How Do You Interpret a Scatter Diagram (Positive, Negative, or No Correlation)?

A scatter diagram shows the direction and strength of the relationship between two variables. An upward trend indicates positive correlation, a downward trend indicates negative correlation, and no clear trend indicates no correlation.

How to interpret the pattern

Read the graph from left to right and imagine a straight line passing through the general pattern of points.

Then describe the strength of correlation. Points clustered closely around an imagined straight line indicate strong correlation, while points spread more widely indicate weak correlation.

For example, a tight downward pattern represents strong negative correlation. A widely scattered upward pattern represents weak positive correlation.

The Pearson product-moment correlation coefficient, $r$, measures linear correlation and satisfies $-1 \leq r \leq 1$. Values closer to $1$ indicate stronger positive correlation, while values closer to $-1$ indicate stronger negative correlation. A value near $0$ indicates weak or no linear correlation.

Look for outliers, which are points far from the overall pattern. An outlier can substantially change $r$ and the regression line, so it should be identified when relevant.

A common misconception is that no linear correlation means no relationship. A curved pattern may show a strong non-linear relationship even when $r$ is near $0$. Another misconception is that correlation proves causation; it does not.

IB exam technique

This is IB Mathematics: Analysis and Approaches SL 4.4. When asked to describe a scatter diagram, state the direction and strength, identify relevant outliers, and refer to a linear relationship. If calculating $r$, use technology as required, normally in a Paper 2 setting, and interpret the value in context.