How do we display two numerical variables together and describe the association we see?
Identify response and explanatory variables, construct a scatterplot, and describe the association in terms of direction, form, strength and outliers.
How to choose response and explanatory variables, plot a scatterplot the correct way round, and describe the association by its direction, form, strength and any outliers.
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What this dot point is asking
Bivariate data is data collected on two numerical variables from the same individuals. Before any correlation coefficient or line is calculated, you must display the pair and describe in words what the display shows.
Response and explanatory variables
The explanatory variable is the one you think might explain or predict changes in the other. The response variable is the one that may respond to it. In a study of study time and test score, study time is explanatory and the score is the response.
If neither variable is naturally explanatory, you may choose either, but you must state which is which and stay consistent.
Constructing the scatterplot
Each individual becomes one point. Scale both axes so the points spread across the plot rather than bunching in a corner. Axes do not need to start at zero, but a broken or non-zero axis should be marked so a reader is not misled.
Describing the association
Once plotted, describe the scatterplot using four features.
- Direction. Positive if tends to rise as rises; negative if tends to fall as rises.
- Form. Linear if the points cluster about a straight line; non-linear (for example curved) otherwise. Only fit a straight line if the form is linear.
- Strength. How tightly the points cluster about the underlying pattern: strong, moderate or weak.
- Outliers. Any points that sit well away from the overall pattern. Note them, because they can distort later calculations.
Why the description matters
The four-feature description decides what you do next. A linear form justifies fitting a least-squares line. A non-linear form tells you to transform the data first. A noted outlier warns you that the correlation coefficient and the line may both shift if that point is removed, which examiners often ask you to comment on.