Scatter Diagram

A scatter diagram (or scatter plot) is the simplest and most direct way to get a first visual impression of whether — and how — two variables are related. Each pair of observations $(X_i, Y_i)$ is plotted as a single point on a graph, with the independent variable conventionally on the horizontal (X) axis and the dependent variable on the vertical (Y) axis.

Reading the pattern of a scatter diagram:

• If the plotted points cluster around an upward-sloping line (as $X$ rises, $Y$ also tends to rise), the diagram indicates positive correlation.
• If the points cluster around a downward-sloping line (as $X$ rises, $Y$ tends to fall), the diagram indicates negative correlation.
• If the points are scattered with no visible pattern or slope at all, the diagram indicates little or no correlation.
• If every point lies exactly on a straight line, the correlation is perfect (positive if upward-sloping, negative if downward-sloping).
• The more tightly the points cluster around an imaginary line (rather than spreading out widely around it), the higher the degree of correlation.

Merits: simple to construct, gives an immediate, easy-to-understand first impression of both the direction and the rough strength of the relationship, and requires no calculation. …