Scatter Diagram

The simplest way to see correlation is to plot the paired observations $(x_1, y_1), (x_2, y_2), \ldots, (x_n, y_n)$ as points on a graph, with one variable on the horizontal ($X$) axis and the other on the vertical ($Y$) axis. The resulting cloud of points is called a scatter diagram (or dot diagram). Its shape reveals the direction, degree and form of the relationship at a glance — before any formula is used.

Reading a scatter diagram:

• If the points rise from lower-left to upper-right, the correlation is positive.
• If the points fall from upper-left to lower-right, the correlation is negative.
• The more tightly the points hug an imaginary straight line, the stronger (higher) the correlation; a widely scattered cloud means weak correlation.
• If the points all lie exactly on a rising line, correlation is perfect positive; on a falling line, perfect negative.
• A shapeless, patternless swarm (or a horizontal/vertical band) indicates no correlation.