Figure 7.1: Interpreting scatterplots
for two variables
In these plots we are looking for a linear relationship between the two variables which is
summarized by the spread and scatter of points. If one variable is linearly related to the
other, then as one variable changes, the other will change in proportion and the points
will tend to fall on a straight line. The size of a Pearson correlation coefficient indicates
the degree to which the points in a scatter diagram tend to fall along a straight line
(summarizes the linear relationship). The value of the Pearson correlation coefficient, can
range between −1 to +1, in both cases this would indicate a perfect linear relationship.
The Pearson correlation is used when the underlying data distribution is normal (see
Chapter 8).
Diagram A indicates a near perfect positive correlation, as X increases Y increases
proportionately, r (the correlation) would be close to +1; Diagram B shows a near perfect
negative correlation as X increases Y decreases proportionately, r would be close to −1;
Diagram C shows no correlation, r would be 0 and Diagram D shows dependence but no
linear correlation, Pearson correlation r should not be used to summarize this
relationship. There are, of course, non-linear relationships that may exist between two
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