
|Figure 3. There is no linear relationship
between the variables, r = 0.
With real data, you would not expect to get values of r of exactly
-1, 0, or -1.
Please answer the questions: