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Scatterplots

In exploring the relation between two reasonably well-behaved quantitative variables, much of what is useful about correlation and regression can be observed visually through the use of scatterplots.

Figure 2 contains four scatterplots.

The plot in “a” illustrates a perfect positive linear correlation. All data points fit on an upward-sloping straight line.

The plot in “b” illustrates a perfect negative linear correlation. All data points fit on a straight line, but this line slopes downward.

A correlation coefficient measures the degree of association, denoted in the figure by r. This measure of correlation is often called Pearson's correlation coefficient, after its originator. In a perfect linear correlation, the correlation coefficient, r, is +1 for a positive correlation and -1 for a negative correlation.

In plot “c”, the eye detects no correlation.

And in plot “d” a correlation exists, but it is not linear.